  The Einstein-Hilbert action for general relativity is not well posed in terms
of the metric $g_{ab}$ as a dynamical variable. There have been many proposals
to obtain an well posed action principle for general relativity, e.g., addition
of the Gibbons-Hawking-York boundary term to the Einstein-Hilbert action. These
boundary terms are dependent on what one fixes on the boundary and in
particular on spacetime dimensions as well. Following recent works of
Padmanabhan we will introduce two new variables to describe general relativity
and the action principle with these new dynamical variables will turn out to be
well posed. Then we will connect these dynamical variables and boundary term
obtained thereof to existing literature and shall comment on a few properties
of Einstein-Hilbert action which might have been unnoticed earlier in the
literature. Before concluding with future prospects and discussions, we will
perform a general analysis of the boundary term of Einstein-Hilbert action for
null surfaces as well.
