New metrics of a spherically symmetric gravitational field passing classical tests of General Relativity

TL;DR

This paper derives a general spherically symmetric metric that reproduces all classical tests of General Relativity, introduces new parameters, and suggests ways to measure them through light speed variations.

Contribution

It presents a new class of metrics with an additional off-diagonal term, consistent with Einstein's equations, that pass all classical tests of GR and offers a method to measure new metric parameters.

Findings

The derived metric reproduces planetary precession and light deflection.

It allows for different light speeds toward and away from the mass.

The metric satisfies Einstein's field equations.

Abstract

A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines $g_{00}(r)$. Geodesic motion under such metric exactly reproduces the precession of a planetary orbit, periastron advance of a binary, deflection of light and {Shapiro time delay} if the determinant of the time-radial parts of the metric is $-1$. In this model, the total time for a radial round trip of light is as in the Schwarzschild model, but it allows for light rays to have different speeds propagating toward or from the massive object. The value of $g_{01}(r) $ could be obtained by measuring these speeds. All of these metrics do satisfy Einstein's field equations