Scalaron-modified null focusing and radial monotonicity in static f(R) gravity
Abstract
We derive an exact radial monotonicity law for static, spherically symmetric spacetimes in metric f(R) gravity. For ds2=A(r)dt2−dr2/B(r)−r2dΩ2, the matter contribution and the scalaron Hessian combine into an effective radial-convergence numerator that fixes the derivative of Q=B/A. On every connected static interval with A>0, B>0, and fR≡ df/dR>0, its sign therefore determines the monotonicity of Q. The integrated identity retains the finite, generally nonzero value of B/A at a regular nondegenerate Killing horizon; consequently, a fixed-sign convergence condition orders the horizon endpoint ratios rather than excluding two horizons. A zero-integral obstruction arises for equal endpoint values, including boundaries where B→0 while A remains finite and nonzero. Saturation is equivalent to B/A=const, and in vacuum requires a scalaron profile linear in the areal radius. We illustrate the strict non-saturated branch, within the General-Relativity sector, using the exact constant-density stellar interior, and apply the equality and consistency diagnostics to the constant-X and power-law solutions of Multamäki and Vilja. In particular, in the Schwarzschild--de Sitter two-horizon parameter range, one constant-X solution crosses fR=0 inside the complete static patch, while a direct substitution into the original radial equation exposes an unresolved exponent mismatch in the displayed power-law family. The results provide a model-independent static-sector diagnostic and a precise starting point for a future horizon-regular treatment of black-hole interiors.
Versions
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BibTeX
@misc{munozpalma2026scalaronmodified,
title = {{Scalaron-modified null focusing and radial monotonicity in static f(R) gravity}},
author = {Maickol Muñoz-Palma and Francisco S. N. Lobo and Jean Báez Cuevas and Francisco Tello-Ortiz},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.08818},
eprint = {2608.08818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08818},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scalaron-modified null focusing and radial monotonicity in static f(R) gravity
AU - Maickol Muñoz-Palma
AU - Francisco S. N. Lobo
AU - Jean Báez Cuevas
AU - Francisco Tello-Ortiz
PY - 2026
DA - 2026/08/09
PB - arXiv
DO - 10.48550/arxiv.2608.08818
UR - https://arxiv.org/abs/2608.08818
AB - We derive an exact radial monotonicity law for static, spherically symmetric spacetimes in metric f(R) gravity. For ds^2=A(r)dt^2−dr^2/B(r)−r^2dΩ^2, the matter contribution and the scalaron Hessian combine into an effective radial-convergence numerator that fixes the derivative of Q=B/A. On every connected static interval with A>0, B>0, and f_R≡ df/dR>0, its sign therefore determines the monotonicity of Q. The integrated identity retains the finite, generally nonzero value of B/A at a regular nondegenerate Killing horizon; consequently, a fixed-sign convergence condition orders the horizon endpoint ratios rather than excluding two horizons. A zero-integral obstruction arises for equal endpoint values, including boundaries where B→0 while A remains finite and nonzero. Saturation is equivalent to B/A=const, and in vacuum requires a scalaron profile linear in the areal radius. We illustrate the strict non-saturated branch, within the General-Relativity sector, using the exact constant-density stellar interior, and apply the equality and consistency diagnostics to the constant-X and power-law solutions of Multamäki and Vilja. In particular, in the Schwarzschild--de Sitter two-horizon parameter range, one constant-X solution crosses f_R=0 inside the complete static patch, while a direct substitution into the original radial equation exposes an unresolved exponent mismatch in the displayed power-law family. The results provide a model-independent static-sector diagnostic and a precise starting point for a future horizon-regular treatment of black-hole interiors.
ER -