Collapsing BTZ Black String and Modified Gravity With Evolving Dimensions

In this thesis we first investigate the gravitational collapse of a (3+1)-dimensional BTZ black string in AdS space in the context of both classical and quantum mechanics. The quantum mechanical effects are implemented in the context of the Functional Schrodinger formalism which allows us to investigate the time-dependent evolution of the quantum mechanical effects. Near the horizon, the classical conclusions for an infalling observer are not changed, meaning the horizon is not an obstacle. However, at the origin, it is found the quantum effects are able to remove the classical singularity, since the wave function is non-singular at the origin. We also investigate the time evolution of the temperature of this collapsing thin domain wall as seen by an asymptotic observer. We find the late temperature exhibited good agreement with the Hawking temperature of a static black hole. In the second part, we show that it is possible to extend the cascading DGP model to lower dimensions within the framework of vanishing dimensions. We embed a 3D-brane into a 4 D-brane and successfully embed them into a 5D bulk. The scalar and graviton propagators are calculated, and the treatment for instability works well in this model.