Parity Horizons in Shape Dynamics

TL;DR

This paper introduces the concept of parity horizons in shape dynamics, showing they are present in various solutions including black holes, and explores their implications for horizon properties and chronology protection.

Contribution

It defines parity horizons in shape dynamics, demonstrates their presence in known and new solutions, and discusses their implications for horizon invariance and chronology protection.

Findings

Event horizons are parity horizons in shape dynamics.

Cauchy horizons also become parity horizons, indicating a chronology protection mechanism.

Parity horizons imply a form of CPT invariance in solutions.

Abstract

I introduce the notion of a parity horizon, and show that many simple solutions of shape dynamics possess them. I show that the event horizons of the known asymptotically flat black hole solutions of shape dynamics are parity horizons and that this notion of parity implies that these horizons possess a notion of CPT invariance that can in some cases be extended to the solution as a whole. I present three new solutions of shape dynamics with parity horizons and find that not only event horizons become parity horizons in shape dynamics, but observer-dependent horizons and Cauchy horizons do as well. The fact that Cauchy horizons become (singular) parity horizons suggests a general chronology protection mechanism in shape dynamics that prevents the formation of closed time-like curves.