Bound states of spin-half particles in a static gravitational field close to the black hole field

Abstract

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.

arXiv comment16 pages, 6 Figures. Submitted to General Relativity and Gravitation

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Cited by in corpus (2)

• Resonance scattering and the passage to bound states in the field of near-black-hole objects
• Dense spectrum of resonances and spin-1/2 particle capture in a near-black-hole metric