  The quasilocal energy associated with a constant stationary time slice of the
  Kerr spacetime is presented. The calculations are based on a recent proposal
\cite{by} in which quasilocal energy is derived from the Hamiltonian of
spatially bounded gravitational systems. Three different classes of boundary
surfaces for the Kerr slice are considered (constant radius surfaces, round
spheres, and the ergosurface). Their embeddings in both the Kerr slice and flat
three-dimensional space (required as a normalization of the energy) are
analyzed. The energy contained within each surface is explicitly calculated in
the slow rotation regime and its properties discussed in detail. The energy is
a positive, monotonically decreasing function of the boundary surface radius.
It approaches the Arnowitt-Deser-Misner (ADM) mass at spatial infinity and
reduces to (twice) the irreducible mass at the horizon of the Kerr black hole.
The expressions possess the correct static limit and include negative
contributions due to gravitational binding. The energy at the ergosurface is
compared with the energies at other surfaces. Finally, the difficulties
involved in an estimation of the energy in the fast rotation regime are
discussed.
