# Black holes and singularities in causal set gravity

## TL;DR

This paper defines black holes within causal set theory by introducing the concept of singular anti-chains, which behave like causal singularities, and discusses their implications for the theory.

## Contribution

It introduces a novel definition of black holes in causal set theory using singular anti-chains, bridging a gap in the theory's treatment of singularities.

## Key findings

- Singular anti-chains behave like causal singularities.
- Causal set theory admits continua despite local finiteness.
- Proposes a new framework for black holes in causal set theory.

## Abstract

A precise definition of a black hole has long been absent in causal set theory. I first show that the local finiteness of the theory cannot be interpreted as a complete discretization condition, and the theory still admits continua, which I call singular anti-chains. After providing a couple of suggestive calculations from general relativity to support the argument that a singular anti-chain behaves like a causal singularity in a space-time, I propose a definition of a causal set black hole based on a singular anti-chain. The paper concludes with brief discussions of questions that causal set black holes and singularities may give rise to.