# Quantum properties of the Dirac field on BTZ black hole backgrounds - Mathematical Physics

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Abstract: We consider a Dirac field on a $1 + 2$-dimensional uncharged BTZ black holebackground. We first find out the Dirac Hamiltonian, and study itsself-adjointness properties. We find that, in analogy to the Kerr-Newman-AdSDirac Hamiltonian in $1+3$ dimensions, essential self-adjointness on$C 0^{\infty}r +,\infty^2$ of the reduced radial Hamiltonian is implementedonly if a suitable relation between the mass $\mu$ of the Dirac field and thecosmological radius $l$ holds true. The very presence of a boundary-likebehaviour of $r=\infty$ is at the root of this problem. Also, we determine in acomplete way qualitative spectral properties for the non-extremal case, forwhich 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 forthe $1 + 2$-dimensional uncharged BTZ black hole. Unlike the correspondingstationary four-dimensional solutions, the formal treatment of the levelcrossing mechanism is much simpler. We find that, even in the extremal case, nolevel crossing takes place. Therefore, no quantum loss of angular momentum viaparticle pair production is allowed.

Author: ** Francesco Belgiorno, Sergio L Cacciatori, Francesco Dalla Piazza, Oliver F Piattella**

Source: https://arxiv.org/