Mass inflation or scalaron rigidity: Cauchy horizons in metric f(R)
Abstract
We develop a double-null framework for Cauchy-horizon dynamics in metric f(R) gravity that separates ordinary mass inflation from scalaron cancellation and genuine escape from the blueshift instability. Starting from the exact spherical Hawking-mass transport equation, we show that a regular nondegenerate Cauchy horizon undergoes mass inflation whenever the effective longitudinal source is eventually nonnegative, uniformly dominates the mixed channel, and has a divergent blueshift-weighted integral. Hence bounded mass requires sufficiently strong blueshift-integrable suppression of this source or an independent competing channel. We then analyze the weaker branch in which the scalaron cancels only the leading Price-tail contribution. Under non-cancelling transverse and trace asymptotics, this forces |R|→∞ and an asymptotically linear high-curvature theory, f(R)/R→ F->0, where F-≡limv→∞fR. The curvature coefficient is fixed explicitly by the transverse asymptotics. For regular model classes with a finite high-curvature fRR limit one obtains fRR→0. More sharply, every eventually viable branch with fRR>0 is forced to R→−∞ and Λ∞>−1; the standard scalaron mass parameter then diverges, while an additional differentiable rate condition yields msc2∼ F/(3fRR)→+∞. In the Einstein frame the scalaron null kinetic contribution is nonnegative, so the Jordan-frame cancellation cannot be interpreted as negative scalaron null energy. The result is a local rigidity classification rather than a global theorem of strong cosmic censorship.
Versions
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BibTeX
@misc{lobo2026mass,
title = {{Mass inflation or scalaron rigidity: Cauchy horizons in metric f(R)}},
author = {Francisco S. N. Lobo and Maickol Muñoz-Palma and Francisco Tello-Ortiz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.27889},
eprint = {2609.27889},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27889},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mass inflation or scalaron rigidity: Cauchy horizons in metric f(R)
AU - Francisco S. N. Lobo
AU - Maickol Muñoz-Palma
AU - Francisco Tello-Ortiz
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2609.27889
UR - https://arxiv.org/abs/2609.27889
AB - We develop a double-null framework for Cauchy-horizon dynamics in metric f(R) gravity that separates ordinary mass inflation from scalaron cancellation and genuine escape from the blueshift instability. Starting from the exact spherical Hawking-mass transport equation, we show that a regular nondegenerate Cauchy horizon undergoes mass inflation whenever the effective longitudinal source is eventually nonnegative, uniformly dominates the mixed channel, and has a divergent blueshift-weighted integral. Hence bounded mass requires sufficiently strong blueshift-integrable suppression of this source or an independent competing channel. We then analyze the weaker branch in which the scalaron cancels only the leading Price-tail contribution. Under non-cancelling transverse and trace asymptotics, this forces |R|→∞ and an asymptotically linear high-curvature theory, f(R)/R→ F_->0, where F_-≡lim_v→∞f_R. The curvature coefficient is fixed explicitly by the transverse asymptotics. For regular model classes with a finite high-curvature f_RR limit one obtains f_RR→0. More sharply, every eventually viable branch with f_RR>0 is forced to R→−∞ and Λ_∞>−1; the standard scalaron mass parameter then diverges, while an additional differentiable rate condition yields m_sc^2∼ F/(3f_RR)→+∞. In the Einstein frame the scalaron null kinetic contribution is nonnegative, so the Jordan-frame cancellation cannot be interpreted as negative scalaron null energy. The result is a local rigidity classification rather than a global theorem of strong cosmic censorship.
ER -