### Cosmological Black Holes as Models of Cosmological Inhomogeneities

### Megan McClure

Doctor of Philosophy 2005

Graduate Department of Astronomy and Astrophysics, University of Toronto
Since cosmological black holes modify the density and pressure of the
surrounding universe, and introduce heat conduction, they produce simple
models of cosmological inhomogeneities that can be used to study the
effect of inhomogeneities on the universe's expansion. In this thesis,
new cosmological black hole solutions are obtained by generalizing the
expanding Kerr-Schild cosmological black holes to obtain the charged
case, by performing a Kerr-Schild transformation of the Einstein-de
Sitter universe (instead of a closed universe) to obtain non-expanding
Kerr-Schild cosmological black holes in asymptotically-flat universes,
and by performing a conformal transformation on isotropic black hole
spacetimes to obtain isotropic cosmological black hole spacetimes. The
latter approach is found to produce cosmological black holes with
energy-momentum tensors that are physical throughout spacetime, unlike
previous solutions for cosmological black holes, which violate the
energy conditions in some region of spacetime. In addition, it is
demonstrated that radiation-dominated and matter-dominated Einstein-de
Sitter universes can be directly matched across a hypersurface of
constant time, and this is used to generate the first solutions for
primordial black holes that evolve from being in radiation-dominated
background universes to matter-dominated background universes. Finally,
the Weyl curvature, volume expansion, velocity field, shear, and
acceleration are calculated for the cosmological black holes. Since the
non-isotropic black holes introduce shear, according to Raychaudhuri's
equation they will tend to decrease the volume expansion of the
universe. Unlike several studies that have suggested the relativistic
backreaction of inhomogeneities would lead to an accelerating expansion
of the universe, it is concluded that shear should be the most likely
influence of inhomogeneities, so they should most likely decrease the
universe's expansion.