Regular Black Holes from Anisotropic Source with Hydrodynamic Equation of State
Abstract
We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the dS metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, P= P(ρ), for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $ P(ρ)$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $ P(ρ)$ has a root and a maximum as it approaches 0+ at large distances. Consequently, the square of the sound speed of perturbations, cs2, changes sign at the point where P reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on cs puts strong constraints on the model parameters, excluding models in which the energy density has an exponential fall off. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which P has its root, and at which P attains its maximum.
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BibTeX
@misc{firouzjahi2026regular,
title = {{Regular Black Holes from Anisotropic Source with Hydrodynamic Equation of State}},
author = {Hassan Firouzjahi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.20109},
eprint = {2606.20109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20109},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regular Black Holes from Anisotropic Source with Hydrodynamic Equation of State
AU - Hassan Firouzjahi
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2606.20109
UR - https://arxiv.org/abs/2606.20109
AB - We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the dS metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, P= P(ρ), for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $ P(ρ)$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $ P(ρ)$ has a root and a maximum as it approaches 0^+ at large distances. Consequently, the square of the sound speed of perturbations, c_s^2, changes sign at the point where P reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on c_s puts strong constraints on the model parameters, excluding models in which the energy density has an exponential fall off. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which P has its root, and at which P attains its maximum.
ER -