Extending [1], 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-Nordström black hole background must be equal to that of a (1 + 1) dimensional blackbody at the Hawking temperature with the appropriate chemical potential.

This is an extended version of our previous letter [1]. In this paper we consider rotating black holes and show that the flux of Hawking radiation can be determined by anomaly cancellation conditions and regularity requirement at the horizon. By using a dimensional reduction technique, each partial wave of quantum fields in a d = 4 rotating black hole background can be interpreted as a (1 + 1)-dimensional charged field with a charge proportional to the azimuthal angular momentum m. From this and the analysis [2] [1] on Hawking radiation from charged black holes, we show that the total flux of Hawking radiation from rotating black holes can be universally determined in terms of the values of anomalies at the horizon by demanding gauge invariance and general coordinate covariance at the quantum level. We also clarify our choice of boundary conditions and show that our results are consistent with the effective action approach where regularity at the future horizon and vanishing of ingoing modes at r = ∞ are imposed (i.e. Unruh vacuum).

It is well known that the perturbation equations of massless fields for the Kerr-de Sitter geometry can be written in the form of separable equations. The equations have five definite singularities, so it has been thought that their analysis would be difficult. We show that these equations can be transformed into Heun's equations, for which we are able to use a known technique to analyze solutions. We reproduce known results for the Kerr geometry and de Sitter geometry in the confluent limits of Heun's functions. Our analysis can be extended to Kerr-Newman-de Sitter geometry for massless fields with spin 0 and ~. §1. IntroductionOne of the most non-trivial aspects of the perturbation equations for Kerr geometry is the separability of the radial and the angular parts. Carter 1) first found that the scalar wave function is separable in the Kerr-Newman-de Sitter geometries. Later, this observation was extended for spin 1/2, electromagnetic fields, gravitational perturbations and gravitinos for the Kerr geometries and even for the Kerr-de Sitter class of geometries. These perturbation equations are called Teukolsky equations. 2 ) Except for electromagnetic and gravitational perturbations, the separability persists even for the Kerr-Newman-de Sitter solutions. An important application of this fact is the proof of the stability of the Kerr black hole. 3) Though the Teukolsky equations for Kerr geometries are separable, both spheroidal and radial equations have two regular singularities and one irregular singularity, so that the solutions cannot be written in a single form of any special functions, but they can be expressed as a series of special functions whose coefficients satisfy three term recurrence relations. 4) -7) The solution of the angular equation is expressed in the form of a series of Jacobi functions. 4 ) The solution of the radial equation is rather complicated, because we need a solution which is valid in the entire region extending from the outer horizon to infinity. The solutions are written in the form of a series of confluent hypergeometric functions 5) which are convergent around infinity and hypergeometric functions 6), 7) which are convergent around the outer horizon. By matching these solutions in the region where both solutions are convergent, we can obtain a solution which is valid from the outer horizon to infinity. 6)-8) The great benefit of this kind of solution is that the coefficients of the series are obtained through the post Minkowskian expansion. 6), 7) This technique has been *)

Quantum fields near black hole horizons can be described in terms of an infinite set of d 2 conformal fields. In this paper, by investigating transformation properties of general higher-spin currents under a conformal transformation, we reproduce the thermal distribution of Hawking radiation in both cases of bosons and fermions. As a by-product, we obtain a generalization of the Schwarzian derivative for higherspin currents.

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 [1] [2]. 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 [3]