We argue that magnetic and electric charges of the Reissner-Nordstrom black hole are quantized in CP conserving theories. Dequantization phenomenon occurs when CP is broken either explicitly or effectively, and, as a result, pure magnetic black holes are not possible. Two examples illustrating this phenomenon are discussed. One is the electric charge induced by the neutral pion field in a magnetically charged black hole, and another is the electric charge induced due to the massive spin-two field emerging from possible higher curvature terms.
Noncommutative black holes in higher dimensions are investigated in the context of holographic principle. Quantization rules for the discrete mass spectrum are derived and compared with the continuous spectrum in the literature. Because of the noncommutative nature of background geometry the minimum mass to form a noncommutative black hole is very large (it becomes larger for discrete spectra), so the current LHC search results for mini black holes cannot exclude the possibility of quantum gravity in higher dimensions.
As a mysterious celestial body predicted by General Relativity, black holes have been confirmed by observations in recent years. But there are still many unknown properties waiting for us to discover, one of the famous problems is the quantization of black holes. The quantization of black holes gives new research significance to black holes, but the quantization of black holes is difficult to prove. Here we propose a new method to verify the quantization of black holes: Carnot cycle. Our results show that if the black holes have quantized energy levels, the work W they impose to us via the Car…
The spectrum of the area operator for a Schwarzschild black hole in loop quantum gravity is fixed by the demand that the entropy of a black hole is maximum. This paper has been withdrawn by the author, due a crucial error in the derivation.
The thermodynamical description of black holes is reviewed and critiqued. We present an alternative, microcanonical description of black holes and discuss the major differences. In particular the decay rates of black holes are compared in the two different pictures.
We study the potential of gravitational wave astronomy to observe the quantum aspects of black holes. According to Bekenstein's quantization, we find that black hole area discretization can have observable imprints on the gravitational wave signal from an inspiraling binary black hole. We study the impact of quantization on tidal heating. We model the absorption lines and compute gravitational wave flux due to tidal heating in such a case. By including the quantization we find the dephasing of the gravitational wave, to our knowledge it has never been done before. We discuss the observability …
Black holes in noncommutative geometry background are considered to be quantized in accordance with the holographic principle. Incomplete gamma function involving the effective black hole mass is replaced by a discrete sum. The mass spectrum as well as the temperature of black holes is presented. The spectra are discrete ones but the shapes are very consistent with the known continuous results.
A previously used quantization mechanism is applied to the continuous states of the shielded strong gravity scenario (hep-th/0602183), yielding two types of spectra for uncharged black hole scalars. Each yields the general morphology for states expected in this scenario at LHC and at arbitrarily higher energies, once the parameters are determined by the two lowest-lying scalar states. A particularized example for the preferred type of quantization is numerically evaluated.
A general covariant quantization of superparticle, Green-Schwarz superstring and a supermembrane with manifest supersymmetry and duality symmetry is proposed. This quantization provides a natural quantum mechanical description of curved BPS-type backgrounds related to the ultra-short supersymmetry multiplets. Half-size commuting and anticommuting Killing spinors admitted by such backgrounds in quantum theory become truncated $κ$-symmetry ghosts. The symmetry of Killing spinors under dualities transfers to the symmetry of the spectrum of states. GS superstring in the generalized semi-light-cone…
A classical black hole is characterized by a horizon that absorbs radiation of all frequencies incident on it. Perturbation of these black holes is well-understood via exponentially damped sinusoids known as quasi-normal modes. Any departure from such classical behavior near the horizon may induce significant modifications in the late time evolution of the perturbation leading to so-called gravitational wave echoes. This work considers the effect of black hole area-quantization on the formation of gravitational wave echoes. We investigate how the resulting echo waveform may depend on various m…
A simple argument is presented in favour of the equidistant spectrum in semiclassical limit for the horizon area of a black hole. The following quantization rules for the mass $M_N$ and horizon area $A_{Nj}$ are proposed: M_N = m_p [N(N+1)]^{1/4}; A_{Nj} = 8πl_p^2 [\sqrt{N(N+1)} + \sqrt{N(N+1) - j(j+1)} ]. Here both $N$ and $j$ are nonnegative integers or half-integers.
Starting from a weak gauge principle we give a new and critical revision of the argument leading to charge quantization on arbitrary spacetimes. The main differences of our approach with respect to previous works appear on spacetimes with non trivial torsion elements on its second integral cohomology group. We show that in these spacetimes there can be topologically non-trivial configurations of charged fields which do not imply charge quantization. However, the existence of a non-exact electromagnetic field always implies the quantization of charges. Another consequence of the theory for spac…
We study a Hamiltonian quantum formalism of a spherically symmetric space-time which can be identified with the interior of a Schwarzschild black hole. The phase space of this model is spanned by two dynamical variables and their conjugate momenta. It is shown that the classical Lagrangian of the model gives rise the interior metric of a Schwarzschild black hole. We also show that the the mass of such a system is a Dirac observable and then by quantization of the model by Wheeler-DeWitt approach and constructing suitable wave packets we get the mass spectrum of the black hole.
We consider the loop quantization of Maxwell theory. A quantization of this type leads to a quantum theory in which the fundamental excitations are loop-like rather than particle-like. Each such loop plays the role of a quantized Faraday's line of electric flux. We find that the quantization depends on an arbitrary choice of a parameter e that carries the dimension of electric charge. For each value of e an electric charge that can be contained inside a bounded spatial region is automatically quantized in units of hbar/4*pi*e. The requirement of consistency with the quantization of electric ch…
The canonical quantization of a Schwarzschild black hole yields a picture of the black hole that is shown to be equivalent to a collection of oscillators whose density of levels is commensurate with that of the statistical bootstrap model. Energy eigenstates of definite parity exhibit the Bekenstein mass spectrum, $M \sim \sqrt{\cal N} M_p$, where ${\cal N} \in {\bf N}$. From the microcanonical ensemble, we derive the statistical entropy of the black hole by explicitly counting the microstates corresponding to a macrostate of fixed total energy.
It was recently observed in \cite{Park:2014tia} that the holographic nature of gravity may hold a key to quantization of gravity. The so-called "holographic quantization" has been carried out in \cite{Park:2014noa,Park:2015ota} for Einstein gravity in a flat background. Generalizing the procedure to a curved background is the main goal of the present work. In particular, we consider the Einstein action expanded around a Schwarzschild background
It has been argued by several authors that the quantum mechanical spectrum of black hole horizon area must be discrete. This has been confirmed in different formalisms, using different approaches. Here we concentrate on two approaches, the one involving quantization on a reduced phase space of collective coordinates of a Black Hole and the algebraic approach of Bekenstein. We show that for non-rotating, neutral black holes in any spacetime dimension, the approaches are equivalent. We introduce a primary set of operators sufficient for expressing the dynamical variables of both, thus mapping th…
In present paper, we investigated the quantization of an electromagnetic field in the background of static spherically symmetric d-dimensional spacetime in the Boulware vacuum. We have also calculated the response rate of a static charge outside both d-dimensional Schwarzschild black hole and the GB black hole in the low-frequency regime, which can be expressed as the summation of hypergeometric functions.
In this letter, the open string is quantized in a time dependent black hole background. The geometry is defined through an adiabatic approximation of the Vaydia metric. The worldsheet two-point function is derived and it is shown to have the same type of singularity as the flat space one. However, the equal times two-point function depends on the particular Cauchy surface where the worldsheet fields are defined. Finite temperature effects are incorporated through the Liouville-von Neumann approach to non equilibrium thermodynamics.
We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this field theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and ex…
Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detec…
The extensions of the Standard Model based on the $SU(3)_{C} \otimes SU(3)_{L} \otimes U(1)_{X}$ gauge group are known as 331 Models. Different properties such as the fermion assignment and the electric charges of the exotic spectrum, that defines a particular 331 model, are fixed by a $β$ parameter. In this article we study the electric charge quantization in two versions of the 331 models, set by the conditions $β=1/\left( 3\sqrt{3}\right)$ and $β=0$. In these frameworks, arise exotic particles, for instance, new leptons and gauge bosons with a fractional electric charge. Additionally, depen…
Quantization of different regions of the Reissner-Nordström space time (charged black hole) is done in the framework of loop quantum gravity. The geometry of Reissner-Nordström space-time is expressed in terms of Ashtekar variables which form the classical phase space of such a black hole. Using the loop quantization of phase space, the issue of singularity avoidance of such a black hole is addressed; based on spherically symmetry reduced models of loop quantum gravity, the operator analogue of the diverging factor of scalar curvature of the charged black hole is constructed and is shown to ex…
Recent results on the quantum mechanics of black holes indicate that the spacetime singularity can be avoided if the space of fields is extended in its domain as well as the vanishing of beta functions required as an equation in target space. Such an approach seems to inevitably lead to the quantization in this space that is the so-called third quantization. We discuss some of the implications of third quantization for the physics of blackholes in two dimensions. By discretizing the transverse dimensions describing the horizon it may also be possible to describe regulated four dimensional grav…
Some approaches to quantization of the horizon area of black holes are discussed. The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. This result is valid for a rather general class of approaches to surface quantization. In the case of rotating black holes no satisfactory solution for the quantization problem has been found up to now.
Quantum aspects of black holes may have observational imprints on their absorption and emission spectrum. In this work, we consider the possibility of non-uniform area quantization and its effects on the phasing of gravitational waveform from coalescing black hole inspirals. These observations may provide detectable effects distinct from that of a uniform area quantization and allow us to put bounds on various parameters of the underlying model. Our work can also be regarded as a novel test for the area-entropy proportionality of black hole solutions in general relativity.
Since the Bekenstein's proposal that a black hole has equally spaced area spectrum, the quasinormal modes as the characteristic modes of a black hole have been used in obtaining the horizon area spectrum of the black hole. However, the area spectrum of the Kerr black hole in some previous works was inconsistent with the Bekenstein's proposal. In this paper, we notice that the Kerr black hole has three types of resonance modes which are quasinormal modes (QNM), total transmission modes (TTM), and total reflection modes (TRM). All of these resonances represent highly damped oscillations and only…
The aim of present work is to extend the application of Weitzeböck Induced Matter Theory (WIMT) to a dyonic Reissner-Nordström Black Hole (RNBH), by proposing a condition compatible with a quantization relation between gravitational mass and both magnetic and electric charges from a geometric product defined as an invariant in 5D.
Starting from the Lagrangian formulation of the Einstein equations for the vacuum static spherically symmetric metric, we develop a canonical formalism in the radial variable $r$ that is time--like inside the Schwarzschild horizon. The Schwarzschild mass turns out to be represented by a canonical function that commutes with the $r$--Hamiltonian. We investigate the Wheeler--DeWitt quantization and give the general representation for the solution as superposition of eigenfunctions of the mass operator.
Starting from a quantization relation for primordial extremal black holes with electric and magnetic charges, it is shown that their entropy is quantized. Furthermore the energy levels spacing for such black holes is derived as a function of the level number $n$, appearing in the quantization relation. Some interesting cosmological consequences are presented for small values of $n$. By producing a mismatch between the mass and the charge the black hole temperature is derived and its behavior investigated. Finally extending the quantum relation to Schwarzschild black holes their temperature is …
We explore the possible microscopic structure of a charged AdS black hole from the quantized viewpoint. A further study shows that some black holes cannot absorb "energy quantum" under certain conditions from the view of quantization. By the quantization of the black hole horizon area, we show the relation between the number of quanta of area and the microscopic degrees of freedom of the black hole. We also interpret a latent heat of thermodynamical phase transition as a transition between the number of quanta of area of large black hole(LBH) and the number of quanta of area of small black hol…
Doubts have been expressed on the universality of holographic/string-inspired quantization rules for the horizon areas of stationary black holes or the products of their radii, already in simple 4-dimensional general relativity. Realistic black holes are not stationary but time-dependent. Using two examples of 4D general-relativistic spacetimes containing dynamical black holes for at least part of the time, it is shown that the quantization rules (even counting virtual horizons) cannot hold, except possibly at isolated instants of time, and do not seem to be universal.
We discuss the possibility that quantum black holes have discrete mass spectrum. Different arguments leading to this conclusion are considered, particularly the decoupling between left and right sectors in string theory - the so-called heterotic principle. The case of a $2+1$ dimensional black holes is considered as an argument in favour of this argument. The possible connection between membrane model of the black hole horizon and topological membrane is briefly discussed.
We investigate duality properties of N-form fields, provide a symmetric way of coupling them to electric/magnetic sources, and check that these charges obey the appropriate quantization requirements. First, we contrast the D=4k case, in which duality is a well-defined SO(2) rotation generated by a Chern-Simons form leaving the action invariant, and D=4k+2 where the corresponding ostensibly SO(1,1) rotation is not only not an invariance but does not even have a generator. When charged sources are included we show explicitly in the Maxwell case how the usual Dirac quantization arises in a fully …
A complete RST quantization of a CGHS model plus Strominger term is carried out. In so doing a conformal invariant theory with $κ=\frac{N}{12}$ is found, that is, without ghosts contribution. The physical consequences of the model are analysed and positive definite Hawking radiation is found.
We extend the foliation-based quantization scheme of \cite{Park:2014tia} to arbitrary asymptotically flat backgrounds including time- and position- dependent ones. One of the ingredients to accomplish the extension is imposition of a Neumann-type boundary condition. The quantization procedure, especially the gauge-fixing-induced reduction, provides a new insight into the black hole information paradox. The hypersurface degrees of freedom in the asymptotic region - whose dynamics should be responsible for part of the `hair' - and transitions among various excitations play a central role in the …
We perform a covariant (Lagrangian) quantization of perturbative gravity in the background of a Schwarzschild black hole. The key tool is a decomposition of the field into spherical harmonics. We fix Regge-Wheeler gauge for modes with angular momentum quantum number $l \geq 2$, while for low multipole modes with $l$ $=$ $0$ or $1$ -- for which Regge-Wheeler gauge is inapplicable -- we propose a set of gauge fixing conditions which are 2D background covariant and perturbatively well-defined. We find that the corresponding Faddeev-Popov ghosts are non-propagating for the $l\geq2$ modes, but are …
We consider the quasinormal spectrum of a charged scalar field in the (charged) Reissner-Nordstrom spacetime, which has two horizons. The spectrum is characterized by two distinct families of asymptotic resonances. We suggest and demonstrate the according to Bohr's correspondence principle and in agreement with the Bekenstein-Mukhanov quantization scheme, one of these resonances corresponds to a fundamental change of Delta A=4hbar ln2 in the surface area of the black-hole outer horizon. The second asymptotic resonance is associated with a fundamental change of Delta Atot=4hbar ln3 in the total…
In the present contribution we show that the introduction of axial currents in electrodynamics can explain the quantization of electric charge and introduces a dynamical discreteness of space-time, justifying thus the regularization of Feymman's integrals.
The quantization of a massless conformally coupled scalar field on the 2+1 dimensional Anti de Sitter black hole background is presented. The Green's function is calculated, using the fact that the black hole is Anti de Sitter space with points identified, and taking into account the fact that the black hole spacetime is not globally hyperbolic. It is shown that the Green's function calculated in this way is the Hartle-Hawking Green's function. The Green's function is used to compute $\langle T^μ_ν\rangle$, which is regular on the black hole horizon, and diverges at the singularity. A particle…
We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr's idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can be also derived from an Ansatz of quantized entropy $ΔS=4πk {ΔR / \lambdabar}$, which was suggested in a previous work to unify the black hole entropy formula and Verlinde's conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This sugge…
We discuss the quantization of a particle near an extreme Reissner-Nordstrom black hole in the canonical formalism. This model appears to be described by a Hamiltonian with no well-defined ground state. This problem can be circumvented by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF). We show that the Hamiltonian with no ground state corresponds to a gauge in which there is an obstruction at the boundary of spacetime requiring a modification of the quantization rules. The redefinition of the Hamiltonian a la DFF corresponds to a different choice of gauge. The latt…
In the present contribution we show that the introduction of a conserved axial current in electrodynamics can explain the quantization of electric charge, preserving parity conservation, and introduces a dynamical discreteness into space-time.
We discuss the quantization of a system of slowly-moving extreme Reissner-Nordstrom black holes. In the near-horizon limit, this system has been shown to possess an SL(2,R) conformal symmetry. However, the Hamiltonian appears to have no well-defined ground state. This problem can be circumvented by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF). We apply the Faddeev-Popov quantization procedure to show that the Hamiltonian with no ground state corresponds to a gauge in which there is an obstruction at the singularities of moduli space requiring a modification of th…
We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild black hole in Kucha\v r-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are non-vanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner (ADM) mass of the black hole according to a relation conjectured long…
A structure model for black holes is proposed by mean field approximation of gravity. The model, which consists of a charged singularity at the center and quantum fluctuation of fields around the singularity, is similar to the atomic structure. The model naturally quantizes the black hole. Especially we find the minimum black hole, whose structure is similar to the hydrogen atom and whose Schwarzschild radius becomes about 1.1287 of the Planck length.
In this work we investigate the thermodynamical properties and modified dynamics of black hole solutions in the semiclassical regime of affine coherent state quantization. Using the weak correspondence principle we build a semiclassical effective action that we use to study thermodynamics in the canonical ensemble and to compare classical analytical solutions with the corresponding semiclassical ones. We determine a strong compatibility of these affine black holes with the thermodynamical properties of the classical counterparts, with only minor restrictions on the free parameters of the model…
Quantum field theory in a semiclassical background can be derived as an approximation to quantum gravity from a weak-coupling expansion in the inverse Planck mass. Such an expansion is studied for evolution on "nice-slices" in the spacetime describing a black hole of mass M. Arguments for a breakdown of this expansion are presented, due to significant gravitational coupling between fluctuations, which is consistent with the statement that existing calculations of information loss in black holes are not reliable. For a given fluctuation, the coupling to subsequent fluctuations becomes of order …
We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, $ω^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun's equation, and we find that the charge as well as the energy must be quantized and state dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun's equation.
Regarding the significant interests in massive gravity and combining it with gravity's rainbow and also BTZ black holes, we apply the formalism introduced by Jiang and Han in order to investigate the quantization of the entropy of black holes. We show that the entropy of BTZ black holes in massive gravity's rainbow is quantized with equally spaced spectra and it depends on the black holes' properties including massive parameters, electrical charge, the cosmological constant and also rainbow functions. In addition, we show that quantization of the entropy results into the appearance of novel pr…
Canonical quantization of local field theories is classical black hole spacetimes with a single horizon leads to a particle number density with a thermal distribution in equilibrium at the Hawking temperature. A complete treatment including non-local quantum gravity effects has shown however that the full "thermal vacuum" of the theory is the false vacuum. In this work we find the true vacuum consistent with the complete semiclassical analysis of quantum black holes. The theory is described by a "microcanonical" quantum field theory with fixed energy E = M, the mass of the black hole. Consider…
We analyze a potential that produces background charges which are automatically quantized. This introduces a new mechanism for charge quantization, although so far it has only been implemented for background charges. We show that this same mechanism can also lead to an alternative means of hiding extra dimensions that is analogous to the Kaluza-Klein approach.
Ever since the pioneer works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is {\it not} quantized in equ…
We present an exact operator quantization of the Euclidean Black Hole CFT using a recently established free field parametrization of the fundamental fields of the classical theory [4,5,6,7]. Quantizing the map to free fields, we show that the resulting quantum fields are causal and transform as covariant fields w.r.t. the Virasoro algebra. We construct the reflection operator of the quantum theory and demonstrate its unitarity. We furthermore discuss the W-algebra of the Euclidean Black Hole model. It turns out that unitarity of the reflection operator is a simple consequence of the fact that …
2+1-dimensional Anti-deSitter gravity is quantized in the presence of an external scalar field. We find that the coupling between the scalar field and gravity is equivalently described by a perturbed conformal field theory at the boundary of AdS_3. We derive the explicit form of this coupling, which allows us to perform a microscopic computation of the transition rates between black hole states due to absorption and induced emission of the scalar field. Detailed thermodynamic balance then yields Hawking radiation as spontaneous emission, and we find agreement with the semiclassical result, inc…
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…
