Geometrodynamics: Spacetime or Space ?

TL;DR

This thesis explores the split of Einstein's field equations with respect to hypersurfaces, deriving geometrodynamics from relational principles, examining alternative gravity theories, and analyzing initial value problem methods in general relativity.

Contribution

It introduces a relational foundation for geometrodynamics, discusses alternative gravity theories using conformal mathematics, and evaluates initial value problem methods for timelike splits.

Findings

Relational principles can derive geometrodynamics.

Conformal mathematics enables alternative gravity theories.

Timelike splits of EFE's are problematic.

Abstract

This thesis concerns the split of Einstein's field equations (EFE's) with respect to nowhere null hypersurfaces. Areas covered include A) the foundations of relativity, deriving geometrodynamics from relational first principles and showing that this form accommodates a sufficient set of fundamental matter fields to be classically realistic, alternative theories of gravity that arise from similar use of conformal mathematics. B) GR Initial value problem (IVP) methods, the badness of timelike splits of the EFE's and studying braneworlds under guidance from GR IVP and Cauchy problem methods.