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Gravitational collapse and singularity avoidance of a homogeneous dust fluid on a brane with timelike extra dimension

Rikpratik Sengupta, Chiranjeeb Singha

TL;DR

The paper analyzes gravitational collapse of a homogeneous dust fluid on a brane with a timelike extra dimension (Shtanov-Sahni model). The interior is modeled by a closed FLRW solution, while the exterior transitions from a Vaidya radiative envelope to a RN-like spacetime with a positive tidal charge due to bulk Weyl effects; crucially, brane corrections with finite tension keep the scalar curvature bounded, thereby avoiding a singularity. The analysis reveals two post-collapse possibilities: (i) a non-singular black hole with an inner horizon and a remnant mass, potentially a dark matter candidate, and (ii) a bounce leading to exponential (de Sitter-like) expansion inside a horizon, potentially evolving into a white hole or cyclic interior. The work highlights how timelike extra dimensions can yield singularity avoidance in gravitational collapse and connects to broader themes in holographic brane dynamics and quantum gravity-inspired bounces.

Abstract

We investigate the gravitational collapse of a homogeneous dust cloud in the Shtanov Sahni braneworld model, which incorporates an extra timelike dimension. The interior of the collapsing configuration is modeled by a Friedmann Lemaitre spacetime, while the exterior is described by a Vaidya radiation envelope that eventually settles into a static Reissner Nordstrom (RN) geometry with a positive tidal charge. Although a smooth matching between the interior and the static exterior is precluded by the breakdown of Birkhoff's theorem in the braneworld scenario, we show that as long as braneworld effects remain significant, the brane tension stays finite. Consequently, the scalar curvature remains bounded, thereby preventing the formation of a singularity.

Gravitational collapse and singularity avoidance of a homogeneous dust fluid on a brane with timelike extra dimension

TL;DR

The paper analyzes gravitational collapse of a homogeneous dust fluid on a brane with a timelike extra dimension (Shtanov-Sahni model). The interior is modeled by a closed FLRW solution, while the exterior transitions from a Vaidya radiative envelope to a RN-like spacetime with a positive tidal charge due to bulk Weyl effects; crucially, brane corrections with finite tension keep the scalar curvature bounded, thereby avoiding a singularity. The analysis reveals two post-collapse possibilities: (i) a non-singular black hole with an inner horizon and a remnant mass, potentially a dark matter candidate, and (ii) a bounce leading to exponential (de Sitter-like) expansion inside a horizon, potentially evolving into a white hole or cyclic interior. The work highlights how timelike extra dimensions can yield singularity avoidance in gravitational collapse and connects to broader themes in holographic brane dynamics and quantum gravity-inspired bounces.

Abstract

We investigate the gravitational collapse of a homogeneous dust cloud in the Shtanov Sahni braneworld model, which incorporates an extra timelike dimension. The interior of the collapsing configuration is modeled by a Friedmann Lemaitre spacetime, while the exterior is described by a Vaidya radiation envelope that eventually settles into a static Reissner Nordstrom (RN) geometry with a positive tidal charge. Although a smooth matching between the interior and the static exterior is precluded by the breakdown of Birkhoff's theorem in the braneworld scenario, we show that as long as braneworld effects remain significant, the brane tension stays finite. Consequently, the scalar curvature remains bounded, thereby preventing the formation of a singularity.
Paper Structure (10 sections, 71 equations, 5 figures)

This paper contains 10 sections, 71 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Basic framework
  3. Gravitational collapse
  4. Exterior
  5. Interior
  6. Mathematical model of collapse
  7. Post collapse dynamics
  8. Case - 1
  9. Case - 2
  10. Discussion

Figures (5)

  • Figure 1: Plot of $v$ as a function of $R$
  • Figure 2: Variation of $a$ with respect to $\eta$
  • Figure 3: Plot showing the variation of $t$ with respect to $r$.
  • Figure 4: Variation of $a$ with respect to $\tau$
  • Figure 5: Plot showing the dependence of $t$ on $R$