Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity
Abstract
The Dolgov-Kawasaki instability tests the local scalaron response in metric f(R) gravity, but does not determine strong-field horizon dynamics. We separate these questions using F=fR and the Legendre potential 𝒰(F)=FR−f. The scalaron restoring coefficient is msc2=(F−RfRR)/(3fRR), whereas exact spherical Wald-area transport identities cancel the scalaron Hessian. Their Einstein-frame interpretation distinguishes longitudinal kinetic focusing from potential-dependent cross-focusing. We prove that, at fixed constant-curvature background with tracefree matter, transport depends only on (f,fR), while the scalaron mass depends on the independently adjustable fRR. Reissner-Nordström in f(R)=R+αR2 gives an exact discriminator: identical background transport coexists with opposite scalaron mass signs. A charged solution with varying F and a cosmological check test the identities beyond this constant-F sector. For a nonzero massive scalaron tail transmitted to a nondegenerate Cauchy horizon, a conditional fixed-background estimate gives a nonintegrable contribution to generalized entropy focusing. This estimate does not establish nonlinear mass inflation or a particular extendibility class. The results provide a layered framework for coupling regularity, background transport, scalaron stability, and nonlinear inner-horizon evolution.
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BibTeX
@misc{lobo2026beyond,
title = {{Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity}},
author = {Francisco S. N. Lobo and Francisco Tello-Ortiz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11649},
eprint = {2610.11649},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11649},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity
AU - Francisco S. N. Lobo
AU - Francisco Tello-Ortiz
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11649
UR - https://arxiv.org/abs/2610.11649
AB - The Dolgov-Kawasaki instability tests the local scalaron response in metric f(R) gravity, but does not determine strong-field horizon dynamics. We separate these questions using F=f_R and the Legendre potential 𝒰(F)=FR−f. The scalaron restoring coefficient is m_sc^2=(F−Rf_RR)/(3f_RR), whereas exact spherical Wald-area transport identities cancel the scalaron Hessian. Their Einstein-frame interpretation distinguishes longitudinal kinetic focusing from potential-dependent cross-focusing. We prove that, at fixed constant-curvature background with tracefree matter, transport depends only on (f,f_R), while the scalaron mass depends on the independently adjustable f_RR. Reissner-Nordström in f(R)=R+αR^2 gives an exact discriminator: identical background transport coexists with opposite scalaron mass signs. A charged solution with varying F and a cosmological check test the identities beyond this constant-F sector. For a nonzero massive scalaron tail transmitted to a nondegenerate Cauchy horizon, a conditional fixed-background estimate gives a nonintegrable contribution to generalized entropy focusing. This estimate does not establish nonlinear mass inflation or a particular extendibility class. The results provide a layered framework for coupling regularity, background transport, scalaron stability, and nonlinear inner-horizon evolution.
ER -