Instabilities of wormholes and regular black holes supported by a phantom scalar field

TL;DR

This paper investigates the stability of wormholes and black holes supported by a phantom scalar field, finding most configurations unstable except for a specific stable class of black universes with calculable quasinormal modes.

Contribution

It introduces a numerical regularization method for analyzing perturbations and identifies conditions under which certain phantom-supported black holes are stable.

Findings

Most phantom-supported wormholes and black holes are unstable under perturbations.

A stable class of black universes is identified where the event horizon is at the minimum area.

Quasinormal modes are computed for the stable black universe configurations.

Abstract

We test the stability of various wormholes and black holes supported by a scalar field with a negative kinetic term. The general axial perturbations and the monopole type of polar perturbations are considered in the linear approximation. Two classes of objects are considered: (i) wormholes with flat asymptotic behavior at one end and AdS on the other (M-AdS wormholes) and (ii) regular black holes with asymptotically de Sitter expansion far beyond the horizon (the so-called black universes). A difficulty in such stability studies is that the effective potential for perturbations forms an infinite wall at throats, if any. Its regularization is in general possible only by numerical methods, and such a method is suggested in a general form and used in the present paper. As a result, we have shown that all configurations under study are unstable under spherically symmetric perturbations, except for a special class of black universes where the event horizon coincides with the minimum of the area function. For this stable family, the frequencies of quasinormal modes of axial perturbations are calculated.