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

K. A. Bronnikov, R. A. Konoplya, and A. Zhidenko
Phys. Rev. D 86, 024028 – Published 18 July 2012

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 anti-de Sitter on the other (Minkowski–anti-de Sitter 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.

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  • Received 11 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.024028

© 2012 American Physical Society

Authors & Affiliations

K. A. Bronnikov*

  • Center for Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya 46, Moscow 119361, Russia; and Institute of Gravitation and Cosmology, PFUR, ul. Miklukho-Maklaya 6, Moscow 117198, Russia

R. A. Konoplya

  • DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom; and Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia, Chile

A. Zhidenko

  • Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Rua Santa Adélia, 166, 09210-170, Santo André, SP, Brazil

  • *kb20@yandex.ru
  • konoplya_roma@yahoo.com
  • olexandr.zhydenko@ufabc.edu.br

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Issue

Vol. 86, Iss. 2 — 15 July 2012

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