Solutions of gravitational field equations for weakly birefringent spacetimes

TL;DR

This paper develops solutions to gravitational field equations in weakly birefringent spacetimes, revealing non-metric modifications to classical solutions like Schwarzschild and gravitational waves.

Contribution

It introduces a perturbative approach to solve gravity equations in birefringent geometries, highlighting non-metric effects on known solutions.

Findings

Non-metric refinements to Schwarzschild solution

Non-metric modifications to gravitational wave solutions

Perturbative solutions for weak birefringence effects

Abstract

The constructive gravity programme applied to electrodynamics with vacuum birefringence yields the---up to unknown gravitational constants---unique compatible gravity theory for the underlying non-metric geometry. Starting from a perturbative variant of this procedure, we solve the resulting gravitational field equations for the geometry perturbation and point out the non-metric refinements to the linear Schwarzschild and the gravitational wave solution.