  This work expands previous efforts, within the classical theories of Special
and General Relativity, to include tachyons (faster-than-light particles) along
with ordinary (slower-than-light) particles at any energy. The objective here
is to construct a Hamiltonian that includes both the particles and the
gravitational field that they produce. We do this with a linear approximation
for the Einstein field equations; and we also assume a time-independent
gravitational metric implied by a static picture of the particles' motion. The
resulting formula will allow serious modelling to test the idea that cosmic
background neutrinos may be tachyons, which can produce the observed
gravitational effects now ascribed to some mysterious Dark Matter.

General Relativity and Quantum Cosmology