arXiv subjects

Alejandro Caceres

Publications and source records attributed to Alejandro Caceres.

2 recordsLinked to original sources

arXiv2005

Minimax determination of the energy spectrum of the Dirac equation in a Schwarzschild background

We calculate the bound-state energy spectrum of the Dirac Equation in a Schwarzschild black hole background using a minimax variational method. Our method extends that of Talman to the case of non-Hermitian interactions, such as a black hole. The trial function is expressed in terms of a basis set that takes into account both the Hermitian limit of the interaction in the non-relativistic approximation, and the general behaviour of the solutions at the origin, the horizon and infinity. Using this trial function an approximation to the full complex energy bound-state spectrum is computed. We study the behaviour of the method as the coupling constant of the interaction is increased, which increases both the relativistic effects and the size of the non-Hermitian part of the interaction. Finally we confirm that the method follows the expected Hylleraas-Undheim behaviour.

quant-ph↗

arXiv2005

Bound states and decay times of fermions in a Schwarzschild black hole background

We compute the spectrum of normalizable fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a hydrogen-like spectrum. The imaginary parts give decay times for the various states, due to the absorption properties of the hole, with states closer to the hole having shorter half-lives. As the coupling increases, the spectrum departs from that of the hydrogen atom, as states close to the horizon become unfavourable. Beyond a certain coupling the 1S1/2 state is no longer the ground state, which shifts to the 2P3/2 state, and then to states of successively greater angular momentum. For each positive energy state a negative energy counterpart exists, with opposite sign of its real energy, and the same decay factor. It follows that the Dirac sea of negative energy states is decaying, which may provide a physical contribution to Hawking radiation.

gr-qc↗