Deciphering the glitches in gravitational wave signals related to non-Kerr objects

01.07.2022 bis 30.06.2024

Black holes, consisting of pure vacuum curved spacetime, are the most extreme objects described by GR. In most gravitational wave events, black holes are involved as at least one of the main constituents of the sources. Although the gravitational wave signals measured by the operating detectors are in full agreement with the corresponding predictions of GR, the quite loud noise of the interferometric detectors cannot give us yet a detailed description of the two members of a binary source. Only spaceborne detectors, like the future LISA, which are sufficiently sensitive to much lower frequencies than their ground-based counterparts can detect binaries of extreme mass ratio that consist of a small black hole orbiting a massive one along an almost geodesic orbit. The adiabatic evolution of the orbit permits waveform analyzers to trace, in exquisite detail, the spacetime of the massive black hole. The black holes, according to GR, form an integrable system describing the geodesics of their background. These geodesics are characterized by 3 integrals of motion: the energy, the angular momentum along the spin axis of black hole and the Carter constant. Due to gravitational wave radiation the orbit will adiabatically change and the fundamental frequencies, that are related to the orbital oscillations (radial, azimuthal, and rotation) will gradually evolve. Whenever a pair of these frequencies form a commensurate ratio, the system is in resonance. While at resonance, the energy and angular-momentum losses are no longer described by formulae that assume that the phase space is covered densely by the orbit, while these formulae are normally used to evolve an orbit adiabatically.

For integrable systems, like that of a small black hole orbiting around a massive one, resonances are not expected to have significant implications in the evolution, since the status of resonance is instantaneous. On the other hand, if 2 for any physical reason -either a non-vacuum environment, or a deviation from the general relativistic description of the black hole itself- the background is not exactly that of a Kerr black hole vacuum. Therefore, the geodesic equations do not form an integrable system, but a slightly perturbed one, and the passage of an orbit through a resonance could deviate drastically from what one would expect from a corresponding integrable Kerr system.

Future observations with LISA will be able to see signals from extreme mass ratio inspirals (EMRISs) that evolve through a resonance. The analysis of such signals could inform us about the details of the passage of an orbit through a resonance. If the evolution is normal with no intricate behavior near the resonance, we could certify unequivocally that the central field is that of a pure Kerr black hole, exactly as described by GR. If, on the other hand, the evolution of the signal is such that the pair of rationally related frequencies stay locked with each other for a finite, measurable period, we could convince ourselves that the actual spacetime background on which the small mass is moving is not the pure vacuum of a Kerr black hole. To further discern the physical cause of non-integrability is a more difficult goal and we plan to address this issue within the framework of the present program. As a matter of fact, the non-geodesic behavior of the orbit due to radiation is by itself a reason that renders the orbit non-integrable, but this type of non-integrability could separately be taken into account in the analysis of the orbital evolution.

Another issue related to the qualitative difference between the signals under the two case scenarios (integrable/nonintegrable) is a possible loss of detection by assuming a waveform evolution that is based on the assumption that the background is a Kerr black hole background. Although the evolution of the non-integrable orbit, while not at resonance, could be very similar to that of an integrable orbit, the passage through a resonance could