Self-Bound Anisotropic Stars in ℛ+αℛ2 Gravity with a Hayward Exterior: Junction Conditions and NICER Constraints
Abstract
Analytic compact-star models in modified gravity usually borrow the junction conditions of general relativity and fix their constants with radii derived for a particular stellar model. Here we avoid both. We study ℱ(ℛ)=ℛ+αℛ2 gravity with a Durgapal-Bannerji interior of embedding class one (Karmarkar condition) and a Hayward exterior. Without Birkhoff's theorem, the exterior is an assumption, and we measure its effect with the Hayward metric, which deforms Schwarzschild by a length ℓ. The junction conditions of quadratic ℱ(ℛ) gravity fix all constants in closed form in terms of M, R and ℓ. The condition pr(R)=0 is replaced by continuity of the trace of the extrinsic curvature. The Ricci scalar jumps at the surface, so there is a thin shell with negative surface energy density for α>0, a gravitational double layer, and a small radial stress. For this stress to be below 1% of the central pressure we need α≲0.2 km2 and ℓ≲0.3M. The interior behaves as a self-bound star. A single surface energy density, ρs=(1.37±0.16)ρ0, reproduces PSR J0740+6620, J0437-4715, J0030+0451 and J0614-3329, and for α=0.1 km2 the model predicts R1.4=11.5 km and a maximum mass of 2.9 M⊙. Because ℓ enters surface observables only at order (ℓ/M)2(M/R)3, the results carry over to a Schwarzschild exterior. Calibrating instead with strange-star radii of eclipsing X-ray pulsars gives R1.4≈9 km, which current data rule out.
Related
- Tidal Love Numbers of Thin-Shell Wormholes, de Sitter Gravastars, and Anti-de Sitter Gravastars via Full Perturbed Junction Conditions
- Astrophysical Signatures of Charged Anisotropic Compact Star in f(R,T) Gravity via Minimal Geometric Deformation
- Black Hole Solutions with Scalar Fields and Anisotropic Matter in Non-Minimal Y(R)F2 Gravity
- Stability, Tidal Deformability, and Statistical Constraints of Anisotropic Compact Stars with a Generalized Polytropic Equation of State : Modelling Observation with Buchdahl Space-Time
- Gravitational Waves and Matter Constraints in Gravity from Entropy
BibTeX
@misc{nazeer2026selfbound,
title = {{Self-Bound Anisotropic Stars in $\mathcalR+α\mathcalR^2$ Gravity with a Hayward Exterior: Junction Conditions and NICER Constraints}},
author = {Furqan Nazeer and Tooba Feroze},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39916},
eprint = {2610.39916},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39916},
}
RIS
TY - UNPB
TI - Self-Bound Anisotropic Stars in ℛ+αℛ^2 Gravity with a Hayward Exterior: Junction Conditions and NICER Constraints
AU - Furqan Nazeer
AU - Tooba Feroze
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39916
UR - https://arxiv.org/abs/2610.39916
AB - Analytic compact-star models in modified gravity usually borrow the junction conditions of general relativity and fix their constants with radii derived for a particular stellar model. Here we avoid both. We study ℱ(ℛ)=ℛ+αℛ^2 gravity with a Durgapal-Bannerji interior of embedding class one (Karmarkar condition) and a Hayward exterior. Without Birkhoff's theorem, the exterior is an assumption, and we measure its effect with the Hayward metric, which deforms Schwarzschild by a length ℓ. The junction conditions of quadratic ℱ(ℛ) gravity fix all constants in closed form in terms of M, R and ℓ. The condition p_r(R)=0 is replaced by continuity of the trace of the extrinsic curvature. The Ricci scalar jumps at the surface, so there is a thin shell with negative surface energy density for α>0, a gravitational double layer, and a small radial stress. For this stress to be below 1% of the central pressure we need α≲0.2 km^2 and ℓ≲0.3M. The interior behaves as a self-bound star. A single surface energy density, ρ_s=(1.37±0.16)ρ_0, reproduces PSR J0740+6620, J0437-4715, J0030+0451 and J0614-3329, and for α=0.1 km^2 the model predicts R_1.4=11.5 km and a maximum mass of 2.9 M_⊙. Because ℓ enters surface observables only at order (ℓ/M)^2(M/R)^3, the results carry over to a Schwarzschild exterior. Calibrating instead with strange-star radii of eclipsing X-ray pulsars gives R_1.4≈9 km, which current data rule out.
ER -