On the Stability of Tolman Oppenheimer Volkoff Fireholes
Abstract
We investigate the radial stability of singular Tolman--Oppenheimer--Volkoff fireholes with a radiation equation of state. These configurations contain a naked, negative point-mass singularity surrounded by a positive-density fluid, whose mass profile develops a Schwarzschild-like plateau before approaching an extended, self-similar atmosphere. Using the Prüfer phase method to identify the fundamental radial mode, we consider two outer boundary conditions: vanishing Lagrangian pressure perturbation (open firehole) and vanishing radial displacement (boxed firehole). For both, the fundamental squared frequency changes from positive to negative as the outer boundary exceeds a critical radius Rc. We find that Rc follows approximately the same scaling with the central mass parameter as the equilibrium firehole radius R. However, the stability thresholds differ significantly: RcO<R for the open firehole, whereas RcB≃ R for the boxed one. The regular zero mode is the derivative of the equilibrium family with respect to the inner lapse normalization at fixed central mass. This gives the boxed threshold a turning-point interpretation and, together with a scaling symmetry of the TOV equations, implies RcB→ R in the limit of large central mass. Variational bounds show that the rigid wall is the most stabilizing separated, self-adjoint outer boundary condition and that the unbounded configuration is unstable. Tolman--Oppenheimer--Volkoff fireholes are therefore radially unstable unless confined within approximately their firehole radius.
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BibTeX
@misc{laguna2026stability,
title = {{On the Stability of Tolman Oppenheimer Volkoff Fireholes}},
author = {Pablo Laguna and Octavio Guerrero and Kostas Kokkotas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28140},
eprint = {2610.28140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28140},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Stability of Tolman Oppenheimer Volkoff Fireholes
AU - Pablo Laguna
AU - Octavio Guerrero
AU - Kostas Kokkotas
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28140
UR - https://arxiv.org/abs/2610.28140
AB - We investigate the radial stability of singular Tolman--Oppenheimer--Volkoff fireholes with a radiation equation of state. These configurations contain a naked, negative point-mass singularity surrounded by a positive-density fluid, whose mass profile develops a Schwarzschild-like plateau before approaching an extended, self-similar atmosphere. Using the Prüfer phase method to identify the fundamental radial mode, we consider two outer boundary conditions: vanishing Lagrangian pressure perturbation (open firehole) and vanishing radial displacement (boxed firehole). For both, the fundamental squared frequency changes from positive to negative as the outer boundary exceeds a critical radius R_c. We find that R_c follows approximately the same scaling with the central mass parameter as the equilibrium firehole radius R. However, the stability thresholds differ significantly: R_c^O<R for the open firehole, whereas R_c^B≃ R for the boxed one. The regular zero mode is the derivative of the equilibrium family with respect to the inner lapse normalization at fixed central mass. This gives the boxed threshold a turning-point interpretation and, together with a scaling symmetry of the TOV equations, implies R_c^B→ R in the limit of large central mass. Variational bounds show that the rigid wall is the most stabilizing separated, self-adjoint outer boundary condition and that the unbounded configuration is unstable. Tolman--Oppenheimer--Volkoff fireholes are therefore radially unstable unless confined within approximately their firehole radius.
ER -