2025/07/15 by De Felice, Antonio, Tsujikawa, Shinji · 2 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2507.11803
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 ϕ'(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 ϕ'(r)=1/r as physically viable and stable configurations.