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arXiv · 2610.11649

Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity

Francisco S. N. Lobo·Francisco Tello-Ortiz
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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 $F=f_R$ and the Legendre potential $\mathcal U(F)=FR-f$. The scalaron restoring coefficient is $m_{\rm sc}^2=(F-Rf_{RR})/(3f_{RR})$, 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.

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Francisco S. N. Lobo, Francisco Tello-Ortiz. 2026-10-08. Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity. https://arxiv.org/abs/2610.11649

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