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We present a first-principles implementation of {\em spatial} scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching. In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential A_k as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious, but physically questionable, theory, the equations of motion of this new theory are second order in time-derivatives. It is tempting to try to interpret the vector potential A_k as the electromagnetic field. We exhibit four independent reasons for not giving into this temptation. A more likely possibility is that it can play the role of ``dark matter''. Indeed, as noted in scale invariance seems to play a role in the MOND phenomenology. Spatial boundary conditions are derived from the free-endpoint variation method and a preliminary analysis of the constraints and their propagation in the Hamiltonian formulation is presented.

Gamma-ray bursts (GRBs) -- rare flashes of ~ MeV gamma-rays lasting from a fraction of a second to hundreds of seconds -- have long been among the most enigmatic of astrophysical transients. Observations during the past decade have led to a revolution in our understanding of these events, associating them with the birth of neutron stars and/ or black holes during either the collapse of a massive star or the merger of two compact objects (e.g., a neutron star and a black hole). GRBs are particularly interesting since NS-NS and NS-BH mergers are the primary target for km-scale gravitational wave observatories such as Advanced LIGO; GRBs are also one of the most promising astrophysical sources of very high- energy neutrinos and may produce many of the neutron-rich heavy elements in nature. In this talk, I will describe the physics of these enigmatic events and summarize outstanding problems. Combined electromagnetic and gravitational-wave observations of these sources in the coming decade have the potential to produce major advances in both astrophysics and fundamental physics (tests of General Relativity and of the equation of state of dense nuclear matter).