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arXiv · 2507.11803

Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections

Antonio De Felice·Shinji Tsujikawa
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Abstract

In four-dimensional scalar-tensor theories derived via dimensional regularization with a conformal rescaling of the metric, we study the stability of planar black holes (BHs) whose horizons are described by two-dimensional compact Einstein spaces with vanishing curvature. By taking an infinite sum of Lovelock curvature invariants, it is possible to construct BH solutions whose metric components remain nonsingular at $r=0$, with a scalar-field derivative given by $\phi'(r)=1/r$, where $r$ is the radial coordinate. We show that such BH solutions suffer from a strong coupling problem, where the kinetic term of the even-parity scalar-field perturbation associated with the timelike coordinate vanishes everywhere. Moreover, we find that these BHs are subject to both ghost and Laplacian instabilities for odd-parity perturbations near $r=0$. Consequently, the presence of these pathological features rules out regular planar BHs with the scalar-field profile $\phi'(r)=1/r$ as physically viable and stable configurations.

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Antonio De Felice, Shinji Tsujikawa. 2025-07-15. Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections. https://doi.org/10.1103/cbyk-b46n

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