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Symmetry
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Symmetry in Gravity Research
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Symmetry in Gravity Research

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 20225

Special Issue Editors

Prof. Dr. Xin Wu

E-Mail Website
Guest Editor
1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
2. Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai 201620, China
3. Guangxi Key Laboratory for Relativistic Astrophysics, Guangxi University, Nanning 530004, China
Interests: statistical physics; observational data statistics and numerical simulation of celestial motions
Prof. Dr. Wenbiao Han

E-Mail Website
Guest Editor
1. Shanghai Astronomical Observatory, CAS, Shanghai 200030, China
2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
Interests: gravitational wave astronomy
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Due to objects with extremely large masses existing in our universe, gravity has not only become the dominant factor in the motion of celestial bodies but also the decisive factor in the structure and evolution of celestial bodies. Newton not only explained the law of planetary motion by using the law of gravitation but also successfully predicted and discovered Neptune. In 1905, Einstein put forward the special theory of relativity, which broke through the concept of absolute time and absolute space. General relativity is a theory that describes the gravitational interaction between matter. Its foundation was completed by Albert Einstein in 1915 and officially published in 1916. This theory represents the first time that the gravitational field was regarded as equivalent to the curvature of space–time. In 1916, Einstein predicted the existence of gravitational waves based on general relativity. The existence of gravitational waves is the result of Lorentz invariance of general relativity, because it introduces the concept of finite propagation velocity of interaction. Fortunately, gravitational waves have been detected. Recently, researchers have paid much attention to the calculation of black hole shadows. In addition, some observational results have forced scientists to generalize or modify the standard general relativity. Because of this, theories of gravity have received great attention. Therefore, gravitational theories and their applications are very important in astronomy and astrophysics. 

Symmetry is a core concept in modern physics. It generally refers to gauge symmetry, local symmetry and global symmetry. It refers to the invariance of a theoretical Lagrangian or equation of motion under the change in some variables. If these variables change with time and space, this invariance is called local symmetry; otherwise, it is called global symmetry. The so-called symmetry refers to the invariance after a certain operation. In general, each symmetry corresponds to a conserved quantity: for example, space translation invariance corresponds to momentum conservation; time shift invariance corresponds to energy conservation; space rotation invariance corresponds to the conservation of angular momentum. Based on symmetry, the gravitational theories will become very simple. That is, symmetry is very important to gravitational physics because it corresponds to some physical properties such as conservation laws. 

The aim of this Special Issue is to collect original and significant contributions dealing with symmetry in gravity research. This Special Issue may also serve as a platform for the exchange of ideas between scientists of different disciplines interested in gravity. It is devoted to discussing physical properties of various symmetric or nonsymmetric gravitational problems involving Newtonian gravity, general relativity and modified gravity theories. It includes, but is not limited to, the following fields: (1) symmetric black hole solutions; (2) symmetry and integrability of gravitational systems; (3) symmetric geometric integration algorithms of gravitational systems; (4) circular orbits, periodic orbits and chaotic orbits of photons or particles in symmetric gravitational systems; (5) gravitational waves in symmetric gravity systems; (6) black hole shadows in symmetric spacetimes; (7) planetary dynamics in symmetric gravity systems.

Prof. Dr. Xin Wu
Prof. Dr. Wenbiao Han
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Newtonian theory of gravity
  • general relativity
  • modified theories of gravity
  • black holes
  • gravitational waves
  • black hole shadows
  • chaos
  • geometric integration algorithms
  • integrability
  • periodic orbits
  • planetary systems

Published Papers (17 papers)

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Research

16 pages, 8040 KiB  
Article
Application of Symmetric Explicit Symplectic Integrators in Non-Rotating Konoplya and Zhidenko Black Hole Spacetime
by Guandong He, Guoqing Huang and Airong Hu
Symmetry 2023, 15(10), 1848; https://doi.org/10.3390/sym15101848 - 30 Sep 2023
Viewed by 607
Abstract
In this study, we construct symmetric explicit symplectic schemes for the non-rotating Konoplya and Zhidenko black hole spacetime that effectively maintain the stability of energy errors and solve the tangent vectors from the equations of motion and the variational equations of the system. [...] Read more.
In this study, we construct symmetric explicit symplectic schemes for the non-rotating Konoplya and Zhidenko black hole spacetime that effectively maintain the stability of energy errors and solve the tangent vectors from the equations of motion and the variational equations of the system. The fast Lyapunov indicators and Poincaré section are calculated to verify the effectiveness of the smaller alignment index. Meanwhile, different algorithms are used to separately calculate the equations of motion and variation equations, resulting in correspondingly smaller alignment indexes. The numerical results indicate that the smaller alignment index obtained by using a global symplectic algorithm is the fastest method for distinguishing between regular and chaotic cases. The smaller alignment index is used to study the effects of parameters on the dynamic transition from order to chaos. If initial conditions and other parameters are appropriately chosen, we observe that an increase in energy E or the deformation parameter η can easily lead to chaos. Similarly, chaos easily occurs when the angular momentum L is small enough or the magnetic parameter Q stays within a suitable range. By varying the initial conditions of the particles, a distribution plot of the smaller alignment in the X–Z plane of the black hole is obtained. It is found that the particle orbits exhibit a remarkably rich structure. Researching the motion of charged particles around a black hole contributes to our understanding of the mechanisms behind black hole accretion and provides valuable insights into the initial formation process of an accretion disk. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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26 pages, 446 KiB  
Article
Spin-Gravity Coupling in a Rotating Universe
by Bahram Mashhoon, Masoud Molaei and Yuri N. Obukhov
Symmetry 2023, 15(8), 1518; https://doi.org/10.3390/sym15081518 - 01 Aug 2023
Cited by 2 | Viewed by 1175
Abstract
The coupling of intrinsic spin with the nonlinear gravitomagnetic fields of Gödel-type spacetimes is studied. We work with Gödel-type universes in order to show that the main features of spin-gravity coupling are independent of causality problems of the Gödel universe. The connection between [...] Read more.
The coupling of intrinsic spin with the nonlinear gravitomagnetic fields of Gödel-type spacetimes is studied. We work with Gödel-type universes in order to show that the main features of spin-gravity coupling are independent of causality problems of the Gödel universe. The connection between the spin–gravitomagnetic field coupling and Mathisson’s spin-curvature force is demonstrated in the Gödel-type universe. That is, the gravitomagnetic Stern–Gerlach force due to the coupling of spin with the gravitomagnetic field reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
14 pages, 677 KiB  
Article
Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian
by Junjie Luo, Jie Feng, Hong-Hao Zhang and Weipeng Lin
Symmetry 2023, 15(7), 1401; https://doi.org/10.3390/sym15071401 - 11 Jul 2023
Viewed by 575
Abstract
The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler–Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only maintain a certain post-Newtonian order and are incoherent Lagrangians [...] Read more.
The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler–Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only maintain a certain post-Newtonian order and are incoherent Lagrangians since the higher-order terms are omitted. This truncation can cause some changes in the constant of motion. However, in celestial mechanics, Hamiltonians are more commonly used than Lagrangians. The conversion from Lagrangianto Hamiltonian can be achieved through the Legendre transformation. The coordinate momentum separable Hamiltonian can be computed by the symplectic algorithm, whereas the inseparable Hamiltonian can be used to compute the evolution of motion by the phase-space expansion method. Our recent work involves the design of a multi-factor correction map for the phase-space expansion method, known as the correction map method. In this paper, we compare the performance of the implicit algorithm in post-Newtonian Lagrangians and the correction map method in post-Newtonian Hamiltonians. Specifically, we investigate the extent to which both methods can uphold invariance of the motion’s constants, such as energy conservation and angular momentum preservation. Ultimately, the results of numerical simulations demonstrate the superior performance of the correction map method, particularly with respect to angular momentum conservation. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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15 pages, 1328 KiB  
Article
A Simple Cosmology in G4v
by Carver Mead
Symmetry 2023, 15(7), 1309; https://doi.org/10.3390/sym15071309 - 25 Jun 2023
Cited by 1 | Viewed by 986
Abstract
There has been a great deal of debate as to the role, if any, of Mach’s Principle in cosmology. We propose that these questions have meaning only in the context of a cosmic gravitational potential. G4v operates with such a four-potential, which imposes [...] Read more.
There has been a great deal of debate as to the role, if any, of Mach’s Principle in cosmology. We propose that these questions have meaning only in the context of a cosmic gravitational potential. G4v operates with such a four-potential, which imposes a different symmetry on its treatment of light propagation than that employed by GR. That combination enables a simple cosmic solution that is Lorentz-invariant in free-fall frames of reference. The solution is compared with supernovae data, which, together with an internal self-consistency condition, fixes the parameters of the solution. The resulting Hubble trajectory is, in broad brush, consistent with many cosmic observations. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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17 pages, 7030 KiB  
Article
Application of Explicit Symplectic Integrators in the Magnetized Reissner–Nordström Spacetime
by Ai-Rong Hu and Guo-Qing Huang
Symmetry 2023, 15(5), 1094; https://doi.org/10.3390/sym15051094 - 16 May 2023
Viewed by 836
Abstract
In recent works by Wu and Wang a class of explicit symplectic integrators in curved spacetimes was presented. Different splitting forms or appropriate choices of time-transformed Hamiltonians are determined based on specific Hamiltonian problems. As its application, we constructed a suitable explicit symplectic [...] Read more.
In recent works by Wu and Wang a class of explicit symplectic integrators in curved spacetimes was presented. Different splitting forms or appropriate choices of time-transformed Hamiltonians are determined based on specific Hamiltonian problems. As its application, we constructed a suitable explicit symplectic integrator for surveying the dynamics of test particles in a magnetized Reissner–Nordström spacetime. In addition to computational efficiency, the scheme exhibits good stability and high precision for long-term integration. From the global phase-space structure of Poincaré sections, the extent of chaos can be strengthened when energy E, magnetic parameter B, or the charge q become larger. On the contrary, the occurrence of chaoticity is weakened with an increase of electric parameter Q and angular momentum L. The conclusion can also be supported by fast Lyapunov indicators. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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28 pages, 4267 KiB  
Article
The Space-Time Properties of Three Static Black Holes
by Yu Wang, Gangqi Shen and Xin Sun
Symmetry 2023, 15(3), 702; https://doi.org/10.3390/sym15030702 - 11 Mar 2023
Viewed by 1647
Abstract
In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy [...] Read more.
In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy term—the kinetic energy term of the four-dimensional curved space-time. In the case of small space-time curvature, linear approximation can be made. That is, under the weak field approximation, the Lagrangian quantity degenerates into the Lagrangian quantity in the axisymmetric gravitational field in Newtonian mechanics. In this paper, the curved space-time composed of axisymmetric equidistant black holes is taken as a model. We study the geodesic motion of the test particles around three black holes with equal mass and static axisymmetric distribution, including time-like particles and photons. The three extreme Reissner–Nordstrom black holes are balanced by electrostatic and gravitational forces. We first give the geodesic motion equation of particles in Three black holes space-time, give the relativistic effective potential, discuss the possible motion state of particles, and classify their motion trajectories. Then, the particle motion of the special plane (equatorial plane) is studied. The circular orbits of the two types of particles in the symmetric plane are studied, respectively. The circular orbits outside the symmetric plane are also studied, and their stability is also discussed. We will show the influence of the separation distance of the three black holes on the geodesic motion and explore the change of the relativistic effective potential. Then, the relationship between the inherent quantity and the coordinate quantity in space-time is analyzed. Finally, the chaos of the test particle orbit is explored. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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19 pages, 1326 KiB  
Article
Thermodynamics of the Acceleration of the Universe in the κ(R, T) Gravity Model
by Archana Dixit, Sanjeev Gupta, Anirudh Pradhan and Aroonkumar Beesham
Symmetry 2023, 15(2), 549; https://doi.org/10.3390/sym15020549 - 18 Feb 2023
Cited by 2 | Viewed by 1368
Abstract
In this article, we examined the behavior of dark energy (DE) and the cosmic acceleration in the framework of κ(R,T) gravity in the standard spherically symmetric coordinates (xi) = [...] Read more.
In this article, we examined the behavior of dark energy (DE) and the cosmic acceleration in the framework of κ(R,T) gravity in the standard spherically symmetric coordinates (xi) = t,r,θ,ϕ, a spatially homogeneous and isotropic FLRW space–time. We discovered some remarkable cosmic characteristics in this investigation that are in line with both observations and the accepted ΛCDM model. We made two assumptions in order to determine a deterministic solution of the modified field equations (MFEs): (i) p=γρ, where γ(1≥γ≥0) is a constant, (ii) Λ = βH2, where β is an arbitrary constant. We solved the MFEs and obtained the expression for the Hubble parameter. The depicted model of κ(R,T) gravity was taken into consideration when discussing the behavior of the accelerating Universe. In κ(R,T) gravity, the statefinder analysis was utilized to distinguish our model from the ΛCDM model. The evolution of the cosmos was studied using an effective equation of state (EoS). We investigated the thermodynamic quantities and the generalized energy conditions in order to test the viability of our model. When dominant and weak energy conditions are satisfied, this validates the model; when the strong energy condition is not satisfied, this accelerates the expansion of the Universe. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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37 pages, 20494 KiB  
Article
Gravitational Waves and Electromagnetic Radiation from Charged Black Hole Binaries
by Carlos A. Benavides-Gallego and Wen-Biao Han
Symmetry 2023, 15(2), 537; https://doi.org/10.3390/sym15020537 - 17 Feb 2023
Cited by 3 | Viewed by 1387
Abstract
In this manuscript, we investigate the electromagnetic radiation of a binary system of electrically charged black holes. Using the results of previous works, we compute the analytical expression for the waveform, the phase, and the Fourier transform during the inspiral phase for both [...] Read more.
In this manuscript, we investigate the electromagnetic radiation of a binary system of electrically charged black holes. Using the results of previous works, we compute the analytical expression for the waveform, the phase, and the Fourier transform during the inspiral phase for both the electromagnetic and gravitational radiations. To do so, we consider the quasi-circular approximation and small values for the charge-to-mass ratio in each black hole. In the case of electromagnetic radiation, we focus on the dipole contribution, but we also include the quadrupole term to complete our discussion. We found that the gravitational and electromagnetic waveforms contain two terms, and so does the Fourier transform. However, the behavior is dominated only by one of them. In the frequency-domain waves, for example, the dipole and quadrupole contributions and the gravitational wave are dominated by terms proportional to f−3/6, f−1/6, and f−7/6, respectively. As expected, the gravitational radiation and the quadrupole contribution have the same phase, in contrast to the dipole contribution. Moreover, the electromagnetic wave is more sensitive to changes in the charge-to-mass ratio than the gravitational wave. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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16 pages, 1366 KiB  
Article
Space-Time Properties of Extreme RN Black Holes in Static Triangular Distribution
by Gangqi Shen, Yu Wang and Houjun Lü
Symmetry 2023, 15(2), 505; https://doi.org/10.3390/sym15020505 - 14 Feb 2023
Viewed by 1167
Abstract
We studied the space-time properties of the triangular symmetric black hole in the case of extreme RN black hole. Because the neutral test particle is only affected by space-time in the curved space-time, we chose the triangular symmetric black hole as the model [...] Read more.
We studied the space-time properties of the triangular symmetric black hole in the case of extreme RN black hole. Because the neutral test particle is only affected by space-time in the curved space-time, we chose the triangular symmetric black hole as the model with which to study the motion of the test particle in this case. The curvature tensor and curvature scalar were calculated by giving the metric and the Christoffel Symbol, and then the kinematics equation of the test particle was obtained and analyzed by using these quantities. Then we analyzed the relationship between the coordinate distance and the inherent distance, the relationship between the coordinate time and the inherent time, the inherent velocity and the coordinate velocity of light, and then verified the correctness of general relativity. Next, the one-dimensional effective potential and two-dimensional effective potential of the system under different separation distances were analyzed. Finally, we analyzed and explored the innermost stable circular orbit, calculated all the Lagrange points under this model, and expounded some applications of circular orbit in astrophysics. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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15 pages, 595 KiB  
Article
Application of Manifold Corrections in Tidal Evolution of Exoplanetary Systems
by Qian-Qian Xiao, Ying Wang, Fu-Yao Liu, Chen Deng and Wei Sun
Symmetry 2023, 15(1), 253; https://doi.org/10.3390/sym15010253 - 16 Jan 2023
Viewed by 1605
Abstract
The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and [...] Read more.
The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and requires reliable numerical methods. The manifold correction method, which strictly satisfies the integrals dissipative quasiintegrals of the system, exhibits good numerical accuracy and stability in the quasi-Kepler problem. Different manifold correction methods adopt different integrals or integral invariant relations to correct the numerical solutions. We apply the uncorrected five- and six-order Runge–Kutta–Fehlberg algorithm [RKF5(6)], as well as corrected by the velocity scaling method and Fukushima’s linear transformation method to solve the tidal evolution of exoplanet systems. The results show that Fukushima’s linear transformation method exhibits the best performance in the accuracy of the semimajor axis and eccentricity. In addition, we predict the tidal timescale of several current close exoplanetary systems by using this method. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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17 pages, 5372 KiB  
Article
Study of Chaos in Rotating Galaxies Using Extended Force-Gradient Symplectic Methods
by Lina Zhang, Wenfang Liu and Xin Wu
Symmetry 2023, 15(1), 63; https://doi.org/10.3390/sym15010063 - 26 Dec 2022
Cited by 2 | Viewed by 937
Abstract
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. [...] Read more.
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the momenta and spatial coordinate. The existing explicit force-gradient symplectic integrators are not applicable to such Hamiltonian problems, but the recently extended force-gradient symplectic methods proposed in previous work are. Numerical comparisons show that the extended force-gradient fourth-order symplectic method with symmetry is superior to the standard fourth-order symplectic method but inferior to the optimized extended force-gradient fourth-order symplectic method in accuracy. The optimized extended algorithm with symmetry is used to explore the dynamical features of regular and chaotic orbits in these rotating galaxy models. The gravity effects and the degree of chaos increase with an increase in the number of radial terms in the series expansions of the potential. There are similar dynamical structures of regular and chaotical orbits in the three types of models for the same number of radial terms in the series expansions, energy and initial conditions. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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9 pages, 277 KiB  
Article
The Quasi-Keplerian Motion of the Charged Test Particle in Reissner-Nordström Spacetime under the Wagoner-Will-Epstein-Haugan Representation
by Bo Yang, Chunhua Jiang, Guansheng He and Wenbin Lin
Symmetry 2022, 14(12), 2661; https://doi.org/10.3390/sym14122661 - 16 Dec 2022
Cited by 1 | Viewed by 999
Abstract
We present the post-Newtonian solution for the quasi-Keplerian motion of a charged test particle in the field of Reissner-Nordström black hole under the Wagoner-Will-Epstein-Haugan representation. The explicit formulations for the charge effects on perihelion precession and the orbital period are achieved, which may [...] Read more.
We present the post-Newtonian solution for the quasi-Keplerian motion of a charged test particle in the field of Reissner-Nordström black hole under the Wagoner-Will-Epstein-Haugan representation. The explicit formulations for the charge effects on perihelion precession and the orbital period are achieved, which may be useful not only in the comparisons with astronomical observations but also in calculating the waveform of the gravitational wave from this kind of system. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
17 pages, 1100 KiB  
Article
Quintessence Behavior of an Anisotropic Bulk Viscous Cosmological Model in Modified f(Q)-Gravity
by Anirudh Pradhan, Archana Dixit and Dinesh Chandra Maurya
Symmetry 2022, 14(12), 2630; https://doi.org/10.3390/sym14122630 - 12 Dec 2022
Cited by 16 | Viewed by 1023
Abstract
In this article, we consider an anisotropic viscous cosmological model having LRS Bianchi type I spacetime with f(Q) gravity. We investigate the modified f(Q) gravity with form f(Q)=αQ2+β [...] Read more.
In this article, we consider an anisotropic viscous cosmological model having LRS Bianchi type I spacetime with f(Q) gravity. We investigate the modified f(Q) gravity with form f(Q)=αQ2+β, where Q is the non-metricity scalar and α, β are the positive constants. From the modified Einstein’s field equation having the viscosity coefficient ξ(t)=ξ0H, the scale factor is derived as a(t)=2sinhm+26ξ0α(2m+1)t. We apply the observational constraints on the apparent magnitude m(z) using the χ2 test formula with the observational data set such as JLA, Union 2.1 compilation and obtained the best approximate values of the model parameters m,α,H0,ξ0. We find a transit universe which is accelerating at late times. We also examined the bulk viscosity equation of state (EoS) parameter ωv and derived its current value satisfying ωv<−1/3, which shows the dark energy dominating universe evolution having a cosmological constant, phantom, and super-phantom evolution stages. It tends to the Λ cold dark matter (ΛCDM) value (ωv=−1) at late times. We also estimate the current age of the universe as t0≈13.6 Gyrs and analyze the statefinder parameters with (s,r)→(0,1) as t→∞. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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19 pages, 2175 KiB  
Article
Measurement of the Central Galactic Black Hole by Extremely Large Mass-Ratio Inspirals
by Shu-Cheng Yang, Hui-Jiao Luo, Yuan-Hao Zhang and Chen Zhang
Symmetry 2022, 14(12), 2558; https://doi.org/10.3390/sym14122558 - 03 Dec 2022
Cited by 2 | Viewed by 1092
Abstract
In the galaxy, extremely large mass-ratio inspirals (X-MRIs) composed of brown dwarfs and the massive black hole at the galactic center are expected to be promising gravitational wave sources for space-borne detectors. In this work, we simulate the gravitational wave signals from twenty [...] Read more.
In the galaxy, extremely large mass-ratio inspirals (X-MRIs) composed of brown dwarfs and the massive black hole at the galactic center are expected to be promising gravitational wave sources for space-borne detectors. In this work, we simulate the gravitational wave signals from twenty X-MRI systems by an axisymmetric Konoplya–Rezzolla–Zhidenko metric with varied parameters. We find that the mass, spin, and deviation parameters of the Kerr black hole can be determined accurately (∼10−5−10−6) with only one X-MRI event with a high signal-to-noise ratio. The measurement of the above parameters could be improved with more X-MRI observations. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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15 pages, 970 KiB  
Article
Shadow Cast of Rotating Charged Black Hole with Scalar Q-Hair
by Meng-He Wu, Hong Guo and Xiao-Mei Kuang
Symmetry 2022, 14(11), 2237; https://doi.org/10.3390/sym14112237 - 25 Oct 2022
Cited by 5 | Viewed by 1169
Abstract
In this paper, we investigate the shadow cast by non-rotating and rotating charged black holes with scalar Q-hair. We find that in addition to the spin parameter of black hole and inclination angle of the observer, the charge parameter and the self-interaction parameters [...] Read more.
In this paper, we investigate the shadow cast by non-rotating and rotating charged black holes with scalar Q-hair. We find that in addition to the spin parameter of black hole and inclination angle of the observer, the charge parameter and the self-interaction parameters of the scalar hair also influence the shape of the black hole shadow. Our studies show that the charged black holes with scalar Q-hair always have smaller shadow size compared to those without hair. Moreover, it is found that the parameters significantly affect the shadow observables. In particular, for the fixed spin parameter and inclination angle, a larger charge parameter will increase the shadow size but decrease the shadow distortion, whilst stronger self-interaction parameters have the opposite influence. In short, the shadow of the charged black hole with scalar Q-hair can be distinguished from the Reissner–Nordstro¨m (RN) black hole or Kerr–Newmann (KN) black hole, and they indeed generate new templates with large deviations from general relativity those are invariably smaller in size. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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18 pages, 347 KiB  
Article
Discontinuous Normals in Non-Euclidean Geometries and Two-Dimensional Gravity
by Emmanuele Battista and Giampiero Esposito
Symmetry 2022, 14(10), 1979; https://doi.org/10.3390/sym14101979 - 21 Sep 2022
Cited by 2 | Viewed by 1311
Abstract
This paper builds two detailed examples of generalized normal in non-Euclidean spaces, i.e., the hyperbolic and elliptic geometries. In the hyperbolic plane we define a n-sided hyperbolic polygon P, which is the Euclidean closure of the hyperbolic plane H, bounded [...] Read more.
This paper builds two detailed examples of generalized normal in non-Euclidean spaces, i.e., the hyperbolic and elliptic geometries. In the hyperbolic plane we define a n-sided hyperbolic polygon P, which is the Euclidean closure of the hyperbolic plane H, bounded by n hyperbolic geodesic segments. The polygon P is built by considering the unique geodesic that connects the n+2 vertices z˜,z0,z1,…,zn−1,zn. The geodesics that link the vertices are Euclidean semicircles centred on the real axis. The vector normal to the geodesic linking two consecutive vertices is evaluated and turns out to be discontinuous. Within the framework of elliptic geometry, we solve the geodesic equation and construct a geodesic triangle. Additionally in this case, we obtain a discontinuous normal vector field. Last, the possible application to two-dimensional Euclidean quantum gravity is outlined. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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13 pages, 7600 KiB  
Article
The Observational Shadow Features of a Renormalization Group Improved Black Hole Considering Spherical Accretions
by Yun-Xian Chen, Ping-Hui Mou and Guo-Ping Li
Symmetry 2022, 14(10), 1959; https://doi.org/10.3390/sym14101959 - 20 Sep 2022
Cited by 3 | Viewed by 1122
Abstract
The study of black hole shadows by considering the surrounding kinds of matter has attracted interest in recent years. In this paper, we use the ray-tracing method to study shadows and photon spheres of renormalization group improved (RGI) black holes, taking into account [...] Read more.
The study of black hole shadows by considering the surrounding kinds of matter has attracted interest in recent years. In this paper, we use the ray-tracing method to study shadows and photon spheres of renormalization group improved (RGI) black holes, taking into account the different thin spherical accretion models. We find that an increase in the parameters Ω and γ, which are excited by renormalization group theory, can decrease the event horizon and the radius of the photon sphere while increasing the effective potential. For static and infalling accretions, these results indicate that black hole shadows are related to the geometry of spacetime, and are nearly unaffected by spherical accretions. However, due to the Doppler effect, the shadow in the infalling case is darker than the static one, and the intensities of the photon sphere decay more slowly from the photon sphere to infinity. In addition, the peak intensities out of the shadow increase with the parameters Ω and γ. Finally, it can be seen that the effect of Ω on the shadow is more distinct by comparing it with that of γ at the same parameter level. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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