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Absence of curvature singularities in symmetric perfect fluid spacetimes in Einstein-Gauss-Bonnet Gravity

Aavishkar Madhunlall, Chevarra Hansraj, Rituparno Goswami, Sunil D. Maharaj

TL;DR

The paper investigates whether curvature singularities are unavoidable in $N$-dimensional perfect-fluid spacetimes within Einstein-Gauss-Bonnet gravity. It extends the FLRW framework to higher dimensions, deriving the ND Friedmann equations with Gauss-Bonnet corrections and analyzing scale-factor evolution under general equations of state. A central result proves that the scale factor is bounded below by a finite $a_{\min}$ for physically reasonable matter, thereby excluding Big Bang/Crunch singularities and suggesting a mechanism for regular black hole formation driven by higher-curvature effects. The work further analyzes linear and Chaplygin gas equations of state, providing explicit $a_{\min}$ expressions in the linear case and revealing a dimension-dependent behavior with a notable peak near $N=9$, underscoring the role of higher-curvature terms in singularity avoidance.

Abstract

In this paper we study the higher dimensional homogeneous and isotropic perfect fluid spacetimes in Einstein-Gauss-Bonnet (EGB) gravity. We solve the modified field equations with higher order curvature terms to determine the evolution of the scale factor. We transparently show that this scale factor cannot become smaller than a finite minimum positive value which depends on the dimension and equation of state. This bound completely eliminates any curvature singularities in the spacetimes, where the scale factor must tend to zero. This is a unique property of EGB gravity which, despite being ghost-free and having quasi-linear field equations like general relativity, allows for the violation of singularity theorems. This phenomenon, thus, gives a natural way to dynamically construct regular black holes via higher dimensional continual gravitational collapse.

Absence of curvature singularities in symmetric perfect fluid spacetimes in Einstein-Gauss-Bonnet Gravity

TL;DR

The paper investigates whether curvature singularities are unavoidable in -dimensional perfect-fluid spacetimes within Einstein-Gauss-Bonnet gravity. It extends the FLRW framework to higher dimensions, deriving the ND Friedmann equations with Gauss-Bonnet corrections and analyzing scale-factor evolution under general equations of state. A central result proves that the scale factor is bounded below by a finite for physically reasonable matter, thereby excluding Big Bang/Crunch singularities and suggesting a mechanism for regular black hole formation driven by higher-curvature effects. The work further analyzes linear and Chaplygin gas equations of state, providing explicit expressions in the linear case and revealing a dimension-dependent behavior with a notable peak near , underscoring the role of higher-curvature terms in singularity avoidance.

Abstract

In this paper we study the higher dimensional homogeneous and isotropic perfect fluid spacetimes in Einstein-Gauss-Bonnet (EGB) gravity. We solve the modified field equations with higher order curvature terms to determine the evolution of the scale factor. We transparently show that this scale factor cannot become smaller than a finite minimum positive value which depends on the dimension and equation of state. This bound completely eliminates any curvature singularities in the spacetimes, where the scale factor must tend to zero. This is a unique property of EGB gravity which, despite being ghost-free and having quasi-linear field equations like general relativity, allows for the violation of singularity theorems. This phenomenon, thus, gives a natural way to dynamically construct regular black holes via higher dimensional continual gravitational collapse.

Paper Structure

This paper contains 11 sections, 1 theorem, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. EGB gravity in $N$-dimensions
  3. $N$-dimensional homogeneous and isotropic spacetimes
  4. FLRW field equations
  5. Solutions in general relativity ($\alpha=0$)
  6. Solutions in EGB gravity ($\alpha\neq 0$)
  7. Absence of Curvature Singularities
  8. Special Cases
  9. Linear equation of state
  10. Nonlinear equation of state: Chaplygin gas
  11. Discussions

Key Result

Theorem 1

An $N$-dimensional homogeneous and isotropic perfect fluid spacetime in Einstein-Gauss Bonnet gravity contains no curvature singularities either in the future or in the past, without violating any energy conditions.

Figures (2)

  • Figure 1: A plot of \ref{['a_0']} showing $a_{\text{min}}$ vs $N$ with $N \in (5 ; 20)$
  • Figure 2: A plot of \ref{['kappa']} showing $\kappa_N$ vs $N$.

Theorems & Definitions (1)

  • Theorem 1