Schwarzschild-type solution in an effective gravitational theory with local Galilean invariance

TL;DR

This paper develops a Schwarzschild-like solution within a five-dimensional, Galilean-invariant gravity theory, analyzing classic tests of relativity and showing it can replicate GR results when a certain parameter is negligible.

Contribution

It introduces a new exact external solution in a Galilean-invariant gravity framework using a five-dimensional manifold, extending classical tests of gravity.

Findings

The solution obeys a Birkhoff-like theorem.

The Galilean theory reproduces GR results when parameter b is negligible.

The parameter b can be estimated from observational data.

Abstract

We construct a Schwarzschild-type exact external solution for a theory of gravity admitting local Galilean invariance. In order to realize the Galilean invariance we need to adopt a five-dimensional manifold. The solution for the gravitational field equations obeys a Birkhoff-like theorem. Three classic tests of general relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The Galilean version of these tests exhibits an additional parameter $b$ related to the fifth-coordinate. This constant $b$ can be estimated by a comparison with observational data. We observe that the Galilean theory is able to reproduce the results traditionally predicted by general relativity in the limit of negligible $b$. This shows that the tests are not specifically Lorentz invariant.