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There have been many attempts to define the notion of quasilocal mass for a spacelike 2-surface in spacetime by the Hamilton-Jacobi analysis. The essential difficulty in this approach is to identify the right choice of the background configuration to be subtracted from the physical Hamiltonian. Quasilocal mass should be nonnegative for surfaces in general spacetime and zero for surfaces in flat spacetime. In this letter, we propose a new definition of gauge-independent quasilocal mass and prove that it has the desired properties.
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This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of General Relativity will be described. Then, the present situation will be reviewed presenting a number of examples. The opportunities given by astrophysical and astrometric observations will be shortly discussed. Coming to terrestrial experiments the attention will be specially focused on ringlasers and a dedicated experiment for the Gran Sasso Laboratories, named by the acronym GINGER, will be presented. Mention will also be made of alternatives to the use of light, such as particle beams and superfluid rings.
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