  Gravitational wave solutions to Einstein's equations and their generation are
examined in D-dimensional flat spacetimes. First the plane wave solutions are
analyzed; then the wave generation is studied with the solution for the metric
tensor being obtained with the help of retarded D-dimensional Green's function.
Due to the difficulties in handling the wave tails in odd dimensions we
concentrate our study in even dimensions. We compute the metric quantities in
the wave zone in terms of the energy momentum tensor at retarded time. Some
special cases of interest are studied: first the slow motion approximation,
where the $D$-dimensional quadrupole formula is deduced. Within the quadrupole
approximation, we consider two cases of interest, a particle in circular orbit
and a particle falling radially into a higher dimensional Schwarzschild black
hole. Then we turn our attention to the gravitational radiation emitted during
collisions lasting zero seconds, i.e., hard collisions. We compute the
gravitational energy radiated during the collision of two point particles, in
terms of a cutoff frequency. In the case in which at least one of the particles
is a black hole, we argue this cutoff frequency should be close to the lowest
gravitational quasinormal frequency. In this context, we compute the scalar
quasinormal frequencies of higher dimensional Schwarzschild black holes.
Finally, as an interesting new application of this formalism, we compute the
gravitational energy release during the quantum process of black hole pair
creation. These results might be important in light of the recent proposal that
there may exist extra dimensions in the Universe, one consequence of which may
be black hole creation at the Large Hadron Collider at CERN.
