Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity
arXiv:2405.14071 · doi:10.1103/PhysRevD.110.044024
Abstract
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 and the areal radius , it may not be appropriate for unambiguously determining the black hole stability because the constant 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.
arXiv comment14 pages, no figures
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