Black hole complementarity with local horizons and Horowitz-Maldacena's proposal

TL;DR

This paper examines the limitations of black hole complementarity assumptions in charged black holes, proposing that Horowitz-Maldacena's proposal might help address potential violations of the principle.

Contribution

It explores the role of local horizons and the Horowitz-Maldacena proposal in maintaining black hole complementarity in non-ideal conditions.

Findings

Event horizon remains close to the outer horizon in simulations

Cauchy horizon can differ from the inner horizon, risking complementarity violation

Horowitz-Maldacena's proposal may serve as a selection principle to preserve complementarity

Abstract

To implement the consistent black hole complementarity principle, we need two assumptions: first, there exists a singularity near the center, and second, global horizons are the same as local horizons. However, these assumptions are not true in general. In this paper, the authors study a charged black hole in which the second assumption may not hold. From the previous simulations, we have argued that the event horizon is quite close to the outer horizon, and it seems not harmful to black hole complementarity; however, the Cauchy horizon can be different from the inner horizon, and a violation of complementarity will be possible. To maintain complementarity, we need to assume a selection principle between the singularity and the Hawking radiation generating surface; we suggest that Horowitz-Maldacena's proposal can be useful for this purpose. Finally, we discussed some conditions under which the selection principle may not work.