Superposition Principle in Relativistic Gravity

TL;DR

This paper introduces a Lorentz-covariant superposition framework for gravitational fields in flat spacetime, aligning with classical tests of General Relativity and enabling analysis of multiple moving sources.

Contribution

It develops a novel superposition principle in Extended Relativity that maintains Lorentz covariance and describes multi-source gravitational configurations.

Findings

Reproduces classical tests of General Relativity in the new framework

Provides explicit superposed metrics for multiple moving sources

Ensures Lorentz covariance in the superposition of gravitational fields

Abstract

We develop a framework for superposition in relativistic gravity within Extended Relativity (ER), a Lorentz-covariant theory formulated in flat spacetime. In this approach, gravitational fields are described by deviations from the Minkowski metric associated with individual sources, and multi-source configurations are constructed through a superposition principle linear in the source parameters. The resulting metric preserves Lorentz covariance and reproduces the standard classical tests of General Relativity in the appropriate limits. We derive the explicit form of the superposed field for multiple moving sources and analyze its properties in both near and far zones. The formalism provides a consistent and physically transparent description of interacting gravitational sources and forms the basis for applications to relativistic dynamics and gravitational radiation.