A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds
Abstract
We present a unification scheme for anisotropic compact stars generated via minimal geometric deformation (MGD), built on a two-parameter seed family ν(r)=Ln[C(1+ar2n)m] whose radial metric potential μ(r)=e−λ(r) is fixed in closed form by the isotropy condition. At n=1 the family reproduces Tolman IV, Korkina--Orlyanskii, Heintzmann IIa, and Durgapal IV--V as the particular cases m=1,2,3,4,5. The key result is a single closure of the MGD θ-sector, through one source function g(r), that integrates the decoupler equation in closed form, in terms of the Gauss hypergeometric function 2F1, for \emph{arbitrary} (n,m): the anisotropic extension of the n=1 family is thus obtained from one master formula. We derive the effective anisotropic matter content, the Darmois--Israel matching to the exterior Schwarzschild vacuum, and the full set of physical acceptability criteria constraining the parameter space, and map the admissible region in compactness and decoupling strength explicitly for the case n=1: Tolman IV and Korkina--Orlyanskii admit physically consistent anisotropic deformations at arbitrarily high compactness, while Heintzmann IIa and Durgapal IV--V are bounded by a compactness ceiling beyond which no value of the decoupling parameter restores causality. Using the same closed-form matter content, we compute the quadrupolar tidal Love number and dimensionless tidal deformability across the admissible region, finding that the decoupling systematically enhances both relative to the isotropic seed at fixed compactness, with a sharp rise near the causal ceiling in the Heintzmann and Durgapal branches.
Related
- Updated Upper Limits on the Isotropic Gravitational-Wave Background from LIGO, Virgo, and KAGRA Data through April 2025
- Regular hairy black holes by gravitational decoupling: de Sitter and Minkowski cores
- On the Mathematical Foundations of Gravitational Decoupling in General Relativity
- Particle Dynamics and Thermodynamics of a Charged-Like Hairy Black Hole in Extended Gravitational Decoupling
- Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA's fourth Observing Run
BibTeX
@misc{pradhan2026closedform,
title = {{A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds}},
author = {Anirudh Pradhan and Safiqul Islam and Ajit Kumar and Muhammad Aamir},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25110},
eprint = {2609.25110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25110},
}
RIS
TY - UNPB
TI - A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds
AU - Anirudh Pradhan
AU - Safiqul Islam
AU - Ajit Kumar
AU - Muhammad Aamir
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.25110
UR - https://arxiv.org/abs/2609.25110
AB - We present a unification scheme for anisotropic compact stars generated via minimal geometric deformation (MGD), built on a two-parameter seed family ν(r)=Ln[C(1+ar^2n)^m] whose radial metric potential μ(r)=e^−λ(r) is fixed in closed form by the isotropy condition. At n=1 the family reproduces Tolman IV, Korkina--Orlyanskii, Heintzmann IIa, and Durgapal IV--V as the particular cases m=1,2,3,4,5. The key result is a single closure of the MGD θ-sector, through one source function g(r), that integrates the decoupler equation in closed form, in terms of the Gauss hypergeometric function _2F_1, for \emph{arbitrary} (n,m): the anisotropic extension of the n=1 family is thus obtained from one master formula. We derive the effective anisotropic matter content, the Darmois--Israel matching to the exterior Schwarzschild vacuum, and the full set of physical acceptability criteria constraining the parameter space, and map the admissible region in compactness and decoupling strength explicitly for the case n=1: Tolman IV and Korkina--Orlyanskii admit physically consistent anisotropic deformations at arbitrarily high compactness, while Heintzmann IIa and Durgapal IV--V are bounded by a compactness ceiling beyond which no value of the decoupling parameter restores causality. Using the same closed-form matter content, we compute the quadrupolar tidal Love number and dimensionless tidal deformability across the admissible region, finding that the decoupling systematically enhances both relative to the isotropic seed at fixed compactness, with a sharp rise near the causal ceiling in the Heintzmann and Durgapal branches.
ER -