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

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 ${\varphi }^{\prime }(r)=1/r$, 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 ${\varphi }^{\prime }(r)=1/r$ as physically viable and stable configurations.

16 pages, 2 figures

References in corpus (18)

• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• Einsteinian cubic gravity
• Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"
• Infinite tower of higher-curvature corrections: Quasinormal modes and late-time behavior of D-dimensional regular black holes
• Regular black holes inspired by quasi-topological gravity
• Relativistic star perturbations in Horndeski theories with a gauge-ready formulation
• Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field
• Instability of nonsingular black holes in nonlinear electrodynamics
• Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models
• Black hole perturbations in Maxwell-Horndeski theories
• Excluding static and spherically symmetric black holes in Einsteinian cubic gravity with unsuppressed higher-order curvature terms
• Pure Lovelock Gravity regular black holes
• Regular BTZ black holes from an infinite tower of corrections
• Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity
• Nonsingular black holes and spherically symmetric objects in nonlinear electrodynamics with a scalar field
• Stability of Schwarzshild black holes in quadratic gravity with Weyl curvature domination
• Strong coupling and instabilities in singularity-free inflation from an infinite sum of curvature corrections