Screened Scalar Hair and the Weak-Lensing Separation of Black Holes from Neutron Stars in Quadratic f(R) Gravity
Abstract
Quadratic f(R) gravity carries a massive scalar degree of freedom, the scalaron, whose finite range λ screens its influence on the geometry outside a compact object. We show that this screening severs the exterior of a black hole from that of a neutron star of the same mass. Correction to the Schwarzschild metric is Yukawa-suppressed, falling as e−r/λ in the coupling, and is thus invisible to any expansion in powers of that coupling; the exterior is moreover intrinsically isotropic, so that inverting the temporal potential alone, as one does for single-potential solutions, fails to solve the field equations. Applying the Gibbons & Werner method of the Gauss-Bonnet theorem to this geometry, we find the leading deflection angle to be exactly the general-relativistic, (b: impact parameter), scalaron contributions cancelling identically in the combination that bends light. First correction carries the unfamiliar signature λ−1/2b−3/2e−b/λ, screened beyond the scalaron range and confirmed against direct quadrature to around 20% at b=4λ, improving to 7% at b=12λ. What survives is the ingredients that deliver it, namely, non-analyticity in the coupling, the intrinsically isotropic gauge, the closed-form screened correction and the pressure-weighted scalar charge, are obtained within a single, self-consistent derivation here. A static black hole carries no scalar hair, and lenses precisely as general relativity requires; a neutron star acquires a scalar charge weighted by the pressure supporting it against collapse, and does not. Weak lensing therefore closes as a discriminant of the theory, whilst the horizon, as against a material surface, remains one in principle. The observational advantage lies in the strong-field imaging of the photon sphere, and in the stellar interior, where the scalar charge is fixed by the equation of state.
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BibTeX
@misc{kumaran2026screened,
title = {{Screened Scalar Hair and the Weak-Lensing Separation of Black Holes from Neutron Stars in Quadratic $f(R)$ Gravity}},
author = {Yashmitha Kumaran and Ilídio Lopes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.04419},
eprint = {2609.04419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04419},
}
RIS
TY - UNPB
TI - Screened Scalar Hair and the Weak-Lensing Separation of Black Holes from Neutron Stars in Quadratic f(R) Gravity
AU - Yashmitha Kumaran
AU - Ilídio Lopes
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.04419
UR - https://arxiv.org/abs/2609.04419
AB - Quadratic f(R) gravity carries a massive scalar degree of freedom, the scalaron, whose finite range λ screens its influence on the geometry outside a compact object. We show that this screening severs the exterior of a black hole from that of a neutron star of the same mass. Correction to the Schwarzschild metric is Yukawa-suppressed, falling as e^−r/λ in the coupling, and is thus invisible to any expansion in powers of that coupling; the exterior is moreover intrinsically isotropic, so that inverting the temporal potential alone, as one does for single-potential solutions, fails to solve the field equations. Applying the Gibbons & Werner method of the Gauss-Bonnet theorem to this geometry, we find the leading deflection angle to be exactly the general-relativistic, (b: impact parameter), scalaron contributions cancelling identically in the combination that bends light. First correction carries the unfamiliar signature λ^−1/2b^−3/2e^−b/λ, screened beyond the scalaron range and confirmed against direct quadrature to around 20% at b=4λ, improving to 7% at b=12λ. What survives is the ingredients that deliver it, namely, non-analyticity in the coupling, the intrinsically isotropic gauge, the closed-form screened correction and the pressure-weighted scalar charge, are obtained within a single, self-consistent derivation here. A static black hole carries no scalar hair, and lenses precisely as general relativity requires; a neutron star acquires a scalar charge weighted by the pressure supporting it against collapse, and does not. Weak lensing therefore closes as a discriminant of the theory, whilst the horizon, as against a material surface, remains one in principle. The observational advantage lies in the strong-field imaging of the photon sphere, and in the stellar interior, where the scalar charge is fixed by the equation of state.
ER -