  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.
