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Symmetry
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String Field Theory and Nonlocal Gravity
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String Field Theory and Nonlocal Gravity

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

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 8415

Special Issue Editor

Dr. Sergey Vernov

E-Mail Website
Guest Editor
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
Interests: string field theory; modified gravity models; nonlocal gravity

Special Issue Information

Dear Colleagues,

One of the main paradigms of modern theoretical physics is the belief that the string theory unifies all known forces and governs the fundamental law of Natures. From this point of view questions in cosmology, related to fundamental physics should be addressed within the string scenario framework. The appearance of nonlocality within the string field theory framework is a good motivation for studying nonlocal cosmological models.

Modified gravity models have been proposed with the hope to find resolutions to the important open problems of General Relativity. One of these problems is the construction of quantum gravity. A possible modification that allows getting a renormalizable theory of quantum gravity including the addition of higher-derivative terms to the Einstein-Hilbert action. Unfortunately, models with the higher-derivative terms have ghosts. In the present time, nonlocal gravity models are considered a possible way to overcome this problem. The role of higher derivatives and nonlocality in the quantization of gravity is actively discussed.

Local modified gravity models that are compatible with the observation data describe the different stages of the Universe evolution from inflation to the late-time accelerating expansion. Nonlocal generalizations of such models are actively investigated. Please note that all submitted papers must be within the general scope of the Symmetry journal.

Dr. Sergey Vernov
Guest Editor

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

  • string field theory
  • nonlocality
  • cosmology
  • inflation
  • analytic infinity derivative gravity
  • ultra-violet completion
  • ghost-free

Published Papers (6 papers)

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Research

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27 pages, 3072 KiB  
Article
Nonlocal Modification of the Kerr Metric
by Valeri P. Frolov and Jose Pinedo Soto
Symmetry 2023, 15(9), 1771; https://doi.org/10.3390/sym15091771 - 15 Sep 2023
Cited by 2 | Viewed by 700
Abstract
In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric gμν=ημν+Φlμlμ. Using Newman’s approach, we identify [...] Read more.
In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric gμν=ημν+Φlμlμ. Using Newman’s approach, we identify a shear free null congruence l with the generators of the null cone with apex at a point p in the complex space. The Kerr metric is obtained if the potential Φ is chosen to be a solution of the flat Laplace equation for a point source at the apex p. To construct the nonlocal modification of the Kerr metric, we modify the Laplace operator ▵ by its nonlocal version exp(−ℓ2▵)▵. We found the potential Φ in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality. AlbertaThy 5–23. Full article
(This article belongs to the Special Issue String Field Theory and Nonlocal Gravity)
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22 pages, 8861 KiB  
Article
Complete Evaporation of Black Holes and Page Curves
by Irina Aref’eva and Igor Volovich
Symmetry 2023, 15(1), 170; https://doi.org/10.3390/sym15010170 - 06 Jan 2023
Cited by 12 | Viewed by 1508
Abstract
The problem of complete evaporation of a Schwarzschild black hole, the simplest spherically symmetric vacuum solution of the Einstein field equation, posed by Hawking, is that when the black hole mass M disappears, an explosion of temperature [...] Read more.
The problem of complete evaporation of a Schwarzschild black hole, the simplest spherically symmetric vacuum solution of the Einstein field equation, posed by Hawking, is that when the black hole mass M disappears, an explosion of temperature T=1/8πM takes place. We consider the Reissner–Nordstrom black hole, a static spherically symmetric solution to the Einstein–Maxwell field equations, and show that if mass M and charge Q<M satisfy the bound Q>M−CM3, C>0 for small M, then the complete evaporation of black holes without blow-up of temperature is possible. We describe curves on the surface of state equations such that the motion along them provides complete evaporation without temperature explosion. In this case, the radiation entropy follows the Page curve and vanishes at the end of evaporation. Similar results for rotating Kerr, Schwarzschild–de Sitter and Reissner–Nordstrom-(Anti)-de Sitter black holes are discussed. Full article
(This article belongs to the Special Issue String Field Theory and Nonlocal Gravity)
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30 pages, 3482 KiB  
Article
Quantum Explosions of Black Holes and Thermal Coordinates
by Irina Aref’eva and Igor Volovich
Symmetry 2022, 14(11), 2298; https://doi.org/10.3390/sym14112298 - 02 Nov 2022
Cited by 8 | Viewed by 1324
Abstract
The Hawking temperature for a Schwarzschild black hole is T=1/8πM, where M is the black hole mass. This formula is derived for a fixed Schwarzschild background metric, where the mass M could be arbitrary small. Note [...] Read more.
The Hawking temperature for a Schwarzschild black hole is T=1/8πM, where M is the black hole mass. This formula is derived for a fixed Schwarzschild background metric, where the mass M could be arbitrary small. Note that, for vanishing M→0, the temperature T becomes infinite. However, the Schwarzschild metric itself is regular when the black hole mass M tends to zero; it is reduced to the Minkowski metric, and there are no reasons to believe that the temperature becomes infinite. We point out that this discrepancy may be due to the fact that the Kruskal coordinates are singular in the limit of the vanishing mass of the black hole. To elucidate the situation, new coordinates for the Schwarzschild metric are introduced, called thermal coordinates, which depend on the black hole mass M and the parameter b. The parameter b specifies the motion of the observer along a special trajectory. The thermal coordinates are regular in the limit of vanishing black hole mass M. In this limit, the Schwarzschild metric is reduced to the Minkowski metric, written in coordinates dual to the Rindler coordinates. Using the thermal coordinates, the Schwarzschild black hole radiation is reconsidered, and it is found that the Hawking formula for temperature is valid only for large black holes, while for small black holes, the temperature is T=1/2π(4M+b). The thermal observer in Minkowski space sees radiation with temperature T=1/2πb, similar to the Unruh effect with non-constant acceleration. The thermal coordinates for more general spherically symmetric metrics, including the Reissner–Nordstrom, de Sitter, and anti-de Sitter, are also considered. In these coordinates, one sees a Planck distribution with constant temperature. One obtains that the thermal Planck distribution of massless particles is not restricted to the cases of black holes or constant acceleration, but is valid for any spherically symmetric metric written in thermal coordinates. Full article
(This article belongs to the Special Issue String Field Theory and Nonlocal Gravity)
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12 pages, 320 KiB  
Article
Nonlocal Gravity: Fundamental Tetrads and Constitutive Relations
by Bahram Mashhoon
Symmetry 2022, 14(10), 2116; https://doi.org/10.3390/sym14102116 - 12 Oct 2022
Cited by 7 | Viewed by 925
Abstract
Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein’s theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. The history dependence enters NLG through a constitutive relation involving a causal kernel that should ultimately be determined via [...] Read more.
Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein’s theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. The history dependence enters NLG through a constitutive relation involving a causal kernel that should ultimately be determined via observational data. The purpose of this paper is to reformulate nonlocal gravity such that the nonlocal aspect of the constitutive relation directly connects measurable quantities as in the nonlocal electrodynamics of media. The resulting constitutive relation turns out to coincide with the recent suggestion of Puetzfeld, Obukhov, and Hehl. With the new constitutive relation of NLG, it is possible to show that de Sitter spacetime is not a solution of NLG. Full article
(This article belongs to the Special Issue String Field Theory and Nonlocal Gravity)
16 pages, 345 KiB  
Article
New Cosmological Solutions of a Nonlocal Gravity Model
by Ivan Dimitrijevic, Branko Dragovich, Zoran Rakic and Jelena Stankovic
Symmetry 2022, 14(1), 3; https://doi.org/10.3390/sym14010003 - 21 Dec 2021
Cited by 7 | Viewed by 1961
Abstract
A nonlocal gravity model (2) was introduced and considered recently, and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark energy background, while the second one is a [...] Read more.
A nonlocal gravity model (2) was introduced and considered recently, and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark energy background, while the second one is a nonsingular time symmetric bounce. In the present paper, we investigate other possible exact cosmological solutions and find some the new ones in nonflat space. Used nonlocal gravity dynamics can change the background topology. To solve the corresponding equations of motion, we first look for a solution of the eigenvalue problem □(R−4Λ)=q(R−4Λ). We also discuss possible extension of this model with a nonlocal operator, symmetric under □⟷□−1, and its connection with another interesting nonlocal gravity model. Full article
(This article belongs to the Special Issue String Field Theory and Nonlocal Gravity)

Review

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46 pages, 791 KiB  
Review
Field Mixing in Curved Spacetime and Dark Matter
by Antonio Capolupo, Aniello Quaranta and Raoul Serao
Symmetry 2023, 15(4), 807; https://doi.org/10.3390/sym15040807 - 26 Mar 2023
Cited by 2 | Viewed by 1301
Abstract
An extensive review of recent results concerning the quantum field theory of particle mixing in curved spacetime is presented. The rich mathematical structure of the theory for both fermions and bosons, stemming from the interplay of curved space quantization and field mixing, is [...] Read more.
An extensive review of recent results concerning the quantum field theory of particle mixing in curved spacetime is presented. The rich mathematical structure of the theory for both fermions and bosons, stemming from the interplay of curved space quantization and field mixing, is discussed, and its phenomenological implications are shown. Fermionic and bosonic oscillation formulae for arbitrary globally hyperbolic spacetimes are derived and the transition probabilities are explicitly computed on some metrics of cosmological and astrophysical interest. The formulae thus obtained are characterized by a pure QFT correction to the amplitudes, which is absent in quantum mechanics, where only the phase of the oscillations is affected by the gravitational background. Their deviation from the flat space probabilities is demonstrated, with the aid of numerical analyses. The condensate structure of the flavor vacuum of mixed fermions is studied, assessing its role as a possible dark matter component in a cosmological context. It is shown that the flavor vacuum behaves as a barotropic fluid, satisfying the equation of the state of cold dark matter. New experiments on the cosmic neutrino background, as PTOLEMY, may validate these theoretical results. Full article
(This article belongs to the Special Issue String Field Theory and Nonlocal Gravity)
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