The (spherical) gravitational shock wave doe to a massless particle moving at the speed of light along the horizon of the Schwarzschild black hole is obtained. Special cases of our procedure yield previous results by Aichelburg and Sexl [1] for a photon in Minkowski space and by Penrose [2] for sourceless shock waves in Minkowski space. A new derivation of the (plane) shock wave of a photon in Minkowski space [I] involving explicit calculation of geodesics crossing the shock wave is also given in order to clarify the underlying physics. Applications to quantum gravity, specifically the possible effect on the Hawking temperature, are briefly discussed.
The definition of angular momentum recently given by Penrose (1982) is analysed on I. It is shown that this definition is essentially a supertranslation of previous definitions. The origin dependence of Penrose's angular momentum is shown to have the correct form. Based on Penrose's expression, the authors then define a momentum for all elements of the BMS Lie algebra, which is the first such expression with the property that its flux vanishes identically in Minkowski space.
We derive an expression for the singular part of the stress-energy tensor on a hypersurface in spacetime in terms of the discontinuities in fundamental forms associated with the surface for both the non-null case, where our results are standard, and the null case. We then derive the minimum conditions which must be satisfied in order to glue two spacetimes together along such a hypersurface. In both cases, the essential requirement is only that the naturally induced (possibly degenerate) 3-merrics on the hypersurface must agree.
We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to their motion. Applications involving possible violations of the second law of thermodynamics are briefly addressed.
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