String excitation inside generic black holes

TL;DR

This paper investigates how strings behave when crossing the inner horizon of charged black holes, revealing conditions under which strings are infinitely excited or can pass through, with implications for cosmic censorship.

Contribution

It provides a detailed analysis of string excitation near black hole inner horizons, showing the dependence on spacetime asymptotics and surface gravity, and discusses implications for cosmic censorship.

Findings

Strings are infinitely excited crossing the inner horizon in flat spacetime.

In de Sitter spacetime, string excitation is finite and crossing is possible under certain conditions.

Strong cosmic censorship is upheld in flat spacetime but violated in de Sitter spacetime from a string theory perspective.

Abstract

We calculate how much a first-quantized string is excited after crossing the inner horizon of charged Vaidya solutions, as a simple model of generic black holes. To quantize a string suitably, we first show that the metric is approximated by a {\it plane-wave} metric near the inner horizon when the surface gravity of the horizon $\kappa_I$ is small enough. Next, it is analytically shown that the string crossing the inner horizon is excited infinitely in an asymptotically flat spacetime, while it is finite in an asymptotically de Sitter spacetime and the string can pass across the inner horizon when $\kappa_I<2\kappa:= 2 {min}\{\kappa_B,\kappa_C \}$, where $\kappa_B$~($\kappa_C$) is the surface gravity of the black hole~(cosmological) event horizon. This implies that the strong cosmic censorship holds in an asymptotically flat spacetime, while it is violated in an asymptotically de Sitter spacetime from the point of view of string theory.