Particle creation by loop black holes

We study the black hole particle production in a regular spacetime metric obtained in a minisuperspace approach to loop quantum gravity. In different previous papers the static solution was obtained and shown to be singularity-free and self-dual. In this paper expanding a previous study of the black hole dynamics we repeat the Hawking analysis which leads to a thermal flux of particles at the future infinity. The evaporation time is infinite and the unitarity is recovered due to the regularity of the spacetime and to the characteristic behavior of the surface gravity.     

Particle creation by charged black holes

A simple derivation is given for the leading term (n=1) in the Schwinger formula for the pair creation by a constant electric field. The same approach is applied then to the charged particle production by a charged black hole. In this case, as distinct from that of a constant electric field, the probability of the charged particle production depends essentially on the particle energy. The production rate by black holes is found in the nonrelativistic and ultrarelativistic limits. The range of values for the mass and charge of a black hole is indicated where the discussed mechanism of radiation dominates the Hawking one.     

On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.