Instability Of Scalar Fields Research Articles

Kerr–Sen-like Lorentz violating black holes and superradiance phenomena

A Kerr–Sen-like black hole solution results from Einstein-bumblebee gravity. It contains a Lorentz violating (LV) parameter that enters when the bumblebee field receives vacuum expectation value through a spontaneously breaking of the symmetry of the classical action. The geometrical structure concerning the singularity of this spacetime is studied with reference to the parameters involved in the Kerr–Sen-like metric. We introduce this Einstein-bumblebee modified gravity to probe the role of spontaneous Lorentz violation on the superradiance scattering phenomena and the instability associated with it. We observe that for the low-frequency range of the scalar wave the superradiance scattering gets enhanced when the Lorentz-violating parameter ell takes the negative values and it reduces when values of ell are positive. The study of the black hole bomb issue reveals that for the negative values of ell , the parameter space of the scalar field instability increase prominently, however, for its positive values, it shows a considerable reduction. We also tried to put constraints on the parameters contained in the Kerr–Sen-like black hole by comparing the deformation of the shadow produced by the black hole parameters with the observed deviation from circularity and the angular deviation from the M87* data.

Black hole superradiance in the presence of Lorentz symmetry violation

In this paper we consider the massive scalar perturbation on the top of a small spinning-like black hole in context of Einstein-bumblebee modified gravity in order to probe the role of spontaneous Lorentz symmetry breaking on the superradiance scattering and corresponding instability. We show that at the low-frequency limit of the scalar wave the superradiance scattering will be enhanced with the Lorentz-violating parameter $\alpha<0$ and will be weakened with $\alpha>0$. Moreover, by addressing the black hole bomb issue, we extract an improved bound in the instability regime indicating that $\alpha<0$ increases the parameter space of the scalar field instability, while $\alpha>0$ decreases it.

From quantum to classical instability in relativistic stars

It has been shown that gravitational fields produced by realistic classical-matter distributions can force quantum vacuum fluctuations of some nonminimally coupled free scalar fields to undergo a phase of exponential growth. The consequences of this unstable phase for the background spacetime have not been addressed so far due to known difficulties concerning backreaction in semiclassical gravity. It seems reasonable to believe, however, that the quantum fluctuations will ``classicalize'' when they become large enough, after which backreaction can be treated in the general-relativistic context. Here we investigate the emergence of a classical regime out of the quantum field evolution during the unstable phase. By studying the appearance of classical correlations and loss of quantum coherence, we show that by the time backreaction becomes important the system already behaves classically. Consequently, the gravity-induced instability leads naturally to initial conditions for the eventual classical description of the backreaction. Our results give support to previous analyses which treat classically the instability of scalar fields in the spacetime of relativistic stars, regardless of whether the instability is triggered by classical or quantum perturbations.

Charged scalar field instability between the event and cosmological horizons

Recently, a new interesting instability of a charged scalar field in the Reissner-Nordstr\"om-de Sitter background has been found [Z. Zhu et al. Phys. Rev. D 90, 044042 (2014)] through the time-domain integration of the perturbation equation. We investigate further properties of this instability, confirm its existence by concordant frequency-domain and time-domain calculations, and show that it occurs at however small value of the coupling $eQ$, where $e$ and $Q$ are charges of a scalar field and black hole, respectively. We also investigate the parametric region of instability and show that the critical values of $eQ$ at which the stabilization happens strongly depends on the value of cosmological constant $\mathrm{\ensuremath{\Lambda}}$ and softly on $Q$. We show that all the unstable modes are superradiant, but not all the superradiant modes are unstable. We analytically prove that superradiance is a necessary (but not sufficient) condition for the instability in this case and, thereby, demonstrate the superradiant origin of the instability.

Quantum versus classical instability of scalar fields in curved backgrounds

General-relativistic stable spacetimes can be made unstable under the presence of certain nonminimally coupled free scalar fields. In this paper, we analyze the evolution of linear scalar-field perturbations in spherically symmetric spacetimes and compare the classical stability analysis with a recently discussed quantum field one. In particular, it is shown that vacuum fluctuations lead to natural seeds for the unstable phase, whereas in the classical framework the presence of such seeds in the initial conditions must be assumed.

Nonlinear instability of scalar fields on extremal black holes

We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate) future event horizon. No analogue of this instability occurs for subextremal black holes or the Minkowski spacetime.

Gravitational instability of an extreme Kerr black hole

Aretakis has proved the existence of an instability of a massless scalar field at the horizon of an extreme Kerr or Reissner-Nordstrom black hole: for generic initial data, a transverse derivative of the scalar field at the horizon does not decay, and higher transverse derivatives blow up. We show that a similar instability occurs for linearized gravitational, and electromagnetic, perturbations of an extreme Kerr black hole. We show also that the massless scalar field instability occurs for extreme black hole solutions of a large class of theories in various spacetime dimensions.

A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time

We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct "hairy" black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.

Scalar field instability in de Sitter space–time

Starting from the equation of motion of the quantum operator of a real scalar field φ in de Sitter space–time, a simple differential equation is derived which describes the evolution of quantum fluctuations 〈φ2〉 of this field. Full de Sitter invariance is assumed and no ad hoc infrared cutoff is introduced. This equation is solved explicitly and in massive case our result agrees with the standard one. In massless case the large time behavior of our solution differs by sign from the expression found in earlier papers. A possible cause of discrepancy may be a spontaneous breaking of de Sitter invariance.

Massive scalar field instability in Kerr spacetime

We study the Klein-Gordon equation for a massive scalar field in Kerr spacetime in the time-domain. We demonstrate that under conditions of super-radiance, the scalar field becomes unstable and its amplitude grows without bound. We also estimate the growth rate of this instability.

Instability of Massive Scalar Fields in Kerr-Newman Spacetime

We investigate the instability of charged massive scalar fields in Kerr-Newman spacetime. Due to the super-radiant effect of the background geometry, the bound state of the scalar field is unstable, and its amplitude grows in time. By solving the Klein-Gordon equation of the scalar field as an eigenvalue problem, we numerically obtain the growth rate of the amplitude of the scalar field. Although the dependence of the scalar field mass and the scalar field charge on this growth rate agrees with the result of the analytic approximation, the maximum value of the growth rate is three times larger than that of the analytic approximation. We also discuss the effect of the electric charge on the instability of the scalar field.

Scalar field instability in multi‐dimensional cosmology

AbstractThe scalar field theory on the background of cosmological models with n(n ≥ 1) spaces of constant curvature is considered. We take the integrable case of Ricci flat internal spaces. The coupling between the scalar and the gravitational fields includes the minimal coupling as well as the conformal case. In the ground state of the scalar field we find the conditions for vacuum instability realized for most of the possible solutions to Einstein's equations if the coupling parameter takes appropriate values. For the excited states of the scalar field we show the induction of massive modes and discuss their properties.

Stability and instability of scalar fields coupled to gravity

We relate the stability criteria of Boucher for a scalar field coupled to gravity to the semi-classical tunnelling calculations of Coleman and DeLuccia. This enables us to prove that the Boucher conditions imply both stability when they are satisfied and instability when they are not. In addition, it provides physical insight into the nature of the Boucher conditions and indicates that the O(4)-invariant, thin-wall approximation used in semi-classical tunnelling computations is reliable.

Gravitational instability of scalar fields and formation of primordial black holes

On considere l'instabilite gravitationnelle d'un etat spatialement uniforme d'un champ scalaire relativiste sur un fond independant du temps. On demontre que l'instabilite est semblable a l'instabilite de Jeans pour la matiere non relativiste du type poussiere. Les effets «hydrodynamiques» peuvent modifier considerablement le caractere de l'instabilite. Application au calcul de la probabilite de formation de trous noirs originels