Generalized Regular Black Holes with Tunable Cores and Geodesic Properties
Abstract
We introduce a family of static and spherically symmetric regular black-hole geometries characterized by a discrete core index n, a regularization scale a, and a dimensionless deformation parameter η. The construction starts from a positive, normalized effective density profile with a tunable central behavior. The lowest member contains the Bardeen geometry as a limiting case, whereas a nonzero deformation parameter generates a Reissner--Nordström-like asymptotic correction. The parameter n controls the order of central depletion: the lowest member possesses a de Sitter-type core, whereas higher members approach a Minkowski-like center with vanishing density and curvature. We determine the horizon structure, extremality condition, Hawking temperature, entropy, and the horizon thermodynamic identity implied by the radial Einstein equation. Null geodesics are analyzed to obtain the photon sphere, critical impact parameter, and shadow radius, including analytic weak-deformation approximations, the exact Schwarzschild and Bardeen limits, and comparison with the leading Reissner--Nordström-like behavior. The photon-orbit angular frequency and Lyapunov exponent are then used to separate orbital and instability timescales; their ratio provides information not already contained in the shadow radius. Weak gravitational lensing and magnification are discussed through a controlled sector-isolated expansion of the asymptotic metric. We further study timelike geodesics, circular motion, the marginally bound orbit, and the innermost stable circular orbit, deriving exact implicit relations and perturbative expressions. The model provides a unified framework for investigating how a tunable regular core and an RN-like exterior deformation affect the thermodynamic and geodesic properties of regular black holes.
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BibTeX
@misc{hassanabadi2026generalized,
title = {{Generalized Regular Black Holes with Tunable Cores and Geodesic Properties}},
author = {Hassan Hassanabadi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25113},
eprint = {2609.25113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25113},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized Regular Black Holes with Tunable Cores and Geodesic Properties
AU - Hassan Hassanabadi
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.25113
UR - https://arxiv.org/abs/2609.25113
AB - We introduce a family of static and spherically symmetric regular black-hole geometries characterized by a discrete core index n, a regularization scale a, and a dimensionless deformation parameter η. The construction starts from a positive, normalized effective density profile with a tunable central behavior. The lowest member contains the Bardeen geometry as a limiting case, whereas a nonzero deformation parameter generates a Reissner--Nordström-like asymptotic correction. The parameter n controls the order of central depletion: the lowest member possesses a de Sitter-type core, whereas higher members approach a Minkowski-like center with vanishing density and curvature. We determine the horizon structure, extremality condition, Hawking temperature, entropy, and the horizon thermodynamic identity implied by the radial Einstein equation. Null geodesics are analyzed to obtain the photon sphere, critical impact parameter, and shadow radius, including analytic weak-deformation approximations, the exact Schwarzschild and Bardeen limits, and comparison with the leading Reissner--Nordström-like behavior. The photon-orbit angular frequency and Lyapunov exponent are then used to separate orbital and instability timescales; their ratio provides information not already contained in the shadow radius. Weak gravitational lensing and magnification are discussed through a controlled sector-isolated expansion of the asymptotic metric. We further study timelike geodesics, circular motion, the marginally bound orbit, and the innermost stable circular orbit, deriving exact implicit relations and perturbative expressions. The model provides a unified framework for investigating how a tunable regular core and an RN-like exterior deformation affect the thermodynamic and geodesic properties of regular black holes.
ER -