  In this thesis, we study the Hamiltonian and covariant phase space
description of gravitational theories. The phase space represents the allowed
field configurations and is accompanied by a closed nondegenerate 2 form- the
symplectic form. We will show that local/gauge symmetries of the action fall
into two different categories in the phase space formulation. Those
corresponding to constraints in the phase space, and those associated with
nontrivial conserved charges. We argue that while the former is related to
redundant gauge degrees of freedom, the latter leads to physically distinct
states of the system, known as surface degrees of freedom and can induce a
lower dimensional dynamics on the system. These ideas are then implemented to
build the phase space of specific gravitational systems: 1) asymptotically AdS3
spacetimes, and 2) near horizon geometries of extremal black holes (NHEG) in
arbitrary dimension. In the AdS3 phase space, we show that Brown-Henneaux
asymptotic symmetries can be extended inside the bulk of spacetime and hence
become symplectic symmetries of the phase space. We will show that in the NHEG
phase space, surface gravitons form a Virasoro algebra in four dimensions, and
a novel generalization of Virasoro in higher dimensions. The central charge of
the algebra is proportional to the entropy of the corresponding extremal black
hole. We study the holographic description of NHEG phase space and show that
the charges can be computed through a Liouville type stress tensor defined over
a lower dimensional torus. We will discuss whether surface gravitons can serve
as the microscopic origin of black hole entropy.
