  We study a recently proposed horizon defining identity for certain black hole
spacetimes. It relates the difference of the Brown-York quasilocal energy and
the Komar charge at the horizon to the total energy of the spacetime. The
Brown-York quasilocal energy is evaluated for some specific choices of
spacetime foliations. With a certain condition imposed on the matter
distribution, we prove this identity for spherically symmetric static black
hole solutions of general relativity. For these cases, we show that the
identity can be derived from a Gauss-Codacci condition that any
three-dimensional timelike boundary embedded around the hole must obey. We also
demonstrate the validity of the identity in other cases by explicitly applying
it to several static, non-static, asymptotically flat, and asymptotically
non-flat black hole solutions. These include the asymptotically FRW solutions
and the case of a black hole with a global monopole charge.
