Periastron shift in Weyl class spacetimes

TL;DR

This paper investigates the periastron shift in Weyl class spacetimes, analyzing static and stationary axially symmetric solutions, and applies findings to the S2-SgrA* binary system to predict measurable orbital precession.

Contribution

It provides explicit calculations of periastron shift in various Weyl solutions, including rotating cases, and connects theoretical results to upcoming astronomical measurements.

Findings

Periastron shift varies with spacetime parameters.

Explicit formulas for static and rotating Weyl solutions.

Application to S2-SgrA* system predicts measurable precession.

Abstract

The periastron position advance for geodesic motion in axially symmetric solutions of the Einstein field equations belonging to the Weyl class of vacuum solutions is investigated. Explicit examples corresponding to either static solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or stationary solution (single rotating Chazy-Curzon and Kerr black hole) are discussed. The results are then applied to the case of S2-SgrA$^*$ binary system of which the periastron position advance will be soon measured with a great accuracy.