Static spherisymmetric solutions, gravitational lensing and perihelion precession in Einstein--Kalb--Ramond theory

TL;DR

This paper derives static, spherically symmetric solutions in Einstein--Kalb--Ramond theory, explores their gravitational lensing and perihelion precession effects, and provides explicit correction formulas due to the KR field.

Contribution

It presents new approximate solutions to Einstein--Kalb--Ramond equations and analyzes their impact on gravitational phenomena, extending previous exact solutions.

Findings

Derived an approximate asymptotically flat solution as an infinite series in 1/r.

Calculated explicit corrections to gravitational lensing due to the KR field.

Analyzed perihelion precession modifications caused by the KR field.

Abstract

Static, spherically symmetric solutions of the Einstein--Kalb--Ramond (KR) field equations are obtained. Besides an earlier known exact solution, we also find an approximate, asymptotically flat solution for which the metric coefficients are obtained as an infinte series in $\frac{1}{r}$. Subsequently, we study gravitational lensing and perihelion precession in these spacetimes and obtain explicit formulae which include corrections to these effects in the presence of the KR field.