Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

TL;DR

This paper develops a formalism for constructing 'bumpy black holes' with altered multipole moments, enabling tests of whether observed compact objects are true black holes as predicted by general relativity.

Contribution

It introduces a method to create spacetimes with slight deviations from black holes, facilitating null tests of the black hole hypothesis through orbital observations.

Findings

Spacetimes are valid deep in the strong field without large r expansion.

Bumpy black holes reduce to standard black holes when bumps are zero.

Tools enable testing the black hole nature of compact objects via orbit comparisons.

Abstract

Observations have established that extremely compact, massive objects are common in the universe. It is generally accepted that these objects are black holes. As observations improve, it becomes possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or with gravitational-waves) and to test whether they have the characteristics of black hole orbits in general relativity. Such measurements can be used to map the spacetime of a massive compact object, testing whether the object's multipoles satisfy the strict constraints of the black hole hypothesis. Such a test requires that we compare against objects with the ``wrong'' multipole structure. In this paper, we present tools for constructing bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. The spacetimes which we present are good deep into the strong field of the object -- we do not use a large r expansion, except to make contact with weak field intuition. Also, our spacetimes reduce to the black hole spacetimes of general relativity when the ``bumpiness'' is set to zero. We propose bumpy black holes as the foundation for a null experiment: if black hole candidates are the black holes of general relativity, their bumpiness should be zero. By comparing orbits in a bumpy spacetime with those of an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are the black holes of general relativity. (Abridged)