  In a foregoing paper, gravity has been interpreted as the pressure force
exerted on matter at the scale of elementary particles by a perfect fluid.
Under the condition that Newtonian gravity must be recovered in the
incompressible case, a scalar field equation has thus been proposed for
gravity, giving a new theory in the compressible case. Here the theory is
reinterpreted so as to describe the relativistic effects, by extending the
Lorentz-Poincar\'e interpretation of special relativity which is first
recalled. Gravitational space-contraction and time-dilatation are postulated,
as a consequence of the principle of local equivalence between the effects of
motion and gravitation. The space-time metric (expressing the proper time along
a trajectory) is hence curved also in the proposed theory. As the result of a
modified Newton law, it is proved that free test particles follow geodesic
lines of this metric. In the spherical static situation, Schwarzschild's
exterior metric is exactly recovered and with it the experimental support of
general relativity, but the interior solution as well as the problematic of
singularities are different in the proposed theory, e.g. the radius of the body
cannot be smaller than the Schwarzschild radius.
