D-dimensional self-gravitating lattice gas in general relativity

TL;DR

This paper explores the formation and evolution of self-gravitating objects in various dimensions using a lattice equation of state and Einstein's equations, revealing dimension-dependent behaviors and stability conditions.

Contribution

It introduces a D-dimensional model combining lattice equations with Einstein's equations to analyze self-gravitating systems and their stability across dimensions.

Findings

In 2+1 dimensions, mass is independent of central pressure, allowing only finite mass objects.

In 3+1 dimensions, self-gravity produces a mass gap similar to neutron stars.

Beyond certain pressure, objects become unstable and may collapse into black holes.

Abstract

Using a lattice equation of state combined with the D-dimensional Tolman-Oppenheimer-Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a $2+1$ dimensional spacetime, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a $3+1$ dimensional spacetime, self-gravity leads to the formation of compact objects with a large gap of mass and the corresponding phase diagram has the same structure as the one for Neutron Star. The results also show that beyond certain critical central pressure, the star is unstable against gravitational collapse, and it may end in a black hole. Analysis of spacetimes of higher dimensions shows that gravity has the stronger effect in $3+1$ dimensions. Numerical solutions of the Friedmann equations show that the effect of the curvature of spacetime increases with increasing temperature, but decreases with increasing dimensionality beyond $D=3$.