[Paper Review] Scalar theory of gravity as a pressure force

Mayeul Arminjon|ArXiv.org|Sep 4, 2007

Relativity and Gravitational Theory3 citations

TL;DR

This paper proposes a scalar theory of gravity where gravity arises from a pressure force exerted by a hypothetical perfect fluid (the 'ether'), with the ether pressure acting as a gravitational potential. By modeling gravity analogously to hydrostatic pressure in fluids and incorporating Lorentz-Poincaré relativity, the theory reproduces Schwarzschild’s exterior metric and predicts non-singular gravitational collapse, gravitational waves, and shock waves even in spherically symmetric vacuum scenarios.

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.

Motivation & Objective

• To reinterpret gravity not as a geometric curvature but as a pressure force exerted by a hypothetical perfect fluid (the 'ether') on matter at the elementary particle scale.
• To derive a scalar field equation for the ether pressure that reproduces Newtonian gravity in the static, incompressible case and extends to non-static situations via acoustics-inspired dynamics.
• To incorporate metric effects using the Lorentz-Poincaré interpretation of special relativity, linking gravitational time dilation and spatial contraction to motion relative to the ether.
• To derive a non-linear scalar field equation for the ether pressure that accounts for both mass and pressure as sources of gravity, leading to modified predictions in strong-field regimes.
• To investigate whether the theory can avoid singularities in gravitational collapse and support gravitational waves with spherical symmetry in vacuum.

Proposed method

• Model gravity as Archimedes' thrust from a perfect fluid (ether), with the ether pressure p_e serving as the gravitational potential.
• Derive a field equation for p_e from the condition of instantaneous Newtonian gravity in an incompressible ether, generalizing it to compressible cases in static configurations.
• Extend the theory to non-static situations using analogies from acoustics, leading to the emergence of gravitational (pressure) waves.
• Apply the Lorentz-Poincaré interpretation of special relativity to relate metric effects (time dilation, length contraction) to motion relative to the ether, enforcing geodesic motion for test particles.
• Express the scalar field equation in terms of physical space and time metrics in the ether frame, where both metrics depend on p_e, resulting in a non-linear equation.
• Solve the non-linear field equation in spherical symmetry to derive the exterior and interior metrics, comparing them with general relativity.

Experimental results

Research questions

• RQ1 Can gravity be consistently described as a pressure force arising from a perfect fluid ether, with the ether pressure acting as the gravitational potential?
• RQ2 Does the resulting scalar theory reproduce the Schwarzschild metric in the exterior region and predict a modified interior metric compared to general relativity?
• RQ3 Can the theory support gravitational waves, including shock waves, in vacuum with spherical symmetry, despite the absence of mass sources?
• RQ4 Does the inclusion of pressure as a gravitational source prevent hydrostatic equilibrium in massive objects, leading to non-singular collapse instead of singularities?
• RQ5 How does the Lorentz-Poincaré interpretation of special relativity, applied to the ether frame, affect the derivation of metric effects and geodesic motion?

Key findings

• The theory reproduces the Schwarzschild exterior metric in the spherically symmetric, static case, confirming agreement with general relativity in weak-field, vacuum conditions.
• The interior metric derived from the theory differs from that of general relativity, indicating a distinct description of gravitational fields inside massive bodies.
• The theory predicts non-singular gravitational collapse: even in free fall, no spacetime singularities form, suggesting a resolution to the black hole singularity problem.
• Gravitational waves, including shock waves, can propagate in vacuum with spherical symmetry, a feature not typically allowed in standard general relativity under such conditions.
• The scalar field equation becomes non-linear due to the dependence of physical space and time metrics on the ether pressure p_e, which itself depends on the gravitational field.
• The theory supports the existence of gravitational waves in vacuo with spherical symmetry, indicating that pressure and its dynamics can generate gravitational radiation without mass sources.