Quantum properties of the Dirac field on BTZ black hole backgrounds

Abstract

We consider a Dirac field on a $(1+2)$-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\infty }(r_{+},\infty {)}^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $\mu$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\infty$ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the $(1+2)$-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.

19 pages; IOP style

References in corpus (6)

• Dirac particles tunneling from BTZ black hole
• Spectral Analysis of Radial Dirac Operators in the Kerr-Newman Metric and its Applications to Time-periodic Solutions
• The Dirac propagator in the Kerr-Newman metric
• Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
• Massive Dirac particles on the background of charged de-Sitter black hole manifolds
• Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background