Suppression of mass inflation by vanishing inner-horizon surface gravity

Saken Toktarbay, Aray Muratkhan, Changjun Gao

2026

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DOI 10.1088/1361-6382/ae8b6b
Data confidence 70 medium
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Abstract

Abstract Mass inflation is conventionally understood as an instability of black-hole interiors driven by the exponential amplification of counter-streaming perturbations near a non-degenerate inner horizon. In this work, we investigate how this picture is modified when the inner-horizon surface gravity vanishes. Focusing on static, spherically symmetric black-hole geometries with degenerate inner horizons, we formulate the interior problem in a double-null framework and analyze the near-horizon asymptotics for weak ingoing and outgoing null perturbations in the case κ in = 0 . We show that inner-horizon degeneracy replaces the standard exponential horizon scaling by an algebraic one and, correspondingly, removes the conventional exponential amplification factor from the transport equations of the Misner–Sharp mass. Within the weak asymptotic regime considered here, the effective mass exhibits at most algebraic or logarithmic growth, depending on the decay rates of the perturbing tails, rather than the usual exponentially amplified behavior of the non-degenerate Cauchy-horizon case. We further examine the associated invariant curvature sector and show that, although the unperturbed degenerate inner horizon is curvature-regular, the perturbed interior may still admit a weaker residual singular response. Our results therefore indicate that vanishing inner-horizon surface gravity suppresses the conventional exponential mass-inflation mechanism without, by itself, implying full regularization of the spacetime interior.