Horndeski theories confront the Gravity Probe B experiment

TL;DR

This paper examines how spinning gyroscopes behave in Horndeski theories, using Gravity Probe B data to distinguish black holes from naked singularities and constrain scalar charges.

Contribution

It develops a formalism for gyroscope motion in Horndeski theories and applies it to various black hole spacetimes, linking theoretical predictions with experimental constraints.

Findings

Gyroscope behavior can differentiate black holes from naked singularities.

Gravity Probe B data constrains scalar charges in Horndeski black holes.

Results suggest potential observational tests for alternative gravity theories.

Abstract

In this work we have investigated various properties of a spinning gyroscope in the context of Horndeski theories. In particular, we have focused on two specific situations --- (a) when the gyroscope follows a geodesic trajectory and (b) when it is endowed with an acceleration. In both these cases, besides developing the basic formalism, we have also applied the same to understand the motion of a spinning gyroscope in various static and spherically symmetric spacetimes pertaining to Horndeski theories. Starting with the Schwarzschild de-Sitter spacetime as a warm up exercise, we have presented our results for two charged Galileon black holes as well as for a black hole in scalar coupled Einstein-Gauss-Bonnet gravity. In all these cases we have shown that the spinning gyroscope can be used to distinguish black holes from naked singularities. Moreover, using the numerical estimation of the geodetic precession from the Gravity Probe B experiment, we have constrained the gauge/scalar charge of the black holes in these Horndeski theories. Implications are also discussed.