Bouncing Dust Collapse and Black-to-White Hole Transition on the Brane
Abstract
We study the spherical collapse of a homogeneous dust cloud on a three-brane in the Shtanov--Sahni braneworld, in which the extra dimension is timelike. In the high-energy regime the brane Friedmann equation acquires a negative quadratic term in the matter density, controlled by a critical density rhoc=2λ, where λ is the magnitude of the negative brane tension. For a spatially closed interior we integrate the dynamics exactly. Every turning point of the scale factor lies above astar=√(3/4πλ), a bounce exists if and only if a simple condition on the comoving density holds, and all curvature invariants stay below bounds fixed by λ alone along the entire cycle. Comoving worldlines are geodesically complete. We then match the cloud across a comoving boundary to a spherically symmetric exterior with a trace-free effective source and solve the Israel conditions in closed form. The exterior is a charged Vaidya geometry whose mass function and tidal charge are fixed by the boundary radius. The tidal charge is positive, opposite in sign to the Randall--Sundrum case, and the exterior cannot be static. A trapped region forms on the boundary if and only if the mass exceeds 2/(3√(πλ)), and in that case the bounce still takes place in an untrapped neighbourhood of the boundary. For trapped clouds we construct an exterior over the full contraction, bounce and re-expansion by joining an advanced and a retarded charged Vaidya patch through a static wedge. The matched metric is of class C1,1, the effective energy conditions hold, and the cloud re-emerges through a white hole region into a second asymptotic region. In the general relativistic limit λ→∞ the Oppenheimer--Snyder solution is recovered.
Related
- Topology of Hawking-Page phase transition and equilibrium phases in AdS brane backgrounds
- Bouncing geodesics, black hole singularities, and singularities of thermal correlators
- Spontaneous Scalarization of Brane Black Holes: Quantum-Enhanced Tachyonic Instabilities
- Spontaneous scalarization of brane black holes: quantum-enhanced tachyonic instabilities
- Black Hole Entropy and Holographic Entanglement Entropy in DGP Brane Gravity
BibTeX
@misc{sengupta2026bouncing,
title = {{Bouncing Dust Collapse and Black-to-White Hole Transition on the Brane}},
author = {Rikpratik Sengupta and Chiranjeeb Singha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04353},
eprint = {2610.04353},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04353},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bouncing Dust Collapse and Black-to-White Hole Transition on the Brane
AU - Rikpratik Sengupta
AU - Chiranjeeb Singha
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04353
UR - https://arxiv.org/abs/2610.04353
AB - We study the spherical collapse of a homogeneous dust cloud on a three-brane in the Shtanov--Sahni braneworld, in which the extra dimension is timelike. In the high-energy regime the brane Friedmann equation acquires a negative quadratic term in the matter density, controlled by a critical density rhoc=2λ, where λ is the magnitude of the negative brane tension. For a spatially closed interior we integrate the dynamics exactly. Every turning point of the scale factor lies above astar=√(3/4πλ), a bounce exists if and only if a simple condition on the comoving density holds, and all curvature invariants stay below bounds fixed by λ alone along the entire cycle. Comoving worldlines are geodesically complete. We then match the cloud across a comoving boundary to a spherically symmetric exterior with a trace-free effective source and solve the Israel conditions in closed form. The exterior is a charged Vaidya geometry whose mass function and tidal charge are fixed by the boundary radius. The tidal charge is positive, opposite in sign to the Randall--Sundrum case, and the exterior cannot be static. A trapped region forms on the boundary if and only if the mass exceeds 2/(3√(πλ)), and in that case the bounce still takes place in an untrapped neighbourhood of the boundary. For trapped clouds we construct an exterior over the full contraction, bounce and re-expansion by joining an advanced and a retarded charged Vaidya patch through a static wedge. The matched metric is of class C^1,1, the effective energy conditions hold, and the cloud re-emerges through a white hole region into a second asymptotic region. In the general relativistic limit λ→∞ the Oppenheimer--Snyder solution is recovered.
ER -