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Surface-charge algebra associated with Bondi-Metzner-Sachs (BMS4) symmetry on the null infinity of asymptotically flat spacetime is studied via a Hamiltonian framework. A coordinate system, where boundaries of constant-time hypersurfaces cross the null infinity, is adopted. The equation itself, which determines the variation of the surface charges, turns out the same as that previously obtained via the covariant framework by Barnich and Troessaert and is nonintegrable for general radiation field CAB. However, if CAB is independent of retarded time «, the variation equation is integrable, and the conserved surface charges generate BMS4 algebra without central extension. [ABSTRACT FROM AUTHOR]

Unimodular gravity (UG) is an important theory which may explain the smallness of the cosmological constant. To get insight into the covariant quantization of UG, we discuss the BRST quantization of general relativity (GR) with a cosmological constant in the unimodular gauge. We develop a novel way to gauge fix the transverse diffeomorphism (TDiff) and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the TDiff. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then study a theory derived by making "Fourier transform" of GR in the unimodular gauge with respect to the cosmological constant as a candidate of "quantum UG." We clarify the difference from GR and point out problems in this theory. [ABSTRACT FROM AUTHOR]