Classical gravity

I am interested in the quest for defining energy and mass of gravitating systems [<a href=''http://arxiv.org/abs/gr-qc/9810033''></a>, <a href=''http://arxiv.org/abs/gr-qc/9906063''>Bose:1998uu</a>, <a href=''http://arxiv.org/abs/hep-th/9911070''>Bose:1999er</a>], as well as their role in characterizing the thermodynamical properties of black holes [<a href=''http://arxiv.org/abs/gr-qc/9702038''>Bose:1997gt</a>, <a href=''http://arxiv.org/abs/gr-qc/9510048''>Bose:1995gy</a>]. In Ref. [<a href=''http://arxiv.org/abs/gr-qc/9702038''>Bose:1997gt</a>], I proved (with Leonard Parker and Yoav Peleg) that the Brown and York (BY) quasilocal energy is actually the value of a Hamiltonian that generates unit-magnitude proper-time translations of a family of spatial hypersurfaces, with certain boundary conditions. A different foliation leads to the Louko-Whiting Hamiltonian (LWH). For spherically symmetric black hole (BH) spacetimes, we showed that whereas the eigenvalue of the BY Hamiltonian is the internal energy, that of the LWH is the Helmhotlz free energy, ${\cal F}$. Thus, we found a new route to BH thermodynamics by obtaining the canonical partition function of such spacetimes as ${\cal Z}=\exp(-\beta {\cal F})$, without (one of the) traditional (Gibbons-Hawking), and still ``mysterious'', routes of Euclideanization of either a Hamiltonian or an action. (Another route is that of combining Hawking's black hole radiation result with the classical laws of black hole mechanics.)