Ellis drainhole solution in Einstein-{\AE}ther gravity and the axial gravitational quasinormal modes

TL;DR

This paper derives a new Ellis drainhole solution within Einstein-{\

Contribution

It introduces a novel Ellis drainhole solution in Einstein-{\

Findings

Derived the Ellis drainhole metric in Einstein-{\

Analyzed axial quasinormal modes using numerical methods.

Explored the impact of scalar coupling on quasinormal spectra.

Abstract

In this work, the Ellis drainhole solution is derived in Einstein-{\AE}ther 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 {\ae}ther 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.