We investigate black hole solutions with time-dependent (scalar) hair in scalar-tensor theories. Known exact solutions exist for such theories at the background level, where the metric takes on a standard GR form (e.g. Schwarzschild-de Sitter), but these solutions are generically plagued by instabilities. Recently, a new such solution was identified in arXiv:2310.11919, in which the time-dependent scalar background profile is qualitatively different from previous known exact solutions - specifically, the canonical kinetic term for the background scalar $X$ is not constant in this solution. We investigate the stability of this new solution by analysing odd parity perturbations, identifying a bound placed by stability and the resulting surviving parameter space. We extract the quasinormal mode spectrum predicted by the theory, identifying a shift of quasinormal mode frequencies and damping times compared to GR. We forecast constraints on these shifts (and the single effective parameter $\hatβ$ controlling them) from current and future gravitational wave experiments, finding constraints at up to the ${\cal O}(10^{-2})$ and ${\cal O}(10^{-6})$ level for LVK and LISA/TianQin, respectively. All calculations performed in this paper are reproducible via a companion Mathematica notebook.
Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of hairy black hole caused by gravitational decoupling for the massless scalar field, electromagnetic field, and gravitational perturbation are investigated. The equations of effective potential for three perturbations are derived in hairy black hole spacetime. We also study the time evolution corresponding to the three perturbations, and the quasinormal mode frequencies are calculated using the Prony method through the time-domain profiles. By analyzing the influence of the hairs ($α$, $l_0…
The quasinormal modes of charged and uncharged massive scalar fields and also of charged Dirac fields against the background of a charged spherical black hole endowed with a scalar hair have been investigated. Special emphasis has been given to the case where negative scalar charge dominates over the electric charge of the black hole which mimics an Einstein-Rosen bridge. Except for the complete monotonic behaviour of the damping (imaginary part of the quasinormal mode) against the charge of the black hole as opposed to the existence of a peak for the pure RN case, the qualitative behaviour do…
We compute the quasinormal frequencies for scalar perturbations of hairy black holes in four-dimensional Einstein-Maxwell-dilaton theory assuming a non-trivial scalar potential for the dilaton field. We investigate the impact on the spectrum of the angular degree, the overtone number, the charges of the black hole as well as the magnitude of the scalar potential. All modes are found to be stable. Our numerical results are summarized in tables, and for better visualization, we show them graphically as well.
Perturbations of black holes with primary hair: time evolutions, quasinormal modes and greybody factors
CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学技术学院物理系CENTRA）
We construct a new class of asymptotically (a)dS black hole solutions of Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrodynamics. The obtained solutions possess a Coulomb electric charge, massive term and a non-abelian hair as well. We calculate the conserved and thermodynamic quantities, and investigate the validity of the first law of thermodynamics. Also, we investigate thermal stability conditions by using the sign of heat capacity through canonical ensemble. Next, we consider the cosmological constant as a thermodynamical pressure and study the van der…
Quasinormal Modes and Hawking Radiation of Black Holes with Primary Scalar Hair
Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所理论物理与天体物理研究中心）；Institute of Cosmology, Department of Physics and Astronomy, Tufts University（塔夫茨大学物理与天文学系宇宙学研究所）；Institute of Physics in Opava, Silesian University in Opava（奥帕瓦西里西亚大学奥帕瓦物理研究所）
The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented compri…
Exceptional Points in Quasinormal Spectra of Hairy Black Holes
College of Physics, Sichuan University（四川大学物理学院）；School of Data Science, Shanghai University of Finance and Economics Zhejiang College（上海财经大学浙江学院数据科学学院）
Holography relates the quasinormal modes frequencies of AdS black holes to the pole structure of the dual field theory propagator. These modes thus provide the timescale for the approach to thermal equilibrium in the CFT. Here, we study how such pole structure and, in particular, the time to equilibrium can get modified in the presence of a black hole hair. More precisely, we consider in AdS a set of relaxed boundary conditions that allow for a low decaying graviton mode near the boundary, which triggers an additional degree of freedom. We solve the scalar field response on such background ana…
Einstein-Maxwell-dilaton theory is an interesting and well-motivated theoretical laboratory to explore the impact of new fundamental degrees of freedom in the context of testing the no-hair conjecture, due to the existence of hairy black hole solutions together with the propagation of scalar, vector and tensor modes. In this paper we compute the quasinormal mode spectrum of static and slowly rotating black holes for generic values of the dilaton coupling, within a weak electric charge approximation. Our results suggest that these spacetimes are stable for generic values of the dilaton coupling…
The present thesis attempts to study the effect of scalar fields on Hawking radiation and quasinormal modes of black holes. We selected a static, spherically symmetric electrically charged black hole with an additional scalar 'hair' for our analysis. The scalar 'hair' is sourced by a scalar field, conformally coupled to the Einstein-Hilbert action. The scalar field can survive even in the absence of the black hole's electric charge and is characterized as a 'primary hair'. This scalar field changes the gravitational constant, and hence modifies the ADM (Arnowitt-Deser-Missner) mass of the blac…
We address quasinormal modes of compact objects in several alternative theories of gravity. In particular, we focus on black holes and neutron stars with scalar hair. We consider black holes in dilaton-Einstein-Gauß-Bonnet theory, and in a generalized scalar-Einstein-Gauß-Bonnet theory. In the latter case scalarized black holes arise, and we study the stability of the different branches of solutions. In particular, we discuss how the spectrum of quasinormal modes is changed by the presence of a non-trivial scalar field outside the black hole horizon. We discuss the existence of an (effective) …
We study the instability of near extremal and extremal four-dimensional AdS charged hairy black hole to radial neutral massive and charged massless scalar field perturbations. We solve the scalar field equation by using the improved asymptotic iteration method and the time domain analysis and we find the quasinormal frequencies. For the charged scalar perturbations, we find the superradiance condition by computing the reflection coefficient in the low-frequency limit and we show that in the superradiance regime, which depends on the scalar hair charge, all modes of radial charged massless pert…
Effective theory of fluctuations based on underlying symmetry plays very important role in understanding the low energy phenomena. Using this powerful technique we study the fluctuation dynamics keeping in mind the following central question: does the effective theory of black hole provide any information about the possible existence of hair? Assuming the symmetry of the hair being that of the underlying black hole space-time, we start by writing down the most general action for the background and the fluctuation in the effective field theory framework. Considering the asymptotically flat and …
In this work we construct a static and spherically symmetric black hole geometry supported by a family of generic mono-parametric sources thorough the Gravitational Decoupling. The parameter characterizing the matter sector can be interpreted as hair which cannot be associated to any global charge. Although the solution is constructed by demanding the weak energy condition, we find that the resulting matter sector satisfies all the energy conditions at and outside the horizon. We study the effect of the hair on the periastron advance and the gravitational lensing of the black hole. We estimate…
We study the quasinormal modes for scalar, axial and radial perturbations of massive static spherically symmetric wormholes supported by a phantom scalar field, calculating the modes directly and employing the WKB approximation. The spectrum of the quasinormal modes is compared with the spectrum of Schwarzschild black holes. For fixed multipole number $l$ and large mass $M$ the wormhole modes approach their black hole counterparts as $1/M$.
In this paper, we investigate the scalar quasinormal modes of Hořava-Lifshitz theory with $U(1)$ symmetry in static Anti-de Sitter spacetime. The static planar and spherical black hole solutions in lower energy limit are derived in non-projectable Hořava-Lifshitz gravity. The equation of motion of a scalar field is obtained, and is utilized to study the quasinormal modes of massless scalar particles. We find that the effect of Hořava-Lifshitz correction is to increase the quasinormal period as well as to slow down the decay of the oscillation magnitude. Besides, the scalar field could be unsta…
In this paper we study the scalar and electromagnetic perturbations of an extended black hole in F(R) gravity. The quasinormal modes in two cases are evaluated and studied their behavior by plotting graphs in each case. To study the quasinormal mode, we use the third order WKB method. The present study shows that the absolute value of imaginary part of complex quasinormal modes increases in both cases, thus the black hole is stable against these perturbations. As the mass of the scalar field increases the imaginary part of the frequency decreases. Thus damping slows down with increasing mass o…
We evaluate the complex frequencies of the normal modes for the massive charged scalar field perturbations around a Reissner-Nördstrom black hole surrounded by a static and spherically symmetric quintessence using third order WKB approximation approach. Due to the presence of quintessence, quasinormal frequencies damp more slowly. We studied the variation of quasinormal frequencies with charge of the black bole, mass and charge of perturbating scalar field and the quintessential state parameter.
Anomalous Decay Rate and Greybody Factors for Regular Black Holes with Scalar Hair
Universidad Católica de Temuco（特木科天主教大学）；Universidad Diego Portales（迭戈·波特莱斯大学）；National Technical University of Athens（雅典国立技术大学）；Universidad de La Serena（拉塞雷纳大学）
We construct static, asymptotically flat black hole solutions with scalar hair. They evade the no-hair theorems by having a scalar potential which is not strictly positive. By including an azimuthal winding number in the scalar field ansatz, we find hairy black hole solutions which are static but axially symmetric only. These solutions possess a globally regular limit, describing scalar solitons. A branch of axially symmetric black holes is found to possess a positive specific heat.
We study polar quasinormal modes of relativistic stars in scalar-tensor theories, where we include a massive gravitational scalar field and employ the standard Brans-Dicke coupling function. For the potential of the scalar field we consider a simple mass term as well as a potential associated with $R^2$ gravity. The presence of the scalar field makes the spectrum of quasinormal modes much richer than the spectrum in General Relativity. We here investigate radial modes ($l=0$) and quadrupole modes ($l=2$). The general relativistic $l=0$ normal modes turn into quasinormal modes in scalar-tensor …
We compute characteristic (quasinormal) frequencies corresponding to decay of a massive charged scalar field in a Reissner-Nordstrom black hole background. It proves that, contrary to the behavior at very late times, at the stage of quasinormal ringing the neutral perturbations will damp slower than the charged ones. In the limit of the extremal black hole the damping rate of charged and neutral perturbations coincides. Possible connection of this with the critical collapse in a massive scalar electrodynamics is discussed.
We present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field $u$ plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass $u$ increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly and the frequencies having a limited value. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.
The analytic forms of the asymptotic quasinormal frequencies of a coupled scalar field in the Garfinkle-Horowitz-Strominger dilaton spacetime is investigated by using the monodromy technique proposed by Motl and Neitzke. It is found that the asymptotic quasinormal frequencies depend not only on the structure parameters of the background spacetime, but also on the coupling between the scalar fields and gravitational field. Moreover, our results show that only in the minimal couple case, i.e., $ξ$ tends zero, the real parts of the asymptotic quasinormal frequencies agrees with the Hod's conjectu…
In this paper we investigate scalar perturbations of black holes embedded in a five dimensional bulk space. It is calculated the quasinormal frequencies of a such black holes using the third order of Wentzel, Kramers, Brillouin (WKB) approximation for scalar perturbations. The results are presented in tables along the text.
Stationary, asymptotically flat black holes in scalar-tensor theories of gravity are studied. It is shown that such black holes have no scalar hair and are the same as in General Relativity.
In this paper using the third-order WKB approximation, a numerical method devised by Schutz, Will and Iyer, we investigate the quasinormal frequencies of the scalar field in the background of five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and makes the scalar field oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and makes the scalar field oscillate more slowly in Lovelock black hole backgroud. On the other hand we also find that quasin…
A new branch of quasinormal modes for a massless scalar field propagating on the Schwarzschild spacetime was recently announced [1807.04513]. We review the quasinormal modes characterisation and arguments and identify the flaws in their proof. Then, we preset explicit counterexamples to such arguments. Finally, we study the modes via alternative methods and do not find the new branch. We conclude against their interpretation.
We address the concerns raised by the author of "Comment: Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime" appeared in arXiv:1807.05940. In particular, we explain why the analysis in our paper [Phys. Rev. D{\bf{98}}, 024017 (2018)] is relevant and correct.
We find quasinormal spectrum of the massive scalar field in the background of the Kerr black holes. We show that all found modes are damped under the quasinormal modes boundary conditions when $μM$ is not large, thereby implying stability of the massive scalar field. This complements the region of stability determined by the Beyer inequality for large masses of the field. We show that, similar to the case of a non-rotating black holes, the massive term of the scalar field does not contribute in the regime of high damping. Thereby, the high damping asymptotic should be the same as for the massl…
We perform the stability analysis on scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory by computing quasinormal mode spectrum. It is noted that the appearance of these black holes with scalar hair is closely related to the instability of Reissner-Nordström black holes without scalar hair in the EMS theory. The scalarized black hole solutions are classified by the node number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental branch and $n=1,2,\cdots$ denote the $n$ excited branches. Here, we show that the $n=1,2$ excited black holes are unstable against against…
We study the propagation of a probe massless nonminimally coupled scalar field in a fixed gravitational background of a cloud of strings in (2+1) dimensions. We obtain exact analytical expressions for the reflection coefficient, the absorption cross section, the decay rate as well as the quasinormal frequencies. The impact of the nonminimal coupling is investigated in detail. Our results show that Universality is not respected in general, and that scalar perturbations are stable.
It is shown that the only static asymptotically flat non-extrema black hole solution of the Einstein-conformally invariant scalar field equations having the scalar field bounded on the horizon, is the Schwarzschild one. Thus black holes cannot be endowed with conformal scalar hair of finite length.
We study condensation of scalar fields around compact reflecting stars in a box. We propose no light scalar hair behaviors that the neutral compact star cannot support the existence of small single positive mass scalar field in it's exterior spacetime for very general self-interacting potentials. Moreover, we find that this no light scalar hair property can be violated by including an additional Maxwell field coupled to the scalar field in a charged compact reflecting star background.
The quasinormal modes for scalar and spinor fields in the background spacetime corresponding to an $f(R)$ global monopole are calculated using the WKB approximation. In the obtained results we emphasize the role played by the parameter $ψ_{0}$, associated with the $f(R)$ gravity. We discuss the appropriate limit $ψ_{0} \rightarrow 0$, in which case the results concerning to the Schwarzschild black hole are obtained, as it should be expected.
In this work we check the validity of the no scalar hair theorem in charged axisymmetric stationary black holes for a wide class of scalar tensor theories.
We study analytically the initial value problem for a self-interacting (massive) scalar-field on a Reissner-Nordström spacetime. Following the no-hair theorem we examine the dynamical physical mechanism by which the self-interacting (SI) hair decays. We show that the intermediate asymptotic behaviour of SI perturbations is dominated by an oscillatory inverse power-law decaying tail. We show that at late-times the decay of a SI hair is slower than any power-law. We confirm our analytical results by numerical simulations.
We evaluate the quasinormal modes of massless scalar field around Reissner-Nordstr$\ddot{\text{o}}$m black hole surrounded by a static and spherically symmetric quintessence by using the continued fraction method. The appropriate Frobenius series for three special cases of the quintessence parameter $ ε= -1/3, -2/3$ and $-1$ are derived successfully. We show that the variation of quasinormal frequencies with charge of the black hole and the quintessential parameters. The numerical results show that quintessence field decreases oscillation frequencies of all angular momentum $l$ modes and incre…
It is shown that the conclusion regarding the existence of a scalar hair for a black hole in a nonminimally coupled self interacting scalar tensor theory can be drawn from the that for a scalar field minimally coupled to gravity by means of a conformal transformation.
