# 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.

## Key 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.