Strong Gravity

To predict the gravitational waves emitted by a black hole binary, one needs to understand the dynamics of the binary in general relativity. No closed form solutions of this problem exist. Instead one must introduce some form of approximation. One such approximation, can be made if one of the components is much heavier than the other, suggesting a perturbative expansion in the mass-ratio. I will review this small mass-ratio (SMR) expansion of the dynamics, and the progress that has been made over the last two decades. In particular, I will discuss some recent results on the convergence of this series, suggesting that at relatively low orders this SMR expansion can be used to model even equal mass binaries.

We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of D->4 solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined D->4 limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in D=2 dimensions. This is a scalar-tensor theory of the Horndeski type obtained by dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to four dimensions is not well defined and contrast the resultant metrics with the actual solutions of the new theory. Theory and solutions in lower dimensions will also be briefly discussed.

We discuss several numerical and analytical studies of the modified gravity theory Einstein dilaton Gauss-Bonnet (EdGB) gravity. This class of modified gravity theories admit scalarized black hole solutions. The theory may then provide significantly different gravitational wave signatures during binary black hole merger as compared to general relativity, so that gravitational wave observations may provide new stringent constraints on EdGB gravity. The theory is also an important member of the Horndeski theories, which have been used to model theories of the early universe, including inflation and ekpyrosis. We describe our investigations of the self-consistency of EdGB gravity for spherically symmetric solutions that differ significantly from those in GR, including scalarized black hole solutions, and find that for solutions where the Gauss-Bonnet corrections to general relativity are not small, the theory no longer admits hyperbolic evolution. We discuss how an effective field theory interpretation of the equations of motion though should always guarantee (locally) hyperbolic evolution for the theory.

With the impressive number of binary black hole mergers observed by the LIGO-Virgo detector network in the recent years, it is now important to understand the formation channels of these systems. This talk focuses on the common envelope phase, crucial to the formation of compact object binaries. During this phase, the two companions evolve inside a shared envelope, with the secondary object orbiting towards the core of the primary star. Drag forces in the stellar envelope pull the two stellar cores into a tighter orbit. Additionally, the embedded object can be modified by accretion from the flow around it. I will present local simulations explaining the hydrodynamics of the common envelope inspiral phase, and highlight the effects of the full set of flow parameters on accretion and drag forces in these episodes. I will then discuss the transformation of binaries in common envelope phases and the effect of this phase on the properties of stellar-mass black hole populations

Observations have shown that nearly all galaxies harbor massive or supermassive black holes at their centers. Gravitational wave (GW) observations of these black holes will shed light on their growth and evolution, and the merger histories of galaxies. Massive and supermassive black holes are also ideal  laboratories for studying strong-field gravity. Pulsar timing arrays (PTAs) use observations of millisecond pulsars to detect low-frequency GWs with frequencies ~1-100 nHz, and can detect GWs emitted by supermassive black hole binaries, which form when two galaxies merge. I will discuss source modeling and detection techniques for PTAs, as well as present limits on nanohertz GWs from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration.

Recent observations of gravitational waves represent a remarkable success of our theoretical models of relativistic binaries. However, accurate models are largely restricted to binaries in which the two members have roughly equal masses; for binaries with more disparate masses, modelling is less mature. This is especially relevant for extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass object orbits a supermassive black hole in a galactic core. EMRIs are uniquely precise probes of black hole spacetimes, and they will be key targets for the space-based detector LISA. They are best modelled by gravitational self-force theory, in which the smaller object generates a small gravitational perturbation that reacts back on it to exert a "self-force", accelerating the object away from geodesic motion. For LISA science, we must work to second order in this perturbative treatment. In this talk, I discuss the foundations of self-force theory, its application to EMRIs, and the current status of first- and second-order models.