Shapiro Delays at the Quadrupole Order for Tests of the No-Hair Theorem Using Pulsars around Spinning Black Holes

TL;DR

This paper derives an analytic expression for pulsar timing delays caused by black hole quadrupole moments, enabling tests of the no-hair theorem through pulsar observations near spinning black holes.

Contribution

It provides a closed-form, fast-computation expression for light travel time delays including quadrupole effects in black-hole spacetimes, aiding no-hair theorem tests.

Findings

Derived an analytic time-delay expression up to quadrupole order.

Facilitates rapid fitting of pulsar timing data near black holes.

Enables testing deviations from Kerr quadrupole in observations.

Abstract

One avenue for testing the no-hair theorem is obtained through timing a pulsar orbiting close to a black hole and fitting for quadrupolar effects on the time-of-arrival of pulses. If deviations from the Kerr quadrupole are measured, then the no-hair theorem is invalidated. To this end, we derive an expression for the light travel time delay for a pulsar orbiting in a black-hole spacetime described by the Butterworth-Ipser metric, which has an arbitrary spin and quadrupole moment. We consider terms up to the quadrupole order in the black-hole metric and derive the time-delay expression in a closed analytic form. This allows for fast computations that are useful in fitting time-of-arrival observations of pulsars orbiting close to astrophysical black holes.