Theoretical gravitational dynamics and radiation

Thesis research on this topic will involve groups from the AEI and the Humboldt University.

The detection of gravitational waves and the interpretation of the astrophysical properties of their sources require detailed knowledge of the expected waveforms. For binary black holes, this entails fleshing out the predictions of general relativity for the properties of black holes and the binary dynamics (masses, spins, and binary’s eccentricity), as well as exploring possible deviations from general relativity.

Illustration of a neutron-star — black hole binary coalescence with low mass ratio. During the inspiral, the neutron star develops tidal bulges (drawn greatly exaggerated). Eventually the black hole’s tidal force overcomes the self-gravity of the neutron star and the material is torn apart. Most of the matter then accretes onto the black hole.

For binaries containing neutron stars, one must also consider the influence of the still unknown internal physics of neutron stars through tidal interactions. Finding a sufficiently accurate, general, and practical solution to the relativistic two-body problem has proven notoriously difficult, but crucial advances have taken place during the last two decades. The field of numerical-relativity uses supercomputing power to directly solve Einstein’s equations, and has found great success, but it remains difficult to cover the entire parameter space (of the black holes' initial masses, spins, and orbital parameters), since a simulation for a given set of parameters can take months, and since simulations still struggle to reach into extreme parts of the parameter space, both large spins and large mass ratios. Successful waveform models from binary  black holes and binary neutron stars have to incorporate both information from numerical relativity and analytic approximations to general relativity.

The two-body problem lends itself to two complementary lines of attack by analytic means, which are valid in two limiting regions of the parameter space. In the limit of weak gravity and slow motion, general relativity reduces to Newtonian gravity; expanding about this limit yields the post-Newtonian approximation. In the limit where one body is much larger than the other, the problem reduces to a test-mass following a geodesic in the stationary spacetime of the large object; expanding about this limit yields the small-mass-ratio approximation, also termed gravitational self-force formalism. The effective-one-body (EOB) formalism synergistically incorporates information from the post-Newtonian limit, the small-mass-ratio limit and from numerical relativity, in an attempt to provide an accurate description of binary motion and radiation throughout the parameter space.

Regimes and approximation schemes for the relativistic two-body problem.

In the last few years, analytical techniques to solve (approximately) the two-body problem have also used methods adapted from the effective—field-theory approach casting the problem into Feynman diagrams which can be efficiently computed, and employing power counting methods to readily identify relevant contributions at each post-Newtonian order. Quite interestingly, it has been suggested recently that modern scattering-amplitude methods of quantum fields could be more efficient in solving the two-body problem in general relativity (e.g., through the so-called double copy method, on-shell recursion relations, etc.). Those methods naturally allow to obtain results in the post-Minkowskian limit, which expands in the Newton constant G.

PhD students will pursue research to advance our knowledge of the two-body problem (including radiation) to higher post-Newtonian, post-Minkowskian and small-mass-ratio orders, and combine those results in the EOB formalism. Some PhD projects will also be devoted to improve the latter, providing a more powerful resummation scheme and with new insights on the description of non-perturbative effects throughout the coalescence stage. These research activities will lead to waveform models that describe more accurately spin effects, tidal interactions, and eccentricity, fulfilling the more demanding requirements of future, more sensitive gravitational waves detectors, and enabling to extract the best science.

Go to Editor View