Screened scalar hair and the weak-lensing separation of black holes from neutron stars in quadratic f(R) gravity
- 1Universidad Nacional Autónoma de México
- 2Universidade de Lisboa–UL
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. The correction to the Schwarzschild metric is Yukawa-suppressed, falling as e−r/λ instead of polynomially in the coupling, and is therefore 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 Gauss–Bonnet theorem to this geometry, we find the leading deflection angle to be exactly the general-relativistic 4GM/b, with b the impact parameter, the scalaron contributions cancelling identically in the combination that bends light. The 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 not a difference of degree but of kind. 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 not in bending angles at large impact parameter but 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
@article{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},
journal = {The European Physical Journal C},
year = {2026},
month = nov,
doi = {10.1140/epjc/s10052-026-16565-4},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16565-4},
note = {CC BY 4.0},
}
RIS
TY - JOUR
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 - 2026/11/05
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16565-4
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16565-4
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. The correction to the Schwarzschild metric is Yukawa-suppressed, falling as e^−r/λ instead of polynomially in the coupling, and is therefore 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 Gauss–Bonnet theorem to this geometry, we find the leading deflection angle to be exactly the general-relativistic 4GM/b, with b the impact parameter, the scalaron contributions cancelling identically in the combination that bends light. The 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 not a difference of degree but of kind. 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 not in bending angles at large impact parameter but 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.
SN - 1434-6052
ER -