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.

arXiv comment19 pages; IOP style

References in corpus (18)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Dirac particles tunneling from BTZ black hole
• Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry
• The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry
• Spectral Analysis of Radial Dirac Operators in the Kerr-Newman Metric and its Applications to Time-periodic Solutions
• Quantum singularities in the BTZ spacetime
• The Dirac propagator in the Kerr-Newman metric
• Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry
• Quantum properties of the electron field in Kerr-Newman black hole manifolds
• The Dirac Equation in Kerr-Newman-AdS Black Hole Background
• 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
• Quantum instability for charged scalar particles on charged Nariai and ultracold black hole manifolds
• Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background
• Pair-production of charged Dirac particles on charged Nariai and ultracold black hole manifolds

Cited by in corpus (3)

• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• Quantum tunneling from rotating black holes with scalar hair in three dimensions
• Logarithmic quasinormal modes of a spin-3 field around the BTZ black hole