| In this thesis we consider three topics: the Penrose inequality (PI), polymer corrected gravitational collapse, and zero mode excitations in a RandallSundrum-2 (RS2) cosmological braneworld model.;In chapter 2, we attempt to construct a counterexample to the PI using prolate spheroidal apparent horizons. One of the nonzero components of the second fundamental form is fixed in order to marginally outer trap the surface. The Arnowitt-Deser-Misner (ADM) mass of the spacetime is defined so that the area of the horizon violates the rigidity condition of PI conjecture. The result is a three parameter set of counterexample candidates. We show that the dominant energy condition is violated at the equator of the horizon for all geometries constructed in this way.;In chapter 3, we add polymer quantization motivated corrections to the Hamiltonian of a massless scalar field, and examine the consequences these corrections have on gravitational collapse. We construct a model, using the Oppenheimer-Snyder procedure, consisting of a Friedmann-Robertson-Walker (FRW) solution joined to a generalized Vaidya spacetime along a timelike, spherical boundary using the Israel junction conditions. We consider both classical and polymer quantized matter for the interior. We show that when the scalar field interior is classical, the ball will collapse to a point, generating a singularity. If the massless scalar field interior has been polymer quantized, the dynamics of the model will depend on whether the FRW interior is spatially closed, or flat. If closed, the ball will bounce and generate a multiple horizon black hole. If it is flat, the ball will approach r = 0 asymptotically with time, and the spacetime will evolve towards Minkowski space.;In chapter 4, we explore the possibility that, in the cosmological braneworld model, bulk gravitational waves will excite an identifiable spectrum in the stochastic gravitational wave background. We introduce a procedure for evolving gravitational waves across a double-null lattice defined in the bulk and bounded by the brane. We determine that the spectrum of the excited zero modes on the brane depends strongly on the details of the initial signal from the bulk. We see no evidence of quasinormal ringing. |
