Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field

TL;DR

This paper develops a framework for mapping spacetime around massive black holes using gravitational waves from inspiraling objects, focusing on deviations from Kerr metrics and their impact on waveform detection.

Contribution

It introduces a method to model quasi-Kerr spacetimes with slight deviations from Kerr, and analyzes how these deviations affect gravitational waveforms and detection strategies.

Findings

Modest deviations from Kerr cause significant waveform mismatches.

Kerr templates may lead to signal loss when applied to non-Kerr spacetimes.

Waveform 'confusion' can occur, complicating spacetime characterization.

Abstract

The future LISA detector will constitute the prime instrument for high-precision gravitational wave observations.LISA is expected to provide information for the properties of spacetime in the vicinity of massive black holes which reside in galactic nuclei.Such black holes can capture stellar-mass compact objects, which afterwards slowly inspiral,radiating gravitational waves.The body's orbital motion and the associated waveform carry information about the spacetime metric of the massive black hole,and 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 Kerr metric. We first provide a simple recipe for building such a `quasi-Kerr' metric by adding to the Kerr metric the deviation in the value of the quadrupole moment. We then study geodesic motion in this metric,focusing on equatorial orbits. We proceed by computing `kludge' 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 EMRIs 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.