Generalized deviation equation and determination of the curvature in General Relativity

TL;DR

This paper derives a generalized deviation equation in General Relativity, enabling more precise measurement of spacetime curvature using test bodies, and provides exact solutions for curvature determination.

Contribution

It introduces a new generalized deviation equation that extends the standard geodesic deviation equation for better curvature measurement in General Relativity.

Findings

Derived a generalized deviation equation for test bodies.

Provided exact solutions for spacetime curvature.

Demonstrated the use of deviation equations in curvature measurement.

Abstract

We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation equation. We show how the standard as well as a generalized deviation equation can be used to measure the curvature of spacetime by means of a set of test bodies. In particular, we provide exact solutions for the curvature by using the standard deviation equation as well as its next order generalization.