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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.

 

Academic science reflects the context in which science is conducted. Thus, the academic scientific enterprise struggles with privilege, racism, sexism, ableism, and homophobia, in Canada, as around the world. In this talk, I will address the uncomfortable and sometimes difficult conversations we must have in order to get to the real work of identifying and removing barriers that limit access and engagement in the scientific enterprise for the full diversity of humanity. We live within a myth of meritocracy in academia and are failing to achieve our full potential as a sector. Moving on from self-awareness as individuals or organizations, we can start to identify the tools and skill sets that individuals and collectives need in order to create cultures of care that achieve inclusive excellence and the very best scientific outputs.

Academic science reflects the context in which science is conducted.  Thus, the academic scientific enterprise struggles with privilege, racism, sexism, ableism, and homophobia, in Canada, as around the world.  In this talk, I will address the uncomfortable and sometimes difficult conversations we must have in order to get to the real work of identifying and removing barriers that limit access and engagement in the scientific enterprise for the full diversity of humanity.  We live within a myth of meritocracy in academia and are failing to achieve our full potential as a sector.  Moving on from self-awareness as individuals or organizations, we can start to identify the tools and skill sets that individuals and collectives need in order to create cultures of care that achieve inclusive excellence and the very best scientific outputs.  

Zoom Link: https://pitp.zoom.us/j/91715376839?pwd=TnBIM1NNek4zOFNyVWFnMHMySE02Zz09