Red and blue shift in spherical and axisymmetric spacetimes and astrophysical constraints

TL;DR

This paper analyzes red and blue shifts in various astrophysical objects using different spacetime models, revealing constraints and proposing experimental setups to improve measurements and address cosmological tensions.

Contribution

It introduces a comprehensive analysis of red and blue shifts across different energy domains using spherical and axisymmetric spacetimes, with new bounds on neutron stars and proposals for improved satellite measurements.

Findings

Large $\delta$ parameters fit neutron star data.

Incompatibility of shifts with Planck cosmological constant.

Suggested experimental setups for better red/blue shift measurements.

Abstract

We compute the red and blue shifts for astrophysical and cosmological sources. In particular, we consider low, intermediate and high gravitational energy domains. Thereby, we handle the binary system Earth - Mars as low energy landscape whereas white dwarfs and neutron stars as higher energy sources. To this end, we take into account a spherical Schwarzschild - de Sitter spacetime and an axially symmetric Zipoy - Voorhees metric to model all the aforementioned systems. Feasible outcomes come from modelling neutron stars and white dwarfs with the Zipoy - Voorhees metric, where quadrupole effects are relevant, and framing solar system objects using a Schwarzschild - de Sitter spacetime. In the first case, large $\delta$ parameters seem to be favorite, leading to acceptable bounds mainly for neutron stars. In the second case, we demonstrate incompatible red and blue shifts with respect to lunar and satellite laser ranging expectations, once the cosmological constant is taken to Planck satellite's best fit. To heal this issue, we suggest coarse-grained experimental setups and propose Phobos for working out satellite laser ranging in order to get more suitable red and blue shift intervals, possibly more compatible than current experimental bounds. Implications to cosmological tensions are also debated.