In this paper we derive Hawking radiation of black holes with higher derivative corrections by the method of trace anomaly. Firstly we derive Hawking radiation for general spherical black holes. We introduce a modified tortoise coordinate to it and find the analyticity of the coordinate. Secondly we apply its method to a black hole with a higher derivative correction and derive the Hawking radiation of it. We found that as an ordinary case the flux depends only on the surface gravity.
The Hawking radiation from the three dimensional rotating acoustic black hole is considered from the viewpoint of anomaly cancellation method initiated by Robinson and Wilczek. Quantum field near the horizon is effectively described by two dimensional charged field with a charge identified as the angular momentum m. The fluxes of charge and energy are obtained from the anomaly cancellation condition and regularity at the horizon, and are shown to match with those of the two dimensional black body radiation at the Hawking temperature.
The universal behavior of Hawking radiation is originated in the conformal symmetries of matter fields near the black hole horizon. We explain the origin of this universality based on (1) the gravitational anomaly and its higher-spin generalizations and (2) conformal transformation properties of fluxes.
The Casimir energy for massless scalar field of two parallel conductor, in two dimensional Schwarzchild black hole background, with Dirichlet boundary conditions is calculated by making use of general properties of renormalized stress tensor. We show that vacuum expectation value of stress tensor can be obtain by Casimir effect, trace anomaly and Hawking radiation. Four-dimensional of this problem, by this method, is under progress by this author.
We construct the theory of 2d dilatonic supergravity(SG) with matter and dilaton supermultiplets coupled to dilaton functions. Trace anomaly and induced effective action for matter supermultiplet are calculated (what gives also large-N effective action for dilatonic SG). Study of black holes and Hawking radiation which turns out to be zero in supersymmetric CGHS model with dilaton coupled matter is presented. In the same way one can study spherically symmetric collapse for other 4d SG using simplified 2d approach.
We apply Wilczek and his collaborators' anomaly cancellation approach to the 3-dimensional Schwarzschild- and BTZ-like brane world black holes induced by the generalized C metrics in the Randall-Sundrum scenario. Based on the fact that the horizon of brane world black hole will extend into the bulk spacetime, we do the calculation from the bulk generalized C metrics side and show that this approach also reproduces the correct Hawking radiation for these brane world black holes. Besides, since this approach does not involve the dynamical equation, it also shows that the Hawking radiation is onl…
Considering gravitational and gauge anomalies at the horizon, a new successful method that to derive Hawking radiations from black holes has been developed recently by Wilczek et al.. By using the dimensional reduction technique, we apply this method to a non-vacuum solution, the 2+1 dimensional spinning black hole. The Hawking temperature and angular velocity on the horizon are obtained. The results may partially imply that this method is independent of the gravity theory, the dimension of spacetime and the topological structure of the event horizon.
We investigate the Hawking radiation of black $p$-branes of superstring theories using the method of anomaly cancelation, specially, we use the method of [S. Iso, H. Umetsu and F. Wilczek, {\sl Phys. Rev. Lett.} {\bf 96}, 151302 (2006); {\sl Phys. Rev. D} {\bf 74}, 044017 (2006)]. The metrics of black $p$-branes are spherically symmetric, but not the Schwarzschild type. In order to simplify the calculation, we first make a coordinate transformation to transform the metric to the Schwarzschild type. Then we calculate its energy-momentum flux from the method of anomaly cancelation of the above m…
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.
Considering gravitational and gauge anomalies at the horizon, a new method that to derive Hawking radiations from black holes has been developed by Wilczek et al. In this paper, we apply this method to non-rotating and rotating Kaluza-Klein black holes with squashed horizon, respectively. For the rotating case, we found that, after the dimensional reduction, an effective U(1) gauge field is generated by an angular isometry. The results show that the gauge current and energy-momentum tensor fluxes are exactly equivalent to Hawking radiation from the event horizon.
The method of anomaly cancellation to derive Hawking radiation initiated by Robinson and Wilczek is applied to 2+1 dimensional stationary black holes. Using the dimensional reduction technique, we find that the near-horizon physics for the fermionic field in the background of the general 2+1 dimensional stationary black hole can be approximated by an infinite collection of two component fermionic fields in 1+1 dimensional spacetime background coupled with dilaton field and U(1) gauge field. By restoring the gauge invariance and the general coordinate covariance for the reduced two dimensional …
We discuss an ambiguity of the derivation of the Hawking radiation through the gravitational anomaly method and propose modifications of this method such that it reproduces the correct thermal fluxes. In this modified gravitational anomaly method, we employ the two-dimensional conformal field theory technique.
The role of chirality is discussed in unifying the anomaly and the tunneling formalisms for deriving the Hawking effect. Using the chirality condition and starting from the familiar form of the trace anomaly, the chiral (gravitational) anomaly, manifested as a nonconservation of the stress tensor, near the horizon of a black hole, is derived. Solution of this equation yields the stress tensor whose asymptotic infinity limit gives the Hawking flux. Finally, use of the same chirality condition in the tunneling formalism gives the Hawking temperature that is compatible with the flux obtained by a…
Recently, Banerjee and Kulkarni (R. Banerjee, S. Kulkarni, arXiv:0707.2449 [hep-th]) suggested that it is conceptually clean and economical to use only the covariant anomaly to derive Hawking radiation from a black hole. Based upon this simplified formalism, we apply the covariant anomaly cancellation method to investigate Hawking radiation from a modified Schwarzschild black hole in the theory of rainbow gravity. Hawking temperature of the gravity's rainbow black hole is derived from the energy-momentum flux by requiring it to cancel the covariant gravitational anomaly at the horizon. We stre…
In order to understand a boundary description of Hawking radiation in the AdS/CFT correspondence, we investigate the trace anomaly method in AdS$_2$ space. In this method, Hawking radiation is derived from the trace anomaly of the energy-momentum tensor in the bulk. We find a correspondence between the energy-momentum tensor and a composite operator in CFT$_1$ and understand the anomalous properties of the energy-momentum tensor in terms of this composite operator. By using this correspondence, we reproduce Hawking radiation from the boundary description. In addition, we find a correspondence …
The quantum stress tensor in the Unruh state for a conformal scalar propagating in a 4D Schwarzschild black hole spacetime is reconstructed in its leading behaviour at infinity and near the horizon by means of an effective action derived by functionally integrating the trace anomaly.
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.
Black hole solutions in the context of a generic matter-coupled two-dimensional dilaton gravity theory are discussed both at the classical and semiclassical level. Starting from general assumptions, a criterion for the existence of black holes is given. The relationship between conformal anomaly and Hawking radiation is extended to a broad class of two-dimensional dilaton gravity models. A general and simple formula relating the magnitude of the Hawking effect to the dilaton potential evaluated on the horizon is derived.
Hawking flux from the Schwarzschild black hole with a global monopole is obtained by using Robinson and Wilczek's method. Adopting a dimension reduction technique, the effective quantum field in the (3+1)--dimensional global monopole background can be described by an infinite collection of the (1+1)--dimensional massless fields if neglecting the ingoing modes near the horizon, where the gravitational anomaly can be cancelled by the (1+1)--dimensional black body radiation at the Hawking temperature.
We investigate the classical and semiclassical features of generic 2D, matter-coupled, dilaton gravity theories. In particular, we show that the mass, the temperature and the flux of Hawking radiation associated with 2D black holes are invariant under dilaton-dependent Weyl rescalings of the metric. The relationship between quantum anomalies and Hawking radiation is discussed.
We show that the diffeomorphism anomaly together with the trace anomaly reveal a chiral Virasoro algebra near the event horizon of a black hole. This algebra is the same irrespective of whether the anomaly is covariant or consistent, thereby manifesting its universal character and the fact that only the outgoing modes are relevant near the horizon. Our analysis therefore clarifies the role of the trace anomaly in the diffeomorphism anomaly approach \cite{wilczek, isowilczek, shailesh, shailesh2, sunandan, sunandan10, rabin10} to the Hawking radiation.
We study the Hawking radiation of the spherically symmetric, asymptotically flat black holes in the infrared modified Horava-Lifshitz gravity by applying the methods of covariant anomaly cancellation and effective action, as well as the approach of Damour-Ruffini-Sannan's. These black holes behave as the usual Schwarzschild ones of the general relativity when the radial distance is very large. We also extend the method of covariant anomaly cancellation to derive the Hawking temperature of the spherically symmetric, asymptotically AdS black holes that represent the analogues of the Schwarzschil…
The anomaly cancelation method proposed by Wilczek et al. is applied to the general charged rotating black holes in five-dimensional minimal gauged supergravity. Thus Hawking temperature and fluxes are found. The Hawking temperature obtained agrees with the surface gravity formula. The black holes have charge and two unequal angular momenta and these give rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. In particular, it is found that the terms in this U(1) gauge field correspond exactly to the correct electrostatic potential and the two angu…
This paper has been withdrawn by the authors due to an incorrect statement on the viability of the Robinson-Wilczek method when applied to the case when the metric determinant vanishes at the horizon. This paper has been replaced by arXiv:0803.1338 [hep-th].
The $d$-dimensional scalar field action may be reduced, in the background geometry of a black hole, to a 2-dimensional effective action. In the near horizon region, it appears a gravitational anomaly: the energy-momentum tensor of the scalar field is not conserved anymore. This anomaly is removed by introducing a term related to the Hawking temperature of the black hole. Even if the temperature term introduced is not covariant, a gauge transformation may restore the covariance. We apply this method to compute the temperature of the black hole of the dilatonic non asymptotically flat black hole…
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…
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 study the thermodynamics of Gödel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed time-like curves and the absence of globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, We extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and effecti…
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.
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.
We compute the corrections, using the tunneling formalisim based on a quantum WKB approach, to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawking's original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.
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…
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.
The discrepancy between the anomaly found by Bousso and Hawking (hep-th/9705236) and that of other workers is explained by the omission of a zero mode contribution to the effective action.
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.
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…
I develop the simplest geometric-discretized analogue of two dimensional scalar field theory, which qualitatively reproduces the trace anomaly of the continuous theory. The discrete analogue provides an interpretation of the trace anomaly in terms of a non-trivial transformation of electric-magnetic duality-invariant modes of resistor networks that accommodate both electric and magnetic charge currents.
Despite the finiteness of stress tensor for a scalar field on the four-dimensional Schwarzschild black hole in the Israel-Hartle-Hawking vacuum, the Tolman temperature in thermal equilibrium is certainly divergent on the horizon due to the infinite blueshift of the Hawking temperature. The origin of this conflict is due to the fact that the conventional Tolman temperature was based on the assumption of a traceless stress tensor, which is, however, incompatible with the presence of the trace anomaly responsible for the Hawking radiation. Here, we present an effective Tolman temperature which is…
In this paper, we show the flux of Hawking radiation in a Plebański-Demiański black hole from the point of view of gauge and gravitational anomalies. We will use the consistent anomaly method to guarantee that our results are valid in the de Sitter space. This is because we are including the cosmological constant into our parameters and the covariant anomaly method gives a wrong value for the Hawking temperature. We also show that these calculations are a general result. In order to verify the consistence of our results, we can reproduce earlier known results as certain limiting cases.
We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by the choice of a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin den…
The field-antifield quantization method is used to calculate the trace anomaly for a massless scalar field in a curved background, by means of the zeta function regularization procedure.
It is logically possible that the trace anomaly in four dimension includes the Hirzebruch-Pontryagin density in CP violating theories. Although the term vanishes at free conformal fixed points, we realize such a possibility in the holographic renormalization group and show that it is indeed possible. The Hirzebruch-Pontryagin term in the trace anomaly may serve as a barometer to understand how much CP is violated in conformal field theories.
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.
We use arguments taken from the electrodynamics of media to deduce the QCD trace anomaly from the expression for the vacuum energy in the presence of an external color magnetic field.
We study the trace anomaly of a Weyl fermion in an abelian gauge background. Although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. In particular, we find that it does not contain any odd-parity contribution proportional to the Chern-Pontryagin density. The latter would be allowed by the consistency conditions. We perform our calculations using Pauli-Villars regularization and heat kernel methods. The issue is analogous to the one recently discussed in the literature about a conjectured contribu…
This note is a comment on some recent papers that have raised a controversy about the existence of the odd-parity trace anomaly in a four-dimensional theory of Weyl fermions. Without going into too technical details we explain why the methods employed in those papers cannot detect it.
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 discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with the gravity is given, besides the minimal one, through an external field. This coupling generalizes the conformal anomaly in the same way as those found in recent literature, but with a diferent motivation. The modification to the Hawking radiation is calculated explicity and shows an additional term that introduces a dependence on the (effective) mass of the black-hole.
We present exact analytical black hole solutions with conformal anomaly in AdS space and discuss the thermodynamical properties of these black hole solutions. These black holes can have a positive, zero and negative constant curvature horizon, respectively. For the black hole with a positive constant curvature horizon, there exists a minimal horizon determined by the coefficient of the trace anomaly, the black hole with a smaller horizon is thermodynamically unstable, while it is stable for the case with a larger horizon. The Hawking-Page transition happens in this case. For the black hole wit…
We calculate the total flux of Hawking radiation from Kerr-(anti)de Sitter black holes by using gravitational anomaly method developed in gr-qc/0502074. We consider the general Kerr-(anti)de Sitter black holes in arbitrary $D$ dimensions with the maximal number [D/2] of independent rotating parameters. We find that the physics near the horizon can be described by an infinite collection of $(1+1)$-dimensional quantum fields coupled to a set of gauge fields with charges proportional to the azimuthal angular momentums $m_i$. With the requirement of anomaly cancellation and regularity at the horiz…
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…
Recently a non-supersymmetric conformal field theory with an exactly marginal deformation in the large $N$ limit was constructed by Chaudhuri-Choi-Rabinovici. On a non-supersymmetric conformal manifold, $c$ coefficient of the trace anomaly in four dimensions would generically change. In this model, we, however, find that it does not change at the first non-trivial order given by three-loop diagrams.
The one-loop effective action for a generic set of quantum fields is calculared as a nonlocal expansion in powers of the curvatures (field strengths). This expansion is obtained to third order in the curvature. It is stressed that the covariant vertices are finite. The trace anomaly in four dimensions is obtained directly by varying the effective action. The nonlocal terms in the action, producing the anomaly, contain non-trivial functions of three operator arguments. The trace anomaly is derived also by making the conformal transformation in the heat kernel.
We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off-shell. We then use the gauge independent Vilkovisky-DeWitt effective action to restore gauge independence to the off-shell case. Additionally we explicitly evaluate trace anomalies for some N-sphere background spacetimes.
In the context of the AdS/CFT correspondence, we perform a direct computation in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs involving SO or Sp gauge groups.
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…
