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I will revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles around a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, I obtain three non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, thereby completing the two quasi-constants of motion found by Rüdiger with one new independent quasi-constant of motion. Finally, I will discuss the implications for the motion of spinning particles in the Kerr geometry.

"We calculate the first order metric perturbation to a Schwarzschild background spacetime induced by a spinning secondary body in the Regge-Wheeler and Zerilli gauges. In particular we specialise to a secondary with spin (anti-)aligned to the total orbital angular momentum in a quasi-circular orbit. From the metric perturbation we can calculate gauge invariant self-force quantities such as Detweiler’s redshift invariant and compare with known PN results. In doing so we present the first strong field calculation of a conservative self-force quantity with a spinning secondary and emphasise: 1) The treatment of the additional spin term to the singular field by deriving additional tensor harmonic regularisation parameters. 2) Parametrising at fixed frequency and practically extracting the linear in spin contribution to the metric perturbation."

We consider the motion of a spinning neutron star with astrophysically relevant speed in the gravity field of a massive black hole. The orbital dynamic is described by the MPD equations which include up to quadrupole interaction. We compare the orbits of the neutron star under geodesic motion and under MPD equations and show that the difference in the orbital motion can translate into a variation of pulse-arrival-time. Such a difference is within the observational limit of the radio telescopes like SKA and FAST.

Hyperbolic scattering orbits, able to penetrate deep into the sub-ISCO region even at relatively low energies, provide an excellent probe of the strong-field regime outside black holes. Self-force calculations of the scatter angle can greatly advance the development of post-Minkowskian theory and of the EOB model of binary dynamics. We develop a frequency-domain method for calculating the 1st order scalar self-force acting on a charge moving along a hyperbolic Schwarzschild geodesic, outlining the formulation of the problem, the challenges faced and our attempted solutions. Particular attention will be paid to issues faced by the usual method of extended homogeneous solutions (EHS) used to circumvent the Gibbs phenomenon.

Hyperbolic-type scattering orbits are excellent probes of the strong-field regime around black holes, and their analysis can inform the construction of an accurate two-body Hamiltonian. In particular, it has been shown that knowledge of the scattering angle through linear order in the mass ratio completely determines the 4PM Hamiltonian. With this motivation in mind, we describe a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. The method is based on a time-domain metric reconstruction from a Hertz potential in a radiation gauge. The crucial ingredient in this formulation are certain jump conditions that (each multipole mode of) the Hertz potential must satisfy along the orbit, in a 1+1-dimensional multipole reduction of the problem. We show a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime, and present a full numerical implementation for a scatter orbit.

We revisit the old problem of the self-force on a particle moving in a weak-field spacetime in the context of renewed interest in gravitational two-body scattering. We calculate the scalar, electromagnetic, and gravitational self-force on a particle moving on a straight-line trajectory in the spacetime of a Newtonian star and use these results to find the associated correction to the scattering angle in each case. In the gravitational case we must also take into account the motion of the star via a ``matter-mediated'' force on the particle, which acts at the same perturbative order as the gravitational self-force.

Future gravitational wave detectors will map out and characterize every binary merger in the history of the universe. The possibilities for new and unexpected scientific discoveries from this wealth of data is staggering, but hinges crucially on complementary advances in our theoretical understanding of the nature of gravitational wave sources. However, the path from Einstein’s equation to precision binary dynamics is notoriously difficult, and conventional methods do not scale to the demands of future detectors. I will describe our recent efforts in solving the relativistic two body problem using tools from quantum field theory.

We revisit the scattering of massless waves of helicity $|h|=0,\frac{1}{2},1,2$ in Schwarzschild and Kerr backgrounds, in the long-wavelength regime. The Newman-Penrose scattering amplitudes arising from the Black Hole Perturbation Theory (BHPT) framework are found in agreement with the classical limit of QFT amplitudes at finite values of the scattering angle and arbitrary spin orientation. The latter amplitudes are obtained from on-shell methods and describe the $2\to 2$ scattering of a massless particle of helicity $|h|$ with a massive particle of arbitrary spin $S$, where $S=0$ corresponds to the Schwarzschild case. The effect of the black hole spin in the polarization of the waves is found in agreement with previous analysis. Finally, unitarity constraints based on partial amplitudes and positive time delay are also discussed.

Recent years have seen a surge of progress in post-Minkowskian (PM, weak-field but arbitrary-speed) approximation methods for the gravitational two-body problem, complementing and reorganizing the still much further developed post-Newtonian (PN, weak-field and slow-motion) approximation. This has been driven by simplifying insights, powerful computational tools, and new results coming from the study of on-shell scattering amplitudes in quantum field theories and their classical limits. We will review some of these developments, focusing on the particularly impactful observation (ultimately also understandable from a purely classical perspective but born of the dialog with quantum amplitudes) that certain PM and PN results for arbitrary mass ratios can be determined from surprisingly low orders in the extreme-mass-ratio/self-force expansion.

We study the problem of learning a Hamiltonian given copies of its Gibbs state at a known inverse temperature. Anshu et al. recently studied the sample complexity (number of copies of the Gibbs state needed) of this problem for geometrically local Hamiltonians. In the high-temperature regime, their algorithm has sample complexity polynomial in the system size, temperature, and accuracy. Their algorithm can also be implemented with polynomial, but suboptimal, time complexity. Here, we study the same question for a more general class of Hamiltonians and present an algorithm that solves this problem with improved sample complexity and time complexity linear in the sample size. Furthermore, we prove a matching lower bound showing that our algorithm's sample complexity is optimal, and hence our time complexity is also optimal. Joint work with Robin Kothari and Ewin Tang.