Scalar theory of gravity as a pressure force

Abstract

The theory starts from a tentative interpretation of gravity as Archimedes' thrust exerted on matter at the scale of elementary particles by an imagined perfect fluid ("ether"): the gravity acceleration is expressed by a formula in which the "ether pressure" p_e plays the role of the Newtonian potential. The instantaneous propagation of Newtonian gravity is obtained with an incompressible ether, giving a field equation for p_e. For a compressible ether, this equation holds in the static case. The extension to non-static situations follows the lines of acoustics and leads to gravitational (pressure) waves. To account for metric effects, the modern version of the Lorentz-Poincare interpretation of special relativity is used. Einstein's equivalence principle (EP) is seen as a correspondence between the metric effects of gravity and those of uniform motion with respect to the ether: a gravitational contraction (dilation) of space (time) standards is assumed. This implies geodesic motion for test particles in a static field. The scalar field equation is now expressed in terms of the physical space and time metrics in the frame of ether. Since both metrics depend on p_e due to the EP, it becomes non-linear in p_e. In the spherical static situation, Schwarzschild's exterior metric is predicted, but the interior metric differs from GR. Since pressure produces gravitation also in the investigated theory, no equilibrium is possible for very massive objects. But the gravitational collapse in free fall does not lead to any singularity. Moreover, gravitational waves, and even shock ones, can exist in vacuo also with spherical symmetry.