Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity
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| Format: | Preprint |
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2024
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| _version_ | 1866917745852940288 |
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| author | Mukohyama, Shinji Tsujikawa, Shinji Wang, Anzhong |
| author_facet | Mukohyama, Shinji Tsujikawa, Shinji Wang, Anzhong |
| contents | In Einstein-Aether gravity, we revisit the issue of linear stabilities of black holes against odd-parity perturbations on a static and spherically symmetric background. In this theory, superluminal propagation is allowed and there is a preferred timelike direction along the unit Aether vector field. If we choose the usual spherically symmetric background coordinates with respect to the Killing time $t$ and the areal radius $r$, it may not be appropriate for unambiguously determining the black hole stability because the constant $t$ hypersurfaces are not necessarily always spacelike. Unlike past related works of black hole perturbations, we choose an Aether-orthogonal frame in which the timelike Aether field is orthogonal to spacelike hypersurfaces over the whole background spacetime. In the short wavelength limit, we show that no-ghost conditions as well as radial and angular propagation speeds coincide with those of vector and tensor perturbations on the Minkowski background. Thus, the odd-parity linear stability of black holes for large radial and angular momentum modes is solely determined by constant coefficients of the Aether derivative couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity Mukohyama, Shinji Tsujikawa, Shinji Wang, Anzhong General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology High Energy Physics - Theory In Einstein-Aether gravity, we revisit the issue of linear stabilities of black holes against odd-parity perturbations on a static and spherically symmetric background. In this theory, superluminal propagation is allowed and there is a preferred timelike direction along the unit Aether vector field. If we choose the usual spherically symmetric background coordinates with respect to the Killing time $t$ and the areal radius $r$, it may not be appropriate for unambiguously determining the black hole stability because the constant $t$ hypersurfaces are not necessarily always spacelike. Unlike past related works of black hole perturbations, we choose an Aether-orthogonal frame in which the timelike Aether field is orthogonal to spacelike hypersurfaces over the whole background spacetime. In the short wavelength limit, we show that no-ghost conditions as well as radial and angular propagation speeds coincide with those of vector and tensor perturbations on the Minkowski background. Thus, the odd-parity linear stability of black holes for large radial and angular momentum modes is solely determined by constant coefficients of the Aether derivative couplings. |
| title | Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.14071 |