The Newtonian Limit of Hermitian Gravity

TL;DR

This paper develops a Hermitian gravity framework, derives its linearized equations, and shows it reproduces Newtonian gravity in three dimensions, while highlighting differences from general relativity in light deflection predictions.

Contribution

It introduces gauge invariant potentials for Hermitian Gravity and analyzes their linearized equations, connecting them to Newtonian limits and exploring their unique reciprocity symmetry.

Findings

Reproduces Newtonian potential in 3D

Exhibits generalized reciprocity symmetry

Differs from GR in light deflection by 25%

Abstract

We construct the gauge invariant potentials of Hermitian Gravity and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the influence of a potential. The theory correctly reproduces the Newtonian limit in three dimensions and the nonrelativistic acceleration equation. However, it differs from the light deflection calculated in linearized generalrelativity by 25%. While the specific complexification of general relativity by extension to Hermitian spaces performed here does not agree with experiment, it does possess useful properties for quantization and is well-behaved around singularities. Another form of complex general relativity may very well agree with experimental data.