Stability Of Static Black Holes Research Articles

Stability of generalized Einstein-Maxwell-scalar black holes

We study the stability of static black holes in generalized Einstein-Maxwell-scalar theories. We derive the master equations for the odd and even parity perturbations. The sufficient and necessary conditions for the stability of black holes under odd-parity perturbations are derived. We show that these conditions are usually not similar to energy conditions even in the simplest case of a minimally coupled scalar field. We obtain the necessary conditions for the stability of even-parity perturbations. We also derived the speed of propagation of the five degrees of freedom and obtained the class of theories for which all degrees of freedom propagate at the speed of light. Finally, we have applied our results to various black holes in nonlinear electrodynamics, scalar-tensor theories and Einstein-Maxwell-dilaton theory. For the latter, we have also calculated the quasinormal modes.

Stability and existence analysis of static black holes in pure Lovelock theories

In this paper, we study the existence and stability of static black holes in Lovelock theories with a particular focus on pure Lovelock black holes. We derive the equation of stability from action without using the S-deformation approach. Although a pure-Lovelock black hole in an even dimension is always unstable, introduction of Λ stabilizes it by prescribing a lower threshold mass while there also exists an upper bound on mass that is given by the existence of a horizon. We also study the stability of dimensionally continued black holes as well as of the pure Lovelock analogue of BTZ black holes in all odd dimensions.

Chapter 6. Perturbations and Stability of Static Black Holes in Higher Dimensions

In this chapter we consider perturbations and stability of higher dimensional black holes focusing on the static background case. We first review a gauge-invariant formalism for linear perturbations in a fairly generic class of (m+n)-dimensional spacetimes with a warped product metric, including black hole geometry. We classify perturbations of such a background into three types, the tensor, vector and scalar-type, according to their tensorial behaviour on the n-dimensional part of the background spacetime, and for each type of perturbations, we introduce a set of manifestly gauge invariant variables. We then introduce harmonic tensors and write down the equations of motion for the expansion coefficients of the gauge invariant perturbation variables in terms of the harmonics. In particular, for the tensor-type perturbations a single master equation is obtained in the (m+n)-dimensional background, which is applicable for perturbation analysis of not only static black holes but also some class of rotating black holes as well as black-branes. For the vector and scalar type, we derive a set of decoupled master equations when the background is a (2+n)-dimensional static black hole in the Einstein-Maxwell theory with a cosmological constant. As an application of the master equations, we review the stability analysis of higher dimensional charged static black holes with a cosmological constant. We also briefly review the recent results of a generalisation of the perturbation formulae presented here and stability analysis to static black holes in generic Lovelock theory.

Catastrophic Instability of Small Lovelock Black Holes

We study the stability of static black holes in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We show that Lovelock black holes are stable under vector perturbations in all dimensions. However, we prove that small Lovelock black holes are unstable under tensor perturbations in even-dimensions and under scalar perturbations in odd-dimensions. Therefore, we can conclude that small Lovelock black holes are unstable in any dimensions. The instability is stronger on small scales and hence catastrophic in the sense that there is no smooth descendant.

Instability of small Lovelock black holes in even dimensions

We study the stability of static black holes in Lovelock theory, which is a natural higher dimensional generalization of Einstein theory. We derive a master equation for tensor perturbations in general Lovelock theory. It turns out that the resultant equation is characterized by one functional which determines the background black hole solutions. Thus, the stability issue of static black holes under tensor perturbations in general dimensions is reduced to an algebraic problem. We show that small Lovelock black holes in even-dimensions are unstable.

Stability of Lovelock black holes under tensor perturbations

We study the stability of static black holes in the third order Lovelock theory. We derive a master equation for tensor perturbations. Using the master equation, we analyze the stability of Lovelock black holes mainly in seven and eight dimensions. We find there are cases where the linear analysis breaks down. If we restrict ourselves to the regime where the linear analysis is legitimate, black holes are always stable in seven dimensions. However, in eight dimensions, there exists a critical mass below which black holes are unstable. Combining our result in the third order Lovelock theory with the previous one in Einstein-Gauss-Bonnet theory, we conjecture that small black holes are unstable in any dimensions. The instability found in this paper will be important for the analysis of black holes at the LHC.