A Tour Through Shape Dynamic Black Holes

TL;DR

This paper explores the differences between shape dynamics and general relativity, focusing on black hole solutions, revealing that while they agree locally, their global structures, especially for black holes, can differ.

Contribution

It introduces the concept of shape dynamic black holes and analyzes their global properties, highlighting differences from general relativity.

Findings

Shape dynamics and general relativity agree locally but differ globally.

Shape dynamic black holes can have distinct global structures from GR black holes.

The study provides insights into the gauge-fixing conditions affecting black hole solutions.

Abstract

Shape dynamics is a classical theory of gravity which agrees with general relativity in many important cases, but possesses different gauge symmetries and constraints. Rather than spacetime diffeomorphism invariance, shape dynamics takes spatial diffeomorphism invariance and spatial Weyl invariance as the fundamental gauge symmetries associated with the gravitational field. Despite these differences, shape dynamics and general relativity generically predict the same dynamics---there exist gauge-fixings of each theory that ensure agreement with the other. However, these gauge-fixing conditions are not necessarily globally well-defined and it is therefore possible to find solutions of the shape dynamics equations of motion that agree with general relativity on some open neighborhoods, but which have different global structures. In particular, the black hole solutions of the two theories disagree globally. Understanding these novel "shape dynamic black holes" is the primary goal of this thesis.