# A Phase Space Diagram for Gravity

## Abstract

**:**

## 1. Introduction

## 2. A Gravitational Phase Space Diagram

**Figure 1.**Phase space diagram for self-gravitating equilibrium configurations. The labelled solid lines give the mass dependant scale radii resulting from the two limit conditions $v=c$ and $a={a}_{0}$, ${r}_{S}=2GM/{c}^{2}$ and ${r}_{M}={(GM/{a}_{0})}^{1/2}$. The approach to the former from below signals the relativistic region, whilst the approach to latter from the left denotes the transition from the Newtonian to the dark matter mimicking regime. The labels identify the regions occupied by different astrophysical objects; the solar system, SS, stars, S, wide binaries, WB, globular clusters, GC, dwarf spheroidal galaxies, dSph, elliptical galaxies, E, spiral galaxies, S Gal and galaxy clusters, GaC. Distinct regions of the diagram are labelled; black holes, BH, appearance of relativistic effects, GR, the Newtonian region, N, the modified gravity regime, M, and the critical density of the universe, or the dark energy density, coinciding with the critical point b = 1 where ${r}_{S}={r}_{M}$.

## 3. Extrapolation to Atomic Scales

## 4. Conclusions

## Acknowledgements

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Hernandez, X.
A Phase Space Diagram for Gravity. *Entropy* **2012**, *14*, 848-855.
https://doi.org/10.3390/e14050848

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Hernandez X.
A Phase Space Diagram for Gravity. *Entropy*. 2012; 14(5):848-855.
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Hernandez, Xavier.
2012. "A Phase Space Diagram for Gravity" *Entropy* 14, no. 5: 848-855.
https://doi.org/10.3390/e14050848