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Two-body dynamics in general relativity: the self-force approach

Final Report Summary - GSF (Two-body dynamics in general relativity: the self-force approach)

The celebrated recent discoveries by the LIGO and Virgo gravitational-wave detectors (Nobel Prize in Physics 2017) have opened up a new window onto the universe, marking the down of gravitational-wave astronomy as a new, exciting field of scientific exploration. These direct observations of merging pairs of black holes and neutron stars vividly demonstrated the potential of gravitational waves as a powerful probe of strong-gravity phenomena inaccessible to standard astronomy. In the near future, the existing array of gravitational-wave detectors will be accompanied by a new type of detector, set in space, called LISA---the Laser Interferometer Space Antenna, with capabilities far exceeding those of ground-based detectors. LISA will observe the cataclysmic mergers of supermassive black holes, as well as the inspiral of small black holes or neutron stars into supermassive black holes (``extreme-mass-ratio inspirals'', or EMRIs). The intricate pattern of gravitational waves emitted during an EMRI encodes an exquisitely detailed map of spacetime geometry around the massive hole. By analysing this pattern we will be able to test gravitational theory in its most extreme regime, and gain a detailed understating of the physics and astrophysics of supermassive black holes and their role in structure formation in the universe.

Our project aimed to develop the necessary theoretical foundation to enable the analysis of EMRI signals, with an important by-product of informing improved theoretical models also for binary black-hole mergers that are observable by LIGO and Virgo. Orbits around black holes have a complicated dynamics, driven by the back-reaction force (``self-force'') exerted on the orbiting object by its own gravitational field. In our project we have set out to provide a precise description of this radiative dynamics within General Relativity. This involved addressing foundational issues relating to the description of motion in curved spacetime, as well as the development of computational methods and tools for actually computing the radiatively evolving orbits and their gravitational-wave signature.

Over the duration of the project we have developed an array of novel theoretical and computational tools that now allow us to compute the gravitational self-force and its effects for any type of orbits around an astrophysically realistic, rotating black hole. Using these calculations we have been able to provide a first quantitative description of several key effects of the self-force, including the finite-mass corrections to the periastron advance, rate of spin precession, gravitational redshift and the frequency of the last stable orbit. We have been able, for the first time, to calculate some secondary back-reaction effects (``second-order self-force'', the back-reaction from secondary gravitational waves sourced by the gravitational field itself) and illustrate their importance within the context of EMRI modelling for LISA. We have worked with collaborators to incorporate all this new physics into a universal, semi-analytical model of the two-body dynamics for use in future gravitational-wave searches by LIGO and Virgo. Knowledge of the self-force allows one to resolve several key outstanding questions in theoretical gravity, including one directly addressed within our project: Can one destroy the event horizon of a black hole by throwing a particle into it? We have rigorously established that such a scenario is ruled out, thereby confirming the validity of the ``cosmic censorship'' conjecture in this case.

Our work has proven exceptionally timely, not only in view of the LIGO/Virgo historical breakthrough in 2015 and the remarkable success of the LISA Pathfinder mission in 2016-17, but also because work to design signal-analysis tools for the LISA mission is now starting in earnest. The EMRI models developed in our ERC project are now providing crucial input for this activity. Based on these models, data-analysis pipelines are now being developed to enable the detection and interpretation of EMRI signals when they are observed by LISA.