Hyperbolic Black Holes and Open String Production

In this paper we investigate open string pair production effects near hyperbolic black holes in AdS$_5$. We study the classical dynamics of D3 probe branes in this background and their quantum tunneling rate across the horizon from the inside using a method similar to that of Kraus, Parikh and Wilczek. The hyperbolic black holes can decay through these tunneling events and their lifetime is estimated. The radiated branes move towards the boundary and do not bounce back. Their world-lines do not intersect directly and they do not hit the singularity either, providing a clean scenario for studying the non-adiabatic pair production effects of open strings stretched between them near horizon. We find that there is a well defined parameter regime where there can be significant pair production. This requires the radiated branes to be highly boosted. However, the radiation of such branes still has small back-reaction on the black hole background, though the open string pair production on them can potentially alter the background. We comment on the possible relation of our model and the AMPS paradox. Some issues and future directions are discussed in the end.