Ellis drainhole solution in Einstein-Æther gravity and the axial gravitational quasinormal modes

Abstract

In this work, the Ellis drainhole solution is derived in Einstein-AEther gravity, and subsequently, the axial quasinormal modes of the resulting drainhole are investigated. Owing to the presence of a minimally coupled scalar field with antiorthodox coupling polarity, the resultant metric solution is featured by a throat instead of a horizon, for which static aether solution becomes feasible. Moreover, the derived master equations for the axial gravitational perturbations consist of two coupled vector degrees of freedom. By utilizing the finite difference method, the temporal profiles of the quasinormal oscillations are evaluated, and, subsequently, the complex frequencies are extracted and compared against the specific values obtained by the WKB method when the coupling is turned off. Besides, the effect of the coupling on the low-lying quasinormal spectrum is explored, and its possible physical relevance is discussed.

An implementation of the matrix method using Chebyshev grid

“…The main difference, however, is that the matrix method makes use of a series of grid points instead of a given position [26]. The method is shown to be capable of handling the metrics with spherical symmetry [27], axial symmetry [28], as well as the system composed of various coupled degrees of freedom [33]. It can be adapted to different boundary conditions [29] and dynamic black hole spacetimes [30].…”