Causal structure of evaporating black holes

TL;DR

This paper rigorously analyzes the causal structure of evaporating black holes, demonstrating that such spacetimes inherently face issues with predictability due to their causal properties.

Contribution

It provides the first rigorous mathematical theorems showing evaporating black hole spacetimes cannot be both causally simple and continuous, impacting predictability.

Findings

Evaporating black hole spacetimes are either not causally simple or not causally continuous.

Theorems connect causal structure properties with predictability issues.

Results relate to recent studies on spacetimes with timelike boundaries.

Abstract

We offer a mathematically rigorous basis for the widely held suspicion that full black hole evaporation is in tension with predictability. Based on conditions expressing the global causal structure of evaporating black hole spacetimes, we prove two theorems in Lorentzian geometry showing that such spacetimes either fail to be causally simple or fail to be causally continuous. These theorems, when combined with recent results \cite{AM} on the causal structure of spacetimes with timelike boundary, bear significantly on the question of whether these spacetimes permit for a predictable evolution.