We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.
We solve the wave equations of arbitrary integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. We show that these quasinormal modes precisely agree with the location of the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We then use these quasinormal modes to construct the one-loop determinant of the higher spin field in the thermal BTZ background. This is shown to agree with that obtained from the corresponding heat kernel constructed recently by group theoreti…
We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using t…
We propose a method of computing one-loop determinants in black hole spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in \cite{Denef:2009kn}. A numerical evaluation must face the fact that the sum over the quasinormal modes, indexed by momentum and overtone numbers, is divergent. A necessary ingredient is then a regularization scheme to handle the diverge…
We calculate the contributions to the one-loop determinant for transverse traceless gravitons in an $n+3$-dimensional Schwarzschild black hole background in the large dimension limit, due to the $SO(n+2)$-type tensor and vector fluctuations, using the quasinormal mode method. Accordingly we find the quasinormal modes for these fluctuations as a function of a fiducial mass parameter $Δ$. We show that the behavior of the one-loop determinant at large $Δ$ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in t…
We find the connection between thermodynamic quantities and quasinormal frequencies in Lifshitz black holes. It is shown that the globally stable Lifshitz black holes have pure imaginary quasinormal frequencies. We also show that by employing the Maggiore's method, both the horizon area and the entropy can be quantized for these black holes.
We study the Lifshitz black hole in 4-dimensions with dynamical exponent z=2 and we calculate analytically the quasinormal modes of scalar perturbations. These quasinormal modes allows to study the stability of the Lifshitz black hole and we have obtained that Lifshitz black hole is stable.
We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius. We verify this correspondence with two black hole families in $4$ and $D$ dimensions, respectively.
Contrary to the wide-spread belief, the correspondence principle does not dictate any relation between the asymptotics of quasinormal modes and the spectrum of quantized black holes. Moreover, this belief is in conflict with simple physical arguments.
It is shown that the scalar wave equation in the near-horizon limit respects a hidden SL(2,R) invariance in the Reissner-Nordstrom (RN) black hole spacetimes. We use the SL(2,R) symmetry to determine algebraically the purely imaginary quasinormal frequencies of the RN black hole. We confirm that these are exactly quasinormal modes of scalar perturbation around the near-extremal black hole.
Using the operator approach, we obtain logarithmic quasinormal modes and frequencies of a traceless spin-3 field around the BTZ black hole at the critical point of the spin-3 topologically massive gravity. The logarithmic quasinormal frequencies are also confirmed by considering logarithmic conformal field theory.
We report the results concerning the influence of vacuum polarization due to quantum massive vector, scalar and spinor fields on the scalar sector of quasinormal modes in spherically symmetric charged black holes. The vacuum polarization from quantized fields produces a shift in the values of the quasinormal frequencies, and correspondingly the semiclassical system becomes a better oscillator with respect to the classical Reissner-Nordström black hole.
We analytically calculate to second order the correction to the asymptotic form of quasinormal frequencies of four dimensional Schwarzschild black holes based on the monodromy analysis proposed by Motl and Neitzke. Our results are in good agreement with those obtained from numerical calculation.
We calculate the quasinormal modes of massless scalar perturbations around small and large four-dimensional Reissner-Nordstrom-Anti de Sitter (RN-AdS) black holes. We find a dramatic change in the slopes of quasinormal frequencies in small and large black holes near the critical point where the Van der Waals like thermodynamic phase transition happens. This further supports that the quasinormal mode can be a dynamic probe of the thermodynamic phase transition.
Employing the operator method, we obtain log-square quasinormal modes and frequencies of a graviton around the BTZ black hole at the tricritical point of the generalized massive gravity. The log-square quasinormal frequencies are also obtained by considering a finite temperature conformal field theory. This shows the AdS/LCFT correspondence at the tricritical point approximately. We discuss a truncation process to the unitary theory on the BTZ black hole background.
We have studied perturbations of scalar and spinor field in the background of three dimensional Gödel black hole. The wave equations are shown to be exactly solvable in terms of hypergeometric functions. The quasinormal modes are analytically calculated by imposing the Dirichlet boundary condition at spatial infinity, which are shown to be of the same form in both cases. By considering the physical interpretation of quasinormal modes, we obtain the consistent transition frequencies from the quasinormal modes of scalar and spinor field. As an application of quasinormal modes, we have also inves…
An exact expression for the quasinormal modes of scalar perturbations on a massless topological black hole in four and higher dimensions is presented. The massive scalar field is nonminimally coupled to the curvature, and the horizon geometry is assumed to have a negative constant curvature.
We study the quasinormal modes of the massless scalar perturbation in the background of a deformed black hole in the Hořava-Lifshitz gravity with coupling constant $λ=1$. Our results show that the quasinormal frequencies depend on the parameter in the Hořava-Lifshitz gravity and the behavior of the quasinormal modes is different from those in the Reissner-Norstr\"{om} and Einstein-Born-Infeld black hole spacetimes. The absolute value of imaginary parts is smaller and the scalar perturbations decay more slowly in the deformed Hořava-Lifshitz black hole spacetime. This information can help us un…
We connect the quasinormal modes corresponding to Dirac fermions in various black holes backgrounds to an N=2 supersymmetric quantum mechanics algebra, which can be constructed from the radial part of the fermionic solutions of the Dirac equation. In the massless fermion case, the quasinormal modes are in bijective correspondence with the zero modes of the fermionic system and this results to unbroken supersymmetry. The massive case is more evolved but as we prove, supersymmetry remains unbroken even in this case.
We compute the quasinormal frequencies of $d$-dimensional spherically symmetric black holes with leading string $α'$ corrections for tensorial gravitational perturbations in the highly damped regime. We solve perturbatively the master differential equation and we compute the monodromies of the master perturbation variable (analytically continued to the complex plane) in different contours, in order to obtain the quasinormal mode spectra. We proceed analogously for the quasinormal modes of test scalar fields. Differently than in Einstein gravity, we obtain distinct results for the two cases.
We study the quasinormal modes of scalar field perturbations in the background of non-Abelian hyperscaling violating Lifshitz black holes. We find that the quasinormal frequencies have no real part so there is no oscillatory behavior in the perturbations, only exponential decay, that is, the system is always overdamped, which guarantees the mode stability of non-Abelian hyperscaling violating Lifshitz black holes. We determine analytically the quasinormal modes for massless scalar fields for a dynamical exponent $z=2$ and hyperscaling violating exponent $\tildeθ>-2$. Also, we obtain numericall…
We have studied the scalar perturbation of static charged dilaton black holes in 2+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2+1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.
Quasinormal modes in the high frequency (eikonal) regime can be obtained analytically as the Mashhoon-Will-Schiutz WKB formula is exact in this case. This regime is interesting because of the correspondence between eikonal quasinormal modes and null geodesics, as well as due to existence of potential eikonal instabilities in some theories of gravity. At the same time in a number of studies devoted to quasinormal modes of spherically symmetric black holes this opportunity was omitted. Here we find analytical quasinormal modes of black holes in various alternative and extended theories of gravit…
We study quasinormal modes related to gravitational and electromagnetic perturbations of spherically symmetric charged black holes in nonlinear electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class of Lagrangian with higher-order corrections written by the electromagnetic field strength and its Hodge dual with arbitrary coefficients, and we parametrize the corrections for quasinormal frequencies in terms of the coefficients. It is confirmed that the isospectrality of quasinormal modes under parity is generally violated due to nonlinear electrodynamics. As applications…
We compute the exact gravitational quasinormal frequencies for massless topological black holes in d-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies.
We study the quasinormal modes of fermionic perturbations for an asymptotically Lifshitz black hole in 4-dimensions with dynamical exponent z=2 and plane topology for the transverse section, and we find analytically and numerically the quasinormal modes for massless fermionic fields by using the improved asymptotic iteration method and the Horowitz-Hubeny method. The quasinormal frequencies are purely imaginary and negative, which guarantees the stability of these black holes under massless fermionic field perturbations. Remarkably, both numerical methods yield consistent results; i.e., both m…
We analytically calculate to leading order the asymptotic form of quasinormal frequencies of Kerr black holes in four, five and seven dimensions. All the relevant quantities can be explicitly expressed in terms of elliptical integrals. In four dimensions, we confirm the results obtained by Keshest and Hod by comparing the analytic results to the numerical ones.
We consider the various perturbations of self-dual warped AdS$_3$ black hole and obtain the exact expressions of quasinormal modes by imposing the vanishing Dirichlet boundary condition at asymptotic infinity. It is expected that the quasinormal modes agree with the poles of retarded Green's functions of the dual CFT. Our results provide a quantitative test of the warped AdS/CFT correspondence.
Two numerical methods are used to calculate quasinormal modes (QNMs) of near-extremal black holes/strings in the generalized spherically/cylindrically symmetric background, the Asymptotic Iteration Method (AIM) and the Spectral Method. The numerical results confirm the accuracy of the approximate analytic formula using the Pöschl-Teller potential. Our analytic formula is used to investigate the Strong Cosmic Censorship conjecture of extremal and near-extremal black holes in Ref. \cite{Burikham:2020dfi}.
Quasinormal modes of a scalar field perturbation are investigated in the background spacetime of Einstein-Yang-Mills black holes. The logarithmic term in the metric function of the five-dimensional Einstein-Yang-Mills black hole eliminates the divergence of the Hawking temperature but maintains the charge-dependent behavior of the quasinormal modes. The real and imaginary parts of quasinormal mode frequencies have the same charge-dependent behavior in different dimensions. Similar to the case of high dimensional Schwarzschild black holes, a compact approximate relation, $ω_{\rm R}\sim D/r_{+}$…
We compute the spectrum of quasinormal frequencies of regular black holes obtained in the presence of Non-Linear Electrodynamics. In particular, we perturb the black hole with a minimally coupled massive scalar field, and we study the corresponding perturbations adopting the 6th order WKB approximation. We analyze in detail the impact on the spectrum of the charge of the black hole, the quantum number of angular momentum and the overtone number. All modes are found to be stable. Finally, a comparison with other charged black holes is made, and an analytical expression for the quasinormal spect…
We study the scalar perturbation in the background of the charged Kaluza-Klein black holes with squashed horizons. We find that the position of infinite discontinuities of the heat capacities can be reflected in quasinormal spectrum. This shows the possible non-trivial relation between the thermodynamical and dynamical properties of black holes.
We explore the relationship between classical quasinormal mode frequencies and black hole quantum mechanics in 2+1 dimensions. Following a suggestion of Hod, we identify the real part of the quasinormal frequencies with the fundamental quanta of black hole mass and angular momentum. We find that this identification leads to the correct quantum behavior of the asymptotic symmetry algebra, and thus of the dual conformal field theory. Finally, we suggest a further connection between quasinormal mode frequencies and the spectrum of a set of nearly degenerate ground states whose multiplicity may be…
We study the propagation of probe scalar fields in the background of 4D Einstein-Gauss-Bonnet black holes with anti-de Sitter (AdS) asymptotics and calculate the quasinormal modes. Mainly, we show that the quasinormal spectrum consists of two different branches, a branch perturbative in the Gauss-Bonnet coupling constant $α$ and another branch nonperturbative in $α$. The perturbative branch consists of complex quasinormal frequencies that approximate to the quasinormal frequencies of the Schwarzschild AdS black hole in the limit of a null coupling constant. On the other hand, the nonperturbati…
We show that the hidden conformal symmetry of the Schwarzschild black hole is realized from the AdS$_2$ sector of the AdS$_2\times S^2$, but not from the Rindler spacetime which is the genuine near-horizon geometry of the Schwarzschild black hole. This implies that purely imaginary quasinormal frequencies obtained using the hidden conformal symmetry is not suitable for describing the largely damped modes around the Schwarzschild black hole.
We demonstrate that an equidistant area spectrum for the link variables in loop quantum gravity can reproduce both the thermodynamics and the quasinormal mode properties of black holes.
In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for the case of spin zero perturbations. We also discuss an improved version of the AIM, more suitable for numerical implementation.
We show that quasinormal modes cannot exist in the extremal BTZ black hole. For this purpose, we consider propagations of a minimally coupled scalar and a single massive graviton obtained from the cosmological topologically massive gravity on the extremal BTZ black hole. The would-be quasinormal modes for a scalar and graviton could not exist because it is impossible to make an ingoing flux into the extremal (degenerate) horizon. This is consistent with the argument that there is no propagating dynamics in the self-dual orbifold of AdS(3) which is just the near-horizon limit of the extremal BT…
We compute the quasinormal frequencies for scalar perturbations of charged black holes in five-dimensional Einstein-power-Maxwell theory. The impact on the spectrum of the electric charge of the black holes, of the angular degree, of the overtone number, and of the mass of the test scalar field is investigated in detail. The quasinormal spectra in the eikonal limit are computed as well for several different space-time dimensionalities.
Analytic exact expressions for the quasinormal modes of scalar and electromagnetic perturbations around a special class of black holes are found in d\ge3 dimensions. It is shown that, the size of the black hole provides a bound for the angular momentum of the perturbation. Quasinormal modes appear when this bound is fulfilled, otherwise the excitations become purely damped.
We study the quasinormal modes of $p$-form fields in spherical black holes in $D$-dimensions. Using the spherical symmetry of the black holes and gauge symmetry, we show the $p$-form field can be expressed in terms of the coexact $p$-form and the coexact $(p-1)$-form on the sphere $S^{D-2}$. These variables allow us to find the master equations. By utilizing the S-deformation method, we explicitly show the stability of $p$-form fields in the spherical black hole spacetime. Moreover, using the WKB approximation, we calculate the quasinormal modes of the $p$-form fields in $D(\leq10)$-dimensions…
We present an exact expression for the quasinormal modes of acoustic disturbances in a rotating 2+1 dimensional sonic black hole (draining bathtub fluid flow) in the low frequency limit and evaluate the adiabatic invariant proposed by Kunstatter. We also compute,via Bohr-Sommerfeld quantization rule the equivalent area spectrum for this acoustic black hole, and we compute the superradiance phenomena for pure spinning 2+1 black holes.
We investigate quasinormal modes of a massless charged scalar field on a small Reissner-Nordström-anti-de Sitter (RN-AdS) black hole both with analytical and numerical approaches. In the analytical approach, by using the small black hole approximation (r_+ << L), we obtain the quasinormal mode frequencies in the limit of r_+/L -> 0, where r_+ and L stand for the black hole event horizon radius and the AdS scale, respectively. We then show that the small RN-AdS black hole is unstable if its quasinormal modes satisfy the superradiance condition and that the instability condition of the RN-AdS bl…
This is a short review of the quasinormal mode spectrum of Schwarzschild, Reissner-Nordstrom and Kerr black holes. The summary includes previously unpublished calculations of i) the eigenvalues of spin-weighted spheroidal harmonics, and ii) quasinormal frequencies of extremal Reissner-Nordstrom black holes.
We analyze the fermionic quasinormal modes of the BTZ black hole in the presence of space-time noncommutativity. Our analysis exploits a duality between a spinless and spinning BTZ black hole, the spin being proportional to the noncommutative deformation parameter. Using the AdS/CFT correspondence we show that the horizon temperatures obtained from the dual CFT pick up noncommutative contributions. We demonstrate the equivalence between the quasinormal and non-quasinormal modes for the noncommutative fermionic probes, which provides further evidence of holography in the noncommutative setting.…
We consider quantum corrections for the Schwarzschild black hole metric by using the generalized uncertainty principle (GUP) to investigate quasinormal modes, shadow and their relationship in the eikonal limit. We calculate the quasinormal frequencies of the quantum-corrected Schwarzschild black hole by using the sixth-order Wentzel-Kramers-Brillouin (WKB) approximation, and also perform a numerical analysis that confirms the results obtained from this approach. We also find that the shadow radius is nonzero even at very small mass limit for finite GUP parameter.
In this paper, we analytically calculate the quasinormal modes of scalar, vector, tensor, and spinor perturbations of the warped dS$_3$ black hole. There are two horizons for the warped dS$_3$ black hole, namely, the black hole horizon $r_b$ and the cosmological horizon $r_c$. In the calculation, we impose the ingoing boundary condition at the black hole horizon and the outgoing boundary condition at the cosmological horizon. We also investigate the hidden conformal symmetry of the warped dS$_3$ black hole in the region between the black hole horizon and the cosmological horizon $r_b<r<r_c$. W…
In this work we have considered a model that includes the interaction of gravity and matter fields with Galilean invariance (the so-called derivative coupling) as well as some corresponding black hole type solutions. Quasinormal perturbations of two kinds of matter fields have been computed by different methods. The effect of the derivative coupling in the quasinormal spectrum has been analyzed and evaluated.
The gravitational consequence of local Lorentz violation (LV) should show itself in derivation of the characteristic quasinormal ringing of black hole mergers from their general relativity case. In this paper, we study quasinormal modes (QNMs) of the scalar and electromagnetic field perturbations to Einstein aether black holes. We find that quasinormal ringing of the first kind aether black hole is similar to that of another Lorentz violation model---the QED-extension limit of standard model extension. These similarities between completely different backgrounds may imply that LV in gravity sec…
We analytically investigate the quasinormal modes of the massive scalar field with a nonminimal coupling in the higher-dimensional de Sitter black hole with a single rotation. According to the separated scalar field equation, the boundary conditions of quasinormal modes are well constructed at the outer and cosmological horizons. Then, under near-extremal conditions, where the outer horizon closes to the cosmological horizon, the quasinormal frequencies are obtained and generalized to universal form in the higher-dimensional spacetime. Here, the real part of the frequency includes the scalar f…
The recent reported gravitational wave detection motivates one to investigate the properties of different black hole models, especially their behavior under (axial) gravitational perturbation. Here, we study the quasinormal modes of black holes in Weyl gravity. We derive the master equation describing the quasinormal radiation by using a relation between the Schwarzschild-anti de Sitter black holes and Weyl solutions, and also the conformal invariance property of the Weyl action. It will be observed that the quasinormal mode spectra of the Weyl solutions deviate from those of the Schwarzschild…
We study the Maxwell quasinormal spectrum on asymptotically anti-de Sitter black holes with a set of two Robin type boundary conditions, by requiring the energy flux to vanish at asymptotic infinity. Focusing, for illustrative purposes, on Schwarzschild-anti-de Sitter black holes both without and with a global monopole, we unveil that, on the one hand, the Maxwell quasinormal spectrum bifurcates as the black hole radius increases for both boundary conditions, which is termed the mode split effect; while on the other hand, with an appropriate fixed black hole radius but increasing the monopole …
We propose a simple and efficient way to compute quasinormal frequencies of spherically symmetric black holes. We revisit an old idea that relates them to bound state energies of anharmonic oscillators by an analytic continuation. This connection enables us to achieve remarkable high-order computations of WKB series by Rayleigh-Schrödinger perturbation theory. The known WKB results are easily reproduced. Our analysis shows that the perturbative WKB series of the quasinormal frequencies turn out to be Borel summable divergent series both for the Schwarzschild and for the Reissner-Nordström blac…
In this paper, we first investigate the thermal stability of black holes in conformal Weyl gravity with a comparison with the Schwarzschild black holes. Then, we consider a minimally coupled massive scalar perturbation and calculate the quasinormal modes in asymptotically dS spacetime by employing the sixth order WKB approximation and asymptotic iteration method. The deviations from those of the Schwarzschild-dS solutions are obtained and the possibility of the presence of quasi-resonance modes for Weyl black hole solutions is investigated. Finally, we consider a massless scalar perturbation i…
In this work, we investigate the quasinormal frequencies of a class of regular black hole solutions which generalize Bardeen and Hayward spacetimes. In particular, we analyze scalar, vector and gravitational perturbations of the black hole both with the semianalytic WKB method and their time-domain profiles. We analyze in detail the behavior of the spectrum depending on the parameter $p/q$ of the black hole, the quantum number of angular momentum and the $s$ number. In addition, we compare our results with the classical solution valid for $p = q = 1$.
We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of the them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution.
Stability criteria of nearly extreme black holes in the perturbations level is one of the interesting issues in gravitational systems. Considering the nearly extreme conformal-de Sitter black holes, in this paper, we obtain an exact relation for the quasinormal modes of scalar perturbations. As for stability criteria, we find a lower bound on the event horizon radius which is corresponding to an upper bound on the value of the quasinormal frequencies. In addition, we show that the asymptotic behavior of quasinormal modes gives highly damped modes which is important due to possible connection b…
