Time evolution of a thin black ring via Hawking radiation

Abstract

Black objects lose their mass and angular momenta through evaporation by Hawking radiation, and the investigation of their time evolution has a long history. In this paper, we study this problem for a five-dimensional doubly spinning black ring. The black ring is assumed to emit only massless scalar particles. We consider a thin black ring with a small thickness parameter, $\ensuremath{\lambda}\ensuremath{\ll}1$, which can be approximated by a boosted Kerr string locally. We show that a thin black ring evaporates with fixing its thickness parameter $\ensuremath{\lambda}$. Further, in the case of an Emparan-Reall black ring, we derive analytic formulas for the time evolution, which has one parameter to be evaluated numerically. We find that the lifetime of a thin black ring is shorter by a factor of $O({\ensuremath{\lambda}}^{2})$ compared to a five-dimensional Schwarzschild black hole with the same initial mass. We also study detailed properties of the Hawking radiation from the thin black ring, including the energy and angular spectra of emitted particles.