Mapping spacetimes with LISA: inspiral of a test body in a ‘quasi-Kerr’ field

By K. Glampedakis, Stanislav Babak. 2005

269 citations recorded by the source corpus.

The future LISA detector will constitute the prime instrument for high-precision gravitational wave observations. Among other goals, LISA is expected to materialize a ‘spacetime-mapping’ program that is to provide information for the properties of spacetime in the vicinity of supermassive black holes which reside in the majority of galactic nuclei. Such black holes can capture stellar-mass compact objects, which afterwards slowly inspiral under the emission of gravitational radiation. The small body's orbital motion and the associated waveform observed at infinity carry information about the spacetime metric of the massive black hole, and in principle it is possible to extract this information and experimentally identify (or not!) a Kerr black hole. In this paper we lay the foundations for a practical spacetime-mapping framework. Our work is based on the assumption that the massive body is not necessarily a Kerr black hole, and that the vacuum exterior spacetime is stationary axisymmetric, described by a metric which deviates slightly from the known Kerr metric. We first provide a simple recipe for building such a ‘quasi-Kerr’ metric by adding to the Kerr metric the leading order deviation which appears in the value of the spacetime's quadrupole moment. We then study geodesic motion of a test body in this metric, mainly focusing on equatorial orbits, but also providing equations describing generic orbits formulated by means of canonical perturbation theory techniques. We proceed by computing approximate ‘kludge’ gravitational waveforms which we compare with their Kerr counterparts. We find that a modest deviation from the Kerr metric is sufficient for producing a significant mismatch between the waveforms, provided we fix the orbital parameters. This result suggests that an attempt to use Kerr waveform templates for studying extreme mass ratio inspirals around a non-Kerr object might result in serious loss of signal-to-noise ratio and total number of detected events. The waveform comparisons also unveil a ‘confusion’ problem, that is the possibility of matching a true non-Kerr waveform with a Kerr template of different orbital parameters.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f5ccb733d4588ffec3b074086962b85a2e7c996d

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Citations in the corpus

TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. IV. RELATIVISTICALLY BROADENED IRON LINES (2012, methodology): “In Psaltis & Johannsen (2012), we showed that the entire iron line profiles in the quasi-Kerr metric (Glampedakis & Babak 2006) are practically indistinguishable for different combinations of the spin and the deviation parameter that have the ISCO at the same coordinate radius, but we had to limit…”
Doing Science with eLISA: Astrophysics and Cosmology in the Millihertz Regime (2012, background): “…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., 2011, Vigeland and Hughes, 2010) – focussed on understanding whether…”
Testing black hole candidates with electromagnetic radiation (2015, methodology): “For instance, the quasi-Kerr metric of Glampedakis & Babak (2006), which is based on a multipole moment expansion and the mass-quadrupole moment of the object is Q = QKerr − M3 , (17) where QKerr = −J2/M is the mass-quadrupole in the Kerr case and is the deformation parameter.”
PHOTON RINGS AROUND KERR AND KERR-LIKE BLACK HOLES (2013, methodology): “This work extends the previous analysis of photon rings in JP10b who studied potential violations of the no-hair theorem in terms of a quasi-Kerr metric (Glampedakis & Babak 2006) up to values of the spin |a| .”
Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion (2008, methodology): “[94] K. Glampedakis and S. Babak, “Mapping spacetimes with LISA: Inspiral of a test-body in a ’quasi-Kerr’ field”, Class.”
TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. II. BLACK HOLE IMAGES (2010, methodology): “…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).”
TESTING THE NO-HAIR THEOREM WITH EVENT HORIZON TELESCOPE OBSERVATIONS OF SAGITTARIUS A* (2013, methodology): “We do this by exploring the consequences of the well-developed quasi-Kerr metric, a parameterized modification of the Kerr metric which contains an independent quadrupole moment in addition to the mass and spin of the black hole (Glampedakis & Babak 2006).”