A Causal Set Black Hole

TL;DR

This paper develops an algorithm to determine causal relationships in Schwarzschild black hole spacetime, advancing the causal set approach in discrete quantum gravity and enabling simulations of black hole phenomena.

Contribution

It provides a method to explicitly compute the causal structure of black holes within the causal set framework, facilitating future quantum gravity research.

Findings

Algorithm for causal relation determination in black hole spacetime

Enables simulation of black hole physics in causal set theory

Supports studies of black hole entropy and Hawking radiation

Abstract

We explicitly compute the causal structure of the Schwarzschild black hole spacetime, by providing an algorithm to decide if any pair of events is causally related. The primary motivation for this study comes from discrete quantum gravity, in particular the causal set approach, in which the fundamental variables can be thought of as the causal ordering of randomly selected events in spacetime. This work opens the way to simulating non-conformally flat spacetimes within the causal set approach, which may allow one to study important questions such as black hole entropy and Hawking radiation on a full four dimensional causal set black hole.