Hyung Won Lee, Yong-Wan Kim, Yun Soo Myung
We calculate quasinormal modes of a massive scalar perturbation on the topologically massive black hole (CS-BTZ black hole). The chiral point of $μ\ell=1$ corresponds to a newly extremal black hole. We show that there is no quasinormal modes at this point. Accordingly, we prove the unitarity of the CS-BTZ black hole at the chiral point.
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Light propagation and quasinormal modes of a topologically charged Schwarzschild-Klinkhamer wormhole
本文理论分析了由几何缺陷产生的虫洞中的零测地线、临界光子轨道和阴影形成，通过弱场和强场下的偏转角研究光传播，并计算了标量扰动的拟正则模和时域解。
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.
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 study quasinormal modes of massless scalar and fermion fields in the near extremal Reissner-Nordstr{ö}m black hole, and relate them to Choptuik scaling form following a recently proposed analytic approach. For both massless cases, quasinormal modes are shown to be proportional to the black hole horizon and the Hawking temperature, and the critical exponents are the same, although for the fermionic case there are two possible discrete quasinormal modes. In addition, the critical exponent of the massive boson is also equivalent to that of the massless case. Finally, we discuss quasinormal mod…
In this work we consider a Generalized Bronnikov-Ellis wormhole and the tideless Morris-Thorne wormhole and we study the propagation of massive scalar fields. We calculate the quasinormal frequencies using the WKB method and the pseudospectal Chebyshev method and we show the presence of an anomalous decay rate for the quasinormal modes in the Generalized Bronnikov-Ellis wormhole. However, such anomalous behaviour is avoided for the fundamental mode in the Morris-Thorne wormhole background.
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.
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…
Quasinormal modes of a massive Dirac field were calculated for various static black hole backgrounds with the help of the WKB formula. These estimations, however, are rough and valid only for very small values of $μM$, where $M$ and $μ$ are mass of the black hole and field respectively. Thus, no accurate calculations of massive Dirac modes are known even for the Schwarzschild black hole and this is all the more so for the Kerr solution. Here we calculate quasinormal modes of a massive Dirac field in the Kerr background. We have shown that the infinitely long-lived quasinormal modes (quasireson…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the unitarity of both topologically massive higher-derivative electromagnetism and topologically massive higher-derivative gravity. The novel and amazing features of these effective field models are also discussed.
The superfield equations of massive IIA supergravity, in the form of constraints on the superspace geometry, are shown to be implied by $κ$-symmetry of the topologically massive D-2-brane.
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 investigate the topologically new massive gravity in three dimensions. It turns out that a single massive mode is propagating in the flat spacetime, comparing to the conformal Chern-Simons gravity which has no physically propagating degrees of freedom. Also we discuss the realization of the BMS/GCA 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}.
The addition of a topologically massive term to an admittedly non-unitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its non-unitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, ca…
We consider renormalizability of topologically massive gravity in three space-time dimensions. With a usual parametrization of the metric tensor, we establish the statement that topologically massive gravity is in fact renormalizable. In this proof, we make use of not only a recently found, new infrared regularization method of scalar mode but also a covariant ultraviolet regulator with a specific combination of higher derivative terms which is motivated by the new massive gravity in three dimensions.
We show that the linking number of two homologically trivial disjoint $p$ and $(D-p-1)$-dimensional submanifolds of a $D$-dimensional manifold can be derived from the topologically massive $BC$ theory in low energy regime.
We find the critical charge for a topologically massive gauge theory for any gauge group, generalising our earlier result for SU(2). The relation between critical charges in TMGT, singular vectors in the WZNW model and logarithmic CFT is investigated.
We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in a perfect agreement with those of the recent numerical study where the full coupled partial differential e…
Using the quasinormal modes of a massless scalar perturbation, we investigate the small/large black hole phase transition in the Lorentz symmetry breaking massive gravity. We mainly focus on two issues: i) the sign change of slope of the quasinormal mode frequencies in the complex-$ω$ diagram; ii) the behaviors of the imaginary part of the quasinormal mode frequencies along the isobaric or isothermal processes. For the first issue, our result shows that, at low fixed temperature or pressure, the phase transition can be probed by the sign change of slope. While increasing the temperature or pre…
We study topologically massive (B \wedge F) Abelian and non-Abelian gauge theories in four dimensions, and reduce them to three dimensions by assuming that the fields do not propagate in one of the spatial directions. For certain gauge choices the reduced theories are the Jackiw-Pi models of massive gauge fields.
We thereby prove that a large class of topologically massive theories of the Cremmer-Scherk-Kalb-Ramond-type in any $d$ dimensions corresponds to gauge non-invariant first-order theories that can be interpreted as self-dual models.
For a (2+1)-dimensional topologically massive Born-Infeld theory, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is equivalent to that of $QED_3$ with a Thirring interaction term among fermions, in the short distance regime.
Using the operator approach, we obtain quasinormal modes (QNMs) of BTZ black hole in spin-3 topologically massive gravity by solving the first-order equation of motion with the transverse-traceless condition. We find that these are different from those obtained when solving the second-order differential equation for the third-rank tensor of spin-3 field subject to suitable boundary conditions and having the sign ambiguity of mass. However, it is shown clearly that two approaches to the left-moving QNMs are identical, while the right-moving QNMs of solving the second-order equation are given by…
We construct higher spin quasinormal modes algebraically in $D$-dimensional de Sitter spacetime using the ambient space formalism. The quasinormal modes fall into two nonunitary lowest-weight representations of $\mathfrak{so}(1, D)$. From a local QFT point of view, the lowest-weight quasinormal modes of massless higher spin fields are produced by gauge-invariant boundary conserved currents and boundary higher-spin Weyl tensors inserted at the southern pole of the past boundary. We also show that the quasinormal spectrum of a massless/massive spin-$s$ field is precisely encoded in the Harish-Ch…
We consider the four dimensional topologically massive electrodynamics in which a gauge field is interacting with 2nd rank antisymmetric tensor field through a topological interaction. The photon becomes massive by eating the 2nd rank tensor field, which is dual to the Higgs mechanism. We explicitly demonstrate the nature of the mechanism by performing a canonical analysis of the theory and discuss various aspects of it.
We study the spectrum of quasinormal mode frequencies for a Proca field on a rotating black hole spacetime. First, we review how the introduction of field mass modifies the spectrum in the scalar-field case, leading to evanescent modes and to quasiresonance. Next, we examine the three physical polarizations of the Proca field and their relation to the electromagnetic field modes in the massless limit. Exploiting a separation of variables, we obtain a five-term recurrence relation from an appropriate ansatz for the radial function. Gaussian elimination and the modified Lentz algorithm are appli…
We explicitly calculate the one-loop effective potential for the supersymmetric topologically massive gauge theory in four dimensions, where the chiral scalar superfield is directly coupled to the field strength for the gauge spinor superfield.
I discuss the applicability in Weyl-invariant induced gravity and topologically massive gravity of certain formulas originally derived by Knizhnik, Polyakov, and Zamolodchikov in the context of diffeomorphism-invariant induced gravity.
So far analysis of the quasinormal spectrum of a massive charged scalar field in the black hole background has been limited by the regime of small μM and qQ, where μ, q (M, Q) are mass and charge of the field (black hole). Here we shall present a comprehensive picture of quasinormal modes, late-time tails and stability of a massive charged scalar field around Kerr-Newman black holes for any physically meaningful values of the parameters. We shall show that despite presence of the two mechanisms of superradiance (owing to black hole's rotation and charge) and the massive term creating growing b…
We investigate the strong cosmic censorship conjecture in lukewarm Reissner-Nordström-de Sitter black holes (and Martínez-Troncoso-Zanelli black holes) using the quasinormal resonance of non-minimally coupled massive scalar field. The strong cosmic censorship conjecture is closely related to the stability of the Cauchy horizon governed by the decay rate of the dominant quasinormal mode. Here, dominant modes are obtained in the limits of small and large mass black holes. Then, we connect the modes by using the WKB approximation. In our analysis, the strong cosmic censorship conjecture is valid …
We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are Stückelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the …
We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that ν, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on ν, and for any positive νthere exist both a trivial and a nontrivial fixed point.
Using the superfield formalism and the master action approach, we prove, both at the classical and quantum levels, the dual equivalence between four-dimensional supersymmetric self-dual and topologically massive models coupled to dynamical matter.
We demonstrate the classical stability of the BTZ black hole within the context of topologically massive gravity. The linearized perturbation equations can be solved exactly in this case. By choosing standard boundary conditions appropriate to the stability problem, we demonstrate the absence of modes which grow in time, for all values of the Chern-Simons coupling.
The (2+1) dimensional non-linear electrodynamics, the so called Pagels--Tomboulis electrodynamics, with the Chern--Simons term is considered. We obtain "generalized self--dual equation" and find the corresponding generalized massive Chern--Simons Lagrangian. Similar results for (2+1) massive dilaton electrodynamics have been obtained.
We discuss the structure of the vacua in $O(2)$ topologically massive gauge theory on a torus. Since $O(2)$ has two connected components, there are four classical vacua. The different vacua impose different boundary conditions on the gauge potentials. We also discuss the non-perturbative transitions between the vacua induced by vortices of the theory.
We construct a novel topologically massive abelian Chern-Simons gauge theory with 32 global supersymmetries in three spacetime dimensions. In spite of the 32 supercharges, the theory exhibits massive excitations only up to spin 1. The possibility of such a multiplet shortening is due to the presence of non-central R-symmetry generators in the Poincare superalgebra, whose supermultiplets are determined.
We manifestly verify that the miraculous cancellation of the infrared divergence of the topologically massive Yang-Mills theory in the Landau gauge is completely determined by a new vector symmetry existing in its large topological mass limit, the Chern-Simons theory. Furthermore, we show that the cancellation theorem proposed by Pisarski and Rao is an inevitable consequence of this new vector symmetry.
The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived {\it analytically}. We show that there exists a critical mass parameter, $μ_c$, below which increasing the mass $μ$ of the field increases the oscillation frequency $\Re(ω)$ of the resonance. On the other hand, above the critical field mass increasing the mass $μ$ increases the damping rate $\Im(ω)$ of the mode. We confirm our analytical results by numerical computations.
In an abelian topologically massive gauge theory, any eigenstate of the Hamiltonian can be decomposed into a factor describing massive propagating gauge bosons and a Chern-Simons wave function describing a set of nonpropagating ``topological'' excitations. The energy depends only on the propagating modes, and energy eigenstates thus occur with a degeneracy that can be parametrized by the Hilbert space of the pure Chern-Simons theory. We show that for a {\em nonabelian} topologically massive gauge theory, this degeneracy is lifted: although the Gauss law constraint can be solved with a similar …
We discuss the possibility for the spectrum of topologically massive quantum electrodynamics with spinor matter fields to contain unexpected and unusual stable particle excitations for certain values of the topological photon mass. The new field theoretical phenomena arising from this novel spectral structure are briefly discussed.
We discuss the evaluation of observables in two-dimensional conformal field theory using the topological membrane description. We show that the spectrum of anomalous dimensions can be obtained perturbatively from the topologically massive quantum field theories by computing radiative corrections to Aharonov-Bohm scattering amplitudes for dynamical charged matter fields. The one-loop corrections in the case of topologically massive Yang-Mills theory are shown to coincide with the scaling dimensions of the induced ordinary and supersymmetric WZNW models. We examine the effects of the dressing of…
The asymptotic solutions of cosmological topologically massive gravity (TMG) are analyzed for values of the mass parameter in the range $μ\geq1$. At non-chiral values, a new term in the Fefferman-Graham expansion is needed to capture the bulk degree of freedom. The CDWW modes provide a basis for the pure non-Einstein solutions at all $μ$, with nonlinear corrections appearing at higher order in the expansion.
In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the Self-Dual Black Hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the Loop Quantum Gravity. From our results, we can check that the Self-Dual Black Hole is stable under the scalar perturbations when assuming small values for the …
In this paper, we consider the Einstein-massive gravity coupled to the Yang-Mills gauge field in five dimensions. Concentrating on the static solutions with planar horizon geometry, we explore the thermodynamic behavior in the extended phase space and examine the validity of the first law of thermodynamics besides local thermal stability by the Hessian matrix. We observe that although the topology of boundary is planar, there exists the van der Waals like phase transition for this kind of solution. We find the critical quantities and discuss how the massive and Yang-Mills parameters affect the…
We investigate in which sense, at the linearized level, one can extend the 3D topologically massive gravity theory beyond three dimensions. We show that, for each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions can be defined describing a massive "spin-2" particle provided one uses a non-standard representation of the massive "spin-2" state which makes use of a two-column Young tableau where each column is of height 2k-1. We work out the case of k=2, i.e. 7D, and show, by canonical analysis, that the model describes, unitarily, 35 massive "spin-2" degrees of freedom. Th…
We investigate the perturbative dynamics of noncommutative topologically massive gauge theories with softly broken supersymmetry. The deformed dispersion relations induced by noncommutativity are derived and their implications on the quantum consistency of the theory are discussed.
We describe the construction of $2+1$-dimensional toplogically massive adS gravity with ${\mathcal{N}}$-extended supersymmetry in superspace by means of introducing a compensating hypermultiplet for the super-Weyl invariance. For $\mathcal{N}\geq 3$ the scalar multiplet must be on shell and the potential for the scalar compensator is completely determined by the geometry. As a consequence the resulting massive theory has no free parameter for $\mathcal{N}\geq 4$. For $\mathcal{N}= 4$ we show that this leads to topologically massive gravity at the chiral point and construct the corresponding of…
We explore topologically massive gauge theories using the covariant colour kinematics duality recently introduced by Cheung and Mangan. We show that the massive bi-adjoint scalar field is simply related to topologically massive gauge theory by the duality, and that enacting the same duality on the gauge theory produces topologically massive gravity coupled to a scalar or, equivalently, an antisymmetric field. We also show that different choices for the replacement of the colour structure constants with kinematic structure constants lead to different theories, including a topologically massive …
The entropy of a Bañados, Teitelboim, and Zanelli black hole in topologically massive gravity had been given with the form inconsistent with the Bekenstein-Hawking entropy. In the paper, we provide a consistent statistical interpretation for the entropy, and confirm it to be thermodynamic entropy by preserving the first and second laws. As a novel extension, the logarithmic correction to the black hole entropy is also discussed.
We quantize the Einstein gravity in the formalism of weak gravitational fields by using the constrained Hamiltonian method. Special emphasis is given to the 2+1 spacetime dimensional case where a (topological) Chern-Simons term is added to the Lagrangian.
Recently, the anomalous decay rate of quasinormal modes has been studied for some geometries under scalar field perturbations, which occurs when the longest-lived modes are the ones with higher angular number, as well as, the existence of a critical scalar field mass, i.e the value of scalar field mass such that the decay rate does not depend appreciably on the angular number, and beyond which the behaviour of the decay rate is inverted. Here, we consider the propagation of fermionic fields in the background of Schwarzschild de Sitter black holes, and we show that the anomalous decay rate beha…
We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of $ψ^{new}$ and $X$ are introduced for a candidate of propagating physical field at the chiral point. However, we show that ($ψ^{new},ψ^L$) form a dipole ghost pair of unphysical fields and $X$ is not a primary. This implies that there is no physically propagating degrees of freedom at the chiral point.
We show that, with the help of a general BRST symmetry, different theories in 3 dimensions can be connected through a fundamental topological field theory related to the classical limit of the Chern-Simons model.
By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant $Λ$, elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via an appropriate partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev-Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dyn…
The set of degenerate ground states of an arbitrary nonabelian topologically massive gauge theory is shown to be in one-to-one correspondence with the Hilbert space of the associated pure Chern-Simons theory. (Paper is being withdrawn: original conclusion is incorrect for the nonabelian case. For a correct treatment, see M. Asorey, S. Carlip, and F. Falceto, hep-th/9304081.)
The first order form of a three dimensional U(1) gauge theory in which a gauge invariant mass term appears is analyzed using the Dirac procedure. The form of the gauge transformation which leaves the action invariant is derived from the constraints present.
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in $\RR^3$ can be defined so that its large-mass limit be the renormalized vacuum expectation value of the Wilson loop for abelian Chern-Simons theory also in $\RR^3$.
We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for qua…
We compute the one-loop beta functions of the cosmological constant, Newton's constant and the topological mass in topologically massive supergravity in three dimensions. We use a variant of the proper time method supplemented by a simple choice of cutoff function. We find that the dimensionless coefficient of the Chern-Simons term, $ν$, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on $ν$; we study analytically the structure of the flow and its fixed points in the limits of small and large $ν$.
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