38 research outputs found
On Gravitational Shock Waves in Curved Spacetimes
Some years ago Dray and 't Hooft found the necessary and sufficient
conditions to introduce a gravitational shock wave in a particular class of
vacuum solutions to Einstein's equations. We extend this work to cover cases
where non-vanishing matter fields and cosmological constant are present. The
sources of gravitational waves are massless particles moving along a null
surface such as a horizon in the case of black holes. After we discuss the
general case we give many explicit examples. Among them are the -dimensional
charged black hole (that includes the 4-dimensional Reissner-Nordstr\"om and
the -dimensional Schwarzschild solution as subcases), the 4-dimensional
De-Sitter and Anti-De-Sitter spaces (and the Schwarzschild-De-Sitter black
hole), the 3-dimensional Anti-De-Sitter black hole, as well as backgrounds with
a covariantly constant null Killing vector. We also address the analogous
problem for string inspired gravitational solutions and give a few examples.Comment: 34 pages, harvmac, THU-94/13 (A few minor corrections are made
(mainly arithmetic factors). Final version to appear in Nucl. Phys. B.
Gravitational Shock Waves for Schwarzschild and Kerr Black Holes
The metrics of gravitational shock waves for a Schwarzschild black hole in
ordinary coordinates and for a Kerr black hole in Boyer-Lindquist coordinates
are derived. The Kerr metric is discussed for two cases: the case of a Kerr
black hole moving parallel to the rotational axis, and moving perpendicular to
the rotational axis. Then, two properties from the derived metrics are
investigated: the shift of a null coordinate and the refraction angle crossing
the gravitational shock wave. Astrophysical applications for these metrics are
discussed in short.Comment: 24 Pages, KOBE--FHD--93--03, {\LaTeX
Shock Wave Mixing in Einstein and Dilaton Gravity
We consider possible mixing of electromagnetic and gravitational shock waves,
in the Planckian energy scattering of point particles in Minkowski space. By
boosting a Reissner-Nordstr\"om black hole solution to the velocity of light,
it is shown that no mixing of shock waves takes place for arbitrary finite
charge carried by the black hole. However, a similar boosting procedure for a
charged black hole solution in dilaton gravity yields some mixing : the wave
function of even a neutral test particle, acquires a small additional phase
factor depending on the dilatonic black hole charge. Possible implications for
poles in the amplitudes for the dilaton gravity case are discussed.Comment: 11 pages, revtex file, no figure