# Dynamical black holes in low-energy string theory

## TL;DR

This paper studies time-dependent black hole solutions in low-energy string theory, analyzing their causal structure, stability under accretion, and generating new dyon solutions using S-duality.

## Contribution

It re-derives and simplifies known radiating solutions, extends them with null dust, and introduces new dyon solutions with electric and magnetic charges in string theory.

## Key findings

- Dynamical solutions lack regular null infinity, indicating non-stationary horizons.
- Regular black holes cannot turn into naked singularities via null dust accretion without violating energy conditions.
- New dyon solutions with both electric and magnetic charges are constructed using S-duality.

## Abstract

We investigate time-dependent spherically symmetric solutions of the four-dimensional Einstein-Maxwell-axion-dilaton system, with the dilaton coupling that occurs in low-energy effective heterotic string theory. A class of dilaton-electrovacuum radiating solutions with a trivial axion, previously found by G\"uven and Y\"or\"uk, is re-derived in a simpler manner and its causal structure is clarified. It is shown that such dynamical spacetimes featuring apparent horizons do not possess a regular light-like past null infinity or future null infinity, depending on whether they are radiating or accreting. These solutions are then extended in two ways. First we consider a Vaidya-like generalisation, which introduces a null dust source. Such spacetimes are used to test the status of cosmic censorship in the context of low-energy string theory. We prove that - within this family of solutions - regular black holes cannot evolve into naked singularities by accreting null dust, unless standard energy conditions are violated. Secondly, we employ S-duality to derive new time-dependent dyon solutions with a nontrivial axion turned on. Although they share the same causal structure as their Einstein-Maxwell-dilaton counterparts, these solutions possess both electric and magnetic charges.