Regular Reissner--Nordström--de Sitter Black Holes: Thin-Shell Matching and Modified Density Profiles
Abstract
We investigate two distinct approaches to regularizing the central singularity of the Reissner--Nordström--de Sitter geometry. In the first approach, a de Sitter interior is matched to an exact Reissner--Nordström--de Sitter exterior across a timelike dust shell. Using the Israel junction conditions, we derive the effective potential governing the shell dynamics and analyze its static equilibrium and radial stability. We show that radial stability requires Λ->Λ+, while the additional requirement of three distinct exterior horizons, with the shell located inside the inner horizon, leads to the stronger analytical result that such stable black-hole configurations exist if and only if Λ->3Λ+. We also derive an upper bound on the exterior mass parameter and recover the Reissner--Nordström limit as Λ+→0. Although the singular center is replaced by a regular core, the stationary exterior geometry remains unchanged, demonstrating that exterior geometric observations alone cannot determine whether the black-hole interior is singular or regular. In the second approach, we modify the divergent energy-density profile and reconstruct a smooth geometry with a de Sitter core while preserving the Reissner--Nordström--de Sitter asymptotics. Regularity fixes the smoothing scale to β=Q2/(2m), leaving no independent regularization parameter. The two constructions thus provide distinct regularization mechanisms, rather than equivalent descriptions of the same spacetime.
Related
- Quasinormal Modes of Reissner-Nordström Black Holes in Modified Gravity
- Nonoscillatory gravitational quasinormal modes of Reissner–Nordström–de Sitter spacetime
- Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field
- Stochastic motion of massless particles near event horizons in Schwarzschild and Reissner-Nordström spacetimes
- Flexible numerical characteristic gluing to extremal Reissner-Nordström black holes
BibTeX
@misc{saadati2026regular,
title = {{Regular Reissner--Nordström--de Sitter Black Holes: Thin-Shell Matching and Modified Density Profiles}},
author = {Reza Saadati and Yu Shi and Vitalii Vertogradov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27578},
eprint = {2610.27578},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27578},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regular Reissner--Nordström--de Sitter Black Holes: Thin-Shell Matching and Modified Density Profiles
AU - Reza Saadati
AU - Yu Shi
AU - Vitalii Vertogradov
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27578
UR - https://arxiv.org/abs/2610.27578
AB - We investigate two distinct approaches to regularizing the central singularity of the Reissner--Nordström--de Sitter geometry. In the first approach, a de Sitter interior is matched to an exact Reissner--Nordström--de Sitter exterior across a timelike dust shell. Using the Israel junction conditions, we derive the effective potential governing the shell dynamics and analyze its static equilibrium and radial stability. We show that radial stability requires Λ_->Λ_+, while the additional requirement of three distinct exterior horizons, with the shell located inside the inner horizon, leads to the stronger analytical result that such stable black-hole configurations exist if and only if Λ_->3Λ_+. We also derive an upper bound on the exterior mass parameter and recover the Reissner--Nordström limit as Λ_+→0. Although the singular center is replaced by a regular core, the stationary exterior geometry remains unchanged, demonstrating that exterior geometric observations alone cannot determine whether the black-hole interior is singular or regular. In the second approach, we modify the divergent energy-density profile and reconstruct a smooth geometry with a de Sitter core while preserving the Reissner--Nordström--de Sitter asymptotics. Regularity fixes the smoothing scale to β=Q^2/(2m), leaving no independent regularization parameter. The two constructions thus provide distinct regularization mechanisms, rather than equivalent descriptions of the same spacetime.
ER -