Dynamics of Quasilocal Horizons: Black Hole and Cosmological

Black holes are described as regions from which light cannot
escape to an asymptotically far away observer, and the boundary of this
black hole region is called an Event Horizon. In the last decades, the
Event Horizon formulation has been used to study classical and quantum
properties of black holes, including their thermodynamics. However, it has
been understood that event horizons are teleological, their present
dynamics depend on boundary conditions set at the future and hence, are
not particularly suitable to understand dynamics. Therefore, it has become
increasingly important that an alternate definition which is local in both
space and time be used instead. We shall argue that the quasilocal
formalism of Dynamical Horizons, based on Penrose’s idea of trapped
surface provides an ideal framework to study the gravitational dynamics of
horizons. In this talk, we shall take a large number of examples to
establish that indeed both the black hole and the cosmological horizon may
be viewed as the time development of trapped surfaces.