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

By N. A. Collins, S. Hughes. 2004

147 citations recorded by the source corpus.

Astronomical observations have established that extremely compact, massive objects are common in the Universe. It is generally accepted that these objects are, in all likelihood, black holes. As observational technology has improved, it has become 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 future gravitational-wave measurements) and to test whether they have the characteristics of black hole orbits in general relativity. Past work has shown that, in principle, such measurements can be used to map the spacetime of a massive compact object, testing in particular whether the object's multipolar structure satisfies the rather strict constraints imposed by the black hole hypothesis. Performing such a test in practice requires that we be able to compare against objects with the ``wrong'' multipole structure. In this paper, we present tools for constructing the spacetimes of bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. In this first analysis, we focus on objects with no angular momentum. Generalization to bumpy Kerr black holes should be straightforward, albeit labor intensive. Our construction has two particularly desirable properties. First, the spacetimes which we present are good deep into the strong field of the object\char22{}we do not use a ``large r'' expansion (except to make contact with weak field intuition). Second, our spacetimes reduce to the exact black hole spacetimes of general relativity in a natural way, by dialing the ``bumpiness'' of the black hole to zero. We propose that bumpy black holes can be used as the foundation for a null experiment: if black hole candidates are indeed the black holes of general relativity, their bumpiness should be zero. By comparing the properties of orbits in a bumpy spacetime with those measured from an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are in fact the black holes of general relativity.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/13040d452485b317c7187065873ff2685aab8e13

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Citations in the corpus

Gravitational wave snapshots of generic extreme mass ratio inspirals (2005, background): “Black hole masses and spins should be measured with fraction of a percent accuracy or better [18]; it should even be possible to check whether the spacetime has the “shape” (higher multipolar structure) required by the no-hair theorems of general relativity [19, 20, 21].”
Rotating neutron stars: an invariant comparison of approximate and numerical space-time models (2004, background): “…from https://academic.oup.com/mnras/article-abstract/358/3/923/1028039 by guest on 26 July 2018 and compact stars can be used, in principle, to map the multipolar structure of the corresponding space–time and check the validity of the BH no-hair theorem (Ryan 1995, 1997; Collins & Hughes 2004).”
Doing Science with eLISA: Astrophysics and Cosmology in the Millihertz Regime (2012, background): “ a deviation from the Kerr metric. These and similar studies of “bumpy” Kerr black holes – spacetime metrics with a multipolar stucture that deviates from the Kerr spacetime by some “tunable” amount (Collins and Hughes, 2004, Glampedakis and Babak, 2006, Hughes, 2006, Ryan, 1995, Vigeland et al., 20”
Gravitational waves from scattering of stellar-mass black holes in galactic nuclei (2008, methodology): “Given the test particle limit of the BH, such encounters are expected to be a stringent test of General Relativity in the strongfield regime (Collins & Hughes 2004; Arun et al. 2006).”
TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. II. BLACK HOLE IMAGES (2010, background): “…tests of the no-hair theorem with observations of gravitational waves from extreme mass-ratio inspirals (Ryan 1995, 1997a, 1997b; Barack & Cutler 2004, 2007; Collins & Hughes 2004; Glampedakis & Babak 2006; Gair et al. 2008; Li & Lovelace 2008; Apostolatos et al. 2009; Vigeland & Hughes 2010).”