We take the method of anomaly cancellation for the derivation of Hawking radiation initiated by Robinson and Wilczek, and apply it to the non-extremal five-dimensional D1-D5 black hole in string theory. The fluxes of the electric charge flow and the energy-momentum tensor from the black hole are obtained. They are shown to match exactly with those of the two-dimensional black body radiation at the Hawking temperature.
I derive the Hawking flux from black holes of constant negative curvature and from a black hole of constant negative curvature conformally coupled to a scalar field, using the covariant gravitational anomalies method.
We apply the method of Banerjee and Kulkarni (arXiv:0707.2449, [hep-th]) to provide a derivation of Hawking radiation from the GHS (stringy) blackhole which falls in the class of the most general spherically symmetric blackholes ($\sqrt{-g}\neq 1$) and also the non-extremal $D1-D5$ blackhole using only covariant gravitational anomalies.
In this paper we obtain the flux of Hawking radiation from Rotating BTZ black holes from gauge and gravitational anomalies point of view. Then we show that the gauge and gravitational anomaly in the BTZ spacetime is cancelled by the total flux of a 2-dimensional blackbody at the Hawking temperature of the spacetime.
The issue concerning semi-classical methods recently developed in deriving the conditions for Hawking radiation as tunneling, is revisited and applied also to rotating black hole solutions as well as to the extremal cases. It is noticed how the tunneling method fixes the temperature of extremal black hole to be zero, unlike the Euclidean regularity method that allows an arbitrary compactification period. A comparison with other approaches is presented.
We adopt the covariant anomaly cancellation method as well as the effective action approach to obtain the Hawking radiation from the Reissner-Nordström blackhole with a global monopole falling in the class of the most general spherically symmetric charged blackhole $(\sqrt{-g}\neq1)$, using only covariant boundary condition at the event horizon.
A new method has been developed recently to derive Hawking radiations from black holes based on considerations of gravitational and gauge anomalies at the horizon gr-qc/0502074 hep-th/0602146. In this paper, we apply the method to Myers-Perry black holes with multiple angular momenta in various dimensions by using the dimensional reduction technique adopted in the case of four-dimensional rotating black holes hep-th/0606018.
We complete the analysis started in [arXiv:0804.0198] of the Hawking radiation calculated by means of anomaly techniques. We concentrate on a static radially symmetric BH, reduced to two dimensions. We compare the two methods used to derive the integrated Hawking radiation, based on the trace and diffeomorphism anomaly, respectively, and show that they can be reduced to the same basic elements. We then concentrate on higher moments of the Hawking radiation and on higher spin currents, and show that, similarly to trace anomalies, also diffeomorphism anomalies are absent from the conservation la…
Hawking radiation is obtained from the Reissner-Nordström blackhole with a global monopole and the Garfinkle-Horowitz-Strominger blackhole falling in the class of the most general spherically symmetric blackholes $(\sqrt{-g}\neq1)$, using only chiral anomaly near the event horizon and covariant boundary condition at the event horizon. The approach differs from the anomaly cancellation approach since apart from the covariant boundary condition, the chiral anomaly near the horizon is the only input to derive the Hawking flux.
Starting from the chiral covariant effective action approach of Banerjee and Kulkarni [Phys. Lett. B 659, 827(2008)], we provide a derivation of the Hawking radiation from a charged black hole in the presence of gravitational back reaction. The modified expressions for charge and energy flux, due to effect of one loop back reaction are obtained.
We apply the "trace anomaly method" to the calculation of moments of the Hawking radiation of a Schwarzschild black hole. We show that they can be explained as the fluxes of chiral currents forming a W-infinity algebra. Then we construct the covariant version of these currents and verify that up to order 6 they are not affected by any trace anomaly. Using cohomological methods we show that actually, for the fourth order current, no trace anomalies can exist. The results reported here are strictly valid in two dimensions.
Robinson and Wilczek suggested a new method of deriving Hawking radiation by the consideration of anomalies. The basic idea of their approach is that the flux of Hawking radiation is determined by anomaly cancellation conditions in the Schwarzschild black hole (BH) background. Iso et al. extended the method to a charged Reissner-Nordstroem BH and a rotating Kerr BH, and they showed that the flux of Hawking radiation can also be determined by anomaly cancellation conditions and regularity conditions of currents at the horizon. Their formulation gives the correct Hawking flux for all the cases a…
We review some results on the connection among supergravity central charges, BPS states and Bekenstein-Hawking entropy. In particular, N=2 supergravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N=8 case when one half of supersymmetry is preserved. We stress the fact that for extremal supergravity black holes the entropy formula is topological, that is the entropy turns out to be a moduli independent quantity and can be written in terms of invariants of the duality group of the supergravi…
We apply the covariant anomaly cancellation method to compute the Hawking fluxes from the event and cosmic horizons of the Schwarzschild-de Sitter black hole. The derivation is new from the existing ones as we split the space in three different regions (near to and away from the event and cosmic horizons) and write down the covariant energy-momentum tensor using three step functions which covers the whole region leading elegantly to the conditions required to compute the Hawking fluxes from the event and cosmic horizons.
In an insightful approach, Robinson and Wilczek proposed that Hawking radiation can be obtained as the compensation of a breakdown of general covariance and gauge invariance and the radiation is a black body radiation at Hawking temperature. We apply this method to two types of black holes in three dimensional spacetime, which share the general form of the metric in that the $tt$ component of the metric is not inverse of the $rr$ component of the metric. First one is the warped $AdS_3$ black hole in three dimensional topologically massive gravity with negative cosmological constant, and second…
It is believed that extremal black holes do not emit Hawking radiation as understood by taking extremal limits of non-extremal black holes. However, it is debated whether one can make such conclusion reliably starting from an extremal black hole, as the associated Bogoliubov coefficients which relate ingoing and outgoing field modes do not satisfy the required consistency condition. We address this issue in a canonical approach firstly by presenting an exact canonical derivation of the Hawking effect for non-extremal Kerr black holes. Subsequently, for extremal Kerr black holes we show that th…
Generalising the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.
We derive Hawking radiation of 5-dimensional black rings from gauge and gravitational anomalies using the method proposed by Robinson and Wilczek. We find as in the black hole case, the problem could reduce to a (1+1) dimensional field theory and the anomalies result in correct Hawking temperature for neutral,dipole and charged black rings.
We complete the analysis carried out in previous papers by studying the Hawking radiation for a Kerr black-hole carried to infinity by fermionic currents of any spin. We find agreement with thermal spectrum of the Hawking radiation for fermionic degrees of freedom. We start by showing that the near-horizon physics for a Kerr black-hole is approximated by an effective two-dimensional field theory of fermionic fields. Then, starting from 2d currents of any spin that form a W(1+infinity) algebra, we construct an infinite set of covariant currents, each of which carry the corresponding moment of t…
We study the Hawking radiation from Rotating black holes from gravitational anomalies point of view. First, we show that the scalar field theory near the Kerr black hole horizon can be reduced to the 2-dimensional effective theory. Then, following Robinson and Wilczek, we derive the Hawking flux by requiring the cancellation of gravitational anomalies. We also apply this method to Hawking radiation from higher dimensional Myers-Perry black holes. In the Appendix, we present the trace anomaly derivation of Hawking radiation to argue the validity of the boundary condition at the horizon.
We give a higher-spin generalization of the anomaly method for the Hawking radiation from black holes. In the paper arXiv:0710.0453 higher-spin generalizations of the gauge (and gravitational) anomalies in d=2 were obtained. By applying these anomalies to black hole physics, we derive the higher moments of the Hawking fluxes. We also give a higher-spin generalization of the trace anomaly method by Christensen and Fulling.
We study the method of calculating the Hawking radiation via gravitational anomalies in gravitational backgrounds of constant negative curvature. We apply the method to topological black holes and also to topological black holes conformally coupled to a scalar field.
The relationship between Hawking radiation emitted by non extremal and extremal Reissner Nordstrom black holes is critically analyzed. A careful study of a series of regular collapsing geometries reveals that the stress energy tensor stays regular in the extremal limit and is smoothly connected to that of non extremal black holes. The unexpected feature is that the late time transients which played little role in the non extremal case are necessary to preserve the well defined character of the flux in the extremal case. The known singular behavior of the static energy density of extremal black…
Hawking radiation is obtained from anomalies resulting from a breaking of diffeomorphism symmetry near the event horizon of a black hole. Such anomalies, manifested as a nonconservation of the energy momentum tensor, occur in two different forms -- covariant and consistent. The crucial role of covariant anomalies near the horizon is revealed since this is the {\it only} input required to obtain the Hawking flux, thereby highlighting the universality of this effect. A brief description to apply this method to obtain thermodynamic entities like entropy or temperature is provided.
We extend the work by S. Iso, H. Umetsu and F. Wilczek [Phys. Rev. Lett. 96 (2006) 151302] to derive the Hawking flux via gauge and gravitational anomalies of a most general two-dimensional non-extremal black hole space-time with the determinant of its diagonal metric differing from the unity ($\sqrt{-g} \neq 1$) and use it to investigate Hawking radiation from the Reissner-Nordstrom black hole with a global monopole by requiring the cancellation of anomalies at the horizon. It is shown that the compensating energy momentum and gauge fluxes required to cancel gravitational and gauge anomalies …
We discuss how long strings can arise at the stretched horizon and how they can account for the Bekenstein-Hawking entropy. We use the thermal scalar field theory to derive the asymptotic density of states and corresponding stress tensor of a microcanonical long string gas in Rindler space. We show that the equality of the Hagedorn and Hawking temperatures gives rise to the tree-level entropy of large black holes in accordance with the Bekenstein-Hawking-Wald formula.
We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS$_4$ electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to comp…
We show that in order to avoid a breakdown of general covariance at the quantum level the total flux in each outgoing partial wave of a quantum field in a black hole background must be equal to that of a (1+1)-dimensional blackbody at the Hawking temperature.
In this paper we investigate the effects of gravitational backreaction for the late time Hawking radiation of evaporating near-extremal black holes. This problem can be studied within the framework of an effective one-loop solvable model on AdS_2. We find that the Hawking flux goes down exponentially and it is proportional to a parameter which depends on details of the collapsing matter. This result seems to suggest that the information of the initial state is not lost and that the boundary of AdS_2 acts, at least at late times, as a sort of stretched horizon in the Reissner-Nordstrom spacetim…
Recently a method has been developed for relating four dimensional Schwarzschild black holes in M-theory to near-extremal black holes in string theory with four charges, using suitably defined ``boosts'' and T-dualities. We show that this method can be extended to obtain the emission rate of low energy massless scalars for the four dimensional Schwarzschild hole from the microscopic picture of radiation from the near extremal hole.
We consider Callan, Giddings, Harvey and Strominger's (CGHS) two dimensional dilatonic gravity with electromagnetic interactions. This model can be also solved classically. Among the solutions describing static black holes, there exist extremal solutions which have zero temperatures. In the extremal solutions, the space-time metric is not singular. We also obtain the solutions describing charged matter (chiral fermions) collapsing into black holes. Through the collapsing, not only future horizon but past horizon is also shifted. The quantum corrections including chiral anomaly are also discuss…
We discuss the string creation in the near-extremal NS1 black string solution. The string creation is described by an effective field equation derived from a fundamental string action coupled to the dilaton field in a conformally invariant manner. In the non-critical string model the dilaton field causes a timelike mirror surface outside the horizon when the size of the black string is comparable to the Planck scale. Since the fundamental strings are reflected by the mirror surface, the negative energy flux does not propagate across the surface. This means that the evaporation stops just befor…
Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is availa…
We comment on the consistence of the epsilon anti-symmetric tensor adopted in [R. Banerjee and S. Kulkarni, arXiv:0707.2449] when it is generalized in the general case where $\sqrt{-g} \neq 1$. It is pointed out that the correct non-minimal consistent gauge and gravitational anomalies should by multiplied a factor $\sqrt{-g} \neq 1$. We also sketch the generalization of their work to the $\sqrt{-g} \neq 1$ case.
We revisit the Schwinger effect in de Sitter, anti-de Sitter spaces and charged black holes, and explore the interplay between quantum electrodynamics and the quantum gravity effect at one-loop level. We then advance a thermal interpretation of the Schwinger effect in curved spacetimes. Finally, we show that the Schwinger effect in a near-extremal black hole differs from Hawking radiation of charged particles in a non-extremal black hole and is factorized into those in an anti-de Sitter space and a Rindler space with the surface gravity for acceleration.
It is well known that extremal black holes do not Hawking radiate, which is usually realized by taking an extremal limit from the nonextremal case. However, one cannot perceive the same phenomenon using the Bogoliubov transformation method starting from an extremal black hole itself, i.e., without the limiting case consideration. In that case, the Bogoliubov coefficients do not satisfy the required normalization condition. In canonical formulation, which closely mimics the Bogoliubov transformation method, one can consistently reproduce the vanishing number density of Hawking quanta for an ext…
Extending gr-qc/0502074, we show that in order to avoid a breakdown of general covariance and gauge invariance at the quantum level the total flux of charge and energy in each outgoing partial wave of a charged quantum field in a Reissner-Nordstrom black hole background must be equal to that of a (1+1) dimensional blackbody at the Hawking temperature with the appropriate chemical potential.
Robinson-Wilczek's recent work, which treats Hawking radiation as a compensating flux to cancel gravitational anomaly at the horizon of a Schwarzschild-type black hole, is extended to study Hawking radiation of rotating black holes in anti-de Sitter spaces, especially that in dragging coordinate system, via gauge and gravitational anomalies. The results show that in order to restore gauge invariance and general coordinate covariance at the quantum level in the effective field theory, the charge and energy flux by requiring to cancel gauge and gravitational anomalies at the horizon, must have a…
We derive the Bekenstein-Hawking entropy formula for four and five dimensional non-supersymmetric black holes (which include the Schwarzchild ones) by counting microscopic states. This is achieved by first showing that these black holes are U-dual to the three-dimensional black hole of Banados-Teitelboim-Zanelli and then counting microscopic states of the latter following Carlip's approach. Higher than five dimensional black holes are also considered. We discuss the connection of our approach to the D-brane picture.
The Hawking Beckenstein entropy of near extremal fivebranes is calculated in terms of a gas of strings living on the fivebrane. These fivebranes can also be viewed as near extremal black holes in five dimensions.
We substantiate the Hawking radiation as quantum tunneling of fields or particles crossing the horizon by using the Rindler coordinate. The thermal spectrum detected by an accelerated particle is interpreted as quantum tunneling in the Rindler spacetime. Representing the spacetime near the horizon locally as a Rindler spacetime, we find the emission rate by tunneling, which is expressed as a contour integral and gives the correct Boltzmann factor. We apply the method to non-extremal black holes such as a Schwarzschild black hole, a non-extremal Reissner-Nordström black hole, a charged Kerr bla…
We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.
We carry out a thorough survey of entropy for a large class of $p$-branes in various dimensions. We find that the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the non-dilatonic $p$-branes, those with the dilaton constant throughout spacetime. The entropy of extremal non-dilatonic $p$-branes is non-vanishing only for the solutions preserving 1/8 of the original supersymmetries. Upon toroidal compactification these reduce to dyonic black holes in 4 and 5 dimensions. For the self-dual string in 6 dimensions, which preserves 1/4 of the original supersymmetr…
String theory is used to count microstates of four-dimensional extremal black holes in compactifications with $N=4$ and $N=8$ supersymmetry. The result agrees for large charges with the Bekenstein-Hawking entropy.
Motivated by the Robinson-Wilczek's recent viewpoint that Hawking radiation can be treated as a compensating energy momentum tensor flux required to cancel gravitational anomaly at the horizon of a Schwarzschild-type black hole, we investigate Hawking radiation from the rotating $(2+1)$-dimensional BTZ black hole and the charged $(2+1)$-dimensional BTZ black hole, via cancellation of gauge and gravitational anomalies at the horizon. To restore gauge invariance and general coordinate covariance at the quantum level, one must introduce the corresponding gauge current and energy momentum tensor f…
Motivated by the success of the recently proposed method of anomaly cancellation to derive Hawking fluxes from black hole horizons of spacetimes in various dimensions, we have further extended the covariant anomaly cancellation method shortly simplified by Banerjee and Kulkarni to explore the Hawking radiation of the (3+1)-dimensional charged rotating black strings and their higher dimensional extensions in anti-de Sitter spacetimes, whose horizons are not spherical but can be toroidal, cylindrical or planar, according to their global identifications. It should be emphasized that our analysis …
The anomaly cancelation method proposed by Wilczek et al. is applied to the black holes of topologically massive gravity (TMG) and topologically massive gravito-electrodynamics (TMGE). Thus the Hawking temperature and fluxes of the ACL and ACGL black holes are found. The Hawking temperatures obtained agree with the surface gravity formula. Both black holes are rotating and this gives rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. It is found that the terms in this U(1) gauge field correspond exactly to the correct angular velocities on the …
A six-dimensional black string is considered and its Bekenstein-Hawking entropy computed. It is shown that to leading order above extremality, this entropy precisely counts the number of string states with the given energy and charges. This identification implies that Hawking decay of the near-extremal black string can be analyzed in string perturbation theory and is perturbatively unitary.
Considering anomalies of quantum field in the (1+1)-dimensional Achucarro-Ortiz black hole background, the stress tensor near and out of the horizon is calculated, meanwhile, the relationship between anomalies and Hawking radiation of the black hole is discussed.
Entropy for two dimensional extremal black holes is computed explicitly in a finite-space formulation of the black hole thermodynamics and is shown to be zero {\it locally}. Our results are in conformity with the recent one by Hawking et al in four dimensions.
Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS$_4$ Black Holes
International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences (UCAS)（国际理论物理中心亚太分中心，中国科学院大学）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论研究中心）；Leinweber Institute for Theoretical Physics, University of Michigan（莱因韦伯理论物理研究所，密歇根大学）
Quantum-Corrected Hawking Radiation from Near-Extremal Kerr-Newman Black Holes
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；University of Science and Technology of China（中国科学技术大学）；University of Michigan（密歇根大学）；The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆理论物理国际中心）
Based on the anomaly cancellation method we are going to compute the Hawking fluxes (the Hawking thermal flux and the total flux of energy-momentum tensor) from a four-dimensional rotating regular black hole with a time-delay. To this purpose, in the three metrics proposed in arXiv:1510.08828, we try to perform the dimensional reduction in which the anomaly cancellation method is feasible at the near-horizon region in a general scalar field theory. As a result we can demonstrate that the dimensional reduction is possible in two of those metrics. Hence we perform the anomaly cancellation method…
Recently, Hawking radiation from a Schwarzschild-type black hole via gravitational anomaly at the horizon has been derived by Robinson and Wilczek. Their result shows that, in order to demand general coordinate covariance at the quantum level to hold in the effective theory, the flux of the energy momentum tensor required to cancel gravitational anomaly at the horizon of the black hole, is exactly equal to that of (1+1)-dimensional blackbody radiation at the Hawking temperature. In this paper, we attempt to apply the analysis to derive Hawking radiation from the event horizons of static, spher…
The fuzzball proposal says that the information of the black hole state is distributed throughout the interior of the horizon in a `quantum fuzz'. There are special microstates where in the dual CFT we have `many excitations in the same state'; these are described by regular classical geometries without horizons. Jejjala et.al constructed non-extremal regular geometries of this type. Cardoso et. al then found that these geometries had a classical instability. In this paper we show that the energy radiated through the unstable modes is exactly the Hawking radiation for these microstates. We do …
We have learnt that the Bekenstein-Hawking entropy of supersymmetric black holes in five-dimensional minimal supergravity can be reproduced from microstate counting via the AdS/CFT and Kerr/CFT correspondence. In this note, we demostrate the coincidence of both formalisms for extremal and near-extremal black holes in five-dimensional minimal supergravity. Connection to AdS_2 gravity is also mentioned.
Motivated by the universality of Hawking radiation and that of the anomaly cancellation technique as well as that of the effective action method, we investigate the Hawking radiation of a Schwarzschild black hole in the isotropic coordinates via the cancellation of gravitational anomaly. After performing a dimensional reduction from the four-dimensional isotropic Schwarzschild metric, we show that this reduction procedure will, in general, result in two classes of two-dimensional effective metrics: the conformal equivalent and the inequivalent ones. For the physically equivalent class, the two…
We explore the method of Robinson and Wilczek for deriving the Hawking temperature of a black hole. In this method, the Hawking radiation restores general covariance in an effective theory of near-horizon physics which otherwise exhibits a gravitational anomaly at the quantum level. The method has been shown to work for broad classes of black holes in arbitrary spacetime dimensions. These include static black holes, accreting or evaporating black holes, charged black holes, rotating black holes, and even black rings. In the case of charged and rotating black holes, the expected super-radiant c…
