Classical and quantum signatures of linear gravitation

In this paper we study a domain of spacetime in which gravitational field is nearly flat. Thus a coordinate system exists for which gαβ ηαβ + hαβ, |hαβ| << 1. We consider the linearized theory as a Lorentz covariant field theory for the gravitational field in flat spacetime. Thus, hαβ| transforms as a tensor with respect to the Lorentz group, and as it is the case of electrodynamics, there is a gauge group. We propose a generalisation of linear gravitoelectromagnetics and the main results can be summarized as follows. 1. Maxwell-type gravitational equations can be written as the single-graviton quantum equation. However, some fundamental electrodynamical and gravitational phenomena are standing beyond the frames of a Maxwell-type theory, that is in non-abelian Yang-Mills regions. 2. A new derivation of the Unruh effect formula on the basis of Einstein's principle of equivalence. 3. Absorption of linearized gravitational waves may be caused by an 'Ohm's gravitational law'. 4. We establish a stronger limit for the longitudinal graviton mass (mgl ≤ 2 x 10-66 g). 5. Energy density of the vacuum is half that of the energy density of cosmic matter. This result agrees with the relation between the density of the vacuum energy and the energy of cosmic matter that has been proposed in order to solve the old problem of cosmological models involving dark matter and critical total energy density. 6. The interaction of a gravitational wave with a free or bounded particle can be studied in a Hamilton-Weber quantum mechanical framework. 7. The possibility of force-free gravitomagnetic fields and reconnection of field lines. 8. Spontaneous generation of gravitomagnetic field in an imploding matter. (authors)