Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections
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| Format: | Preprint |
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2025
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| _version_ | 1866911186656690176 |
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| author | De Felice, Antonio Tsujikawa, Shinji |
| author_facet | De Felice, Antonio Tsujikawa, Shinji |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_11803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections De Felice, Antonio Tsujikawa, Shinji General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.11803 |