Exact gravitational lensing and rotation curve

TL;DR

This paper derives the rotation curve and gravitational lensing effects in a static spherically symmetric spacetime without relying on Einstein's equations, providing a model-independent analysis within general relativity.

Contribution

It introduces a method to determine the metric function from rotation curves and derives lensing equations and corrections in the weak field limit.

Findings

Rotation curve determines the metric function independently.

Lensing equation and corrections are derived from null geodesics.

Analysis is valid within the weak field approximation of GR.

Abstract

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation and corrections to it.