Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: I. Properties of a Quasi-Kerr Spacetime

TL;DR

This paper develops a parametric framework to test the no-hair theorem by analyzing how deviations in the quadrupole moment of black holes affect observable electromagnetic signals.

Contribution

It introduces a quasi-Kerr spacetime model with an independent quadrupole moment to interpret electromagnetic observations of black holes for testing the no-hair theorem.

Findings

Quadrupole deviations significantly affect innermost stable circular orbit locations.

Gravitational lensing is sensitive to quadrupole moment deviations.

Observations of black hole images and spectra can test the no-hair theorem.

Abstract

According to the no-hair theorem, an astrophysical black hole is uniquely described by only two quantities, the mass and the spin. In this series of papers, we investigate a framework for testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. We formulate our approach in terms of a parametric spacetime which contains a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation of the black-hole quadrupole moment from its Kerr value has to be zero. We analyze in detail the properties of this quasi-Kerr spacetime that are critical to interpreting observations of black holes and demonstrate their dependence on the spin and quadrupole moment. In particular, we show that the location of the innermost stable circular orbit and the gravitational lensing experienced by photons are affected significantly at even modest deviations of the quadrupole moment from the value predicted by the no-hair theorem. We argue that observations of black-hole images, of relativistically broadened iron lines, as well as of thermal X-ray spectra from accreting black holes will lead in the near future to an experimental test of the no-hair theorem.