We introduce a classical version of the loop corrected soft graviton theorem and we use it to compute the universal part of the one-loop (2PM) waveform up to sub-subleading order in the energy ω of the emitted graviton for spinless black holes scattering. In particular, we compute the action of the soft operators on the classically resummed four-point amplitude, that can be written in terms of the exponential of the eikonal phase (and is therefore non-perturbative in the Newton's constant G_N) and then we perform the usual Post-Minkowskian expansion in powers of G_N. We find perfect agreement with the existing 2PM literature at the orders ω⁻¹, log⁡ ω and ω log² ⁡ω, which are universal. Furthermore, we use this method to compute the universal part of the ω log ⁡ω contribution to the 2PM waveform. Even if in the present analysis we limit ourselves to compute the soft 2PM waveform, our general formulae can be used to extract all universal PM orders of the terms connected with the infrared divergences up to non-linear memory contributions, once the impulse at the corresponding precision is known. Our approach, based on the resummed eikonal amplitude, gives a unified picture of the various computations of the classical soft graviton behaviour that are present in the literature since the seminal paper by Weinberg (1965 Phys. Rev. 140 B516–24).

Infrared effects in the scattering of particles in gravity and electrodynamics entail an exchange of relativistic angular momentum between pairs of particles and the gauge field. Due to this exchange particles can carry an asymptotically non-vanishing “pairwise” boost-like angular momentum proportional to the product of their couplings to the field. At the quantum level this asymptotic angular momentum suggests the existence of a new quantum number carried by multi-particle states. We argue that such quantum number is related to a modification of the action of the generators of Lorentz transformations on multi-particle states. We derive such a modification using a group-theoretic argument based on the little group of the conformal primary basis for asymptotic states. The corresponding representation is an extension of the ordinary multi-particle Fock representation of the Poincaré group. The new multi-particle states belonging to such representation no longer factorize into tensor products of one-particle states. Viewed from a gravitational point of view, our results provide evidence for a universal breakdown of the description of multi-particle sates in terms of tensor products of one-particle states due to infrared back-reaction.

We argue that gravitational interactions between particles require a departure from the conventional picture of the quantum state of a multiparticle system in terms of tensor products of one-particle states. This modification is essential in order to accommodate the existence of a new boost-like relativistic angular momentum charge which pairs of particles must carry asymptotically due to long-range effects of gravity. These findings challenge conventional assumptions, prompting a re-evaluation of the constraints on quantum entanglement between particle subsystems in a black hole geometry.

We construct a new Yang-Mills Lagrangian based on a notion of minimal coupling that incorporates classical spin effects. The construction relies on the introduction of a new covariant derivative, which we name classical spin covariant derivative, that is compatible with the three-point interaction of the Kerr \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{\textrm{Kerr}} $$\end{document} solution with the gauge field. The resulting Lagrangian, besides the correct three-point coupling, predicts a unique choice for contact terms and therefore it can be used to compute higher-point amplitudes such as the Compton, unaffected by spurious poles. Using double copy techniques we use this theory to extract gravity amplitudes and observables that are relevant to describe Kerr binary dynamics to all orders in the spin. In particular, we compute the 2PM ( O \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document} ( G N 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {G}_N<^>2 $$\end{document} )) 2 -> 2 elastic scattering amplitude between two classically spinning objects to all orders in the spin and use it to extract the 2PM scattering angle.

Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency limit, retaining an exact dependence on the kinematics of the massive objects. This allows us to study independently the ultrarelativistic or massless limit, where we find agreement with the literature, and the small-deflection or post-Minkowskian (PM) limit, where we provide explicit results up to (G⁵). These confirm that the high-velocity limit of a given PM order is smoothly connected to the corresponding massless result whenever the latter is analytic in the Newton constant G. We also provide explicit expressions for the waveforms to order ω⁻¹, log ω, ω(log ω)² in the soft limit, ω → 0, expanded up to sub-subleading PM order, as well as a conjecture for the logarithmic soft terms of the type ωⁿ⁻¹(log ω)ⁿ with n ≥ 3.

Starting from the leading soft term of the 5-point amplitude, involving a graviton and two Kerr black holes, that factorises into the product of the elastic amplitude without the graviton and the leading soft factor, we compute the infrared divergent contribution to the imaginary part of the two-loop eikonal. Then, using analyticity and crossing symmetry, we determine the radiative contribution to the real part of the two-loop eikonal and from it the radiative part of the deflection angle for spins aligned to the orbital angular momentum, the loss of angular momentum and the zero frequency limit of the energy spectrum for any spin and for any spin orientation. For spin one we find perfect agreement with recent results obtained with the supersymmetric worldline formalism.

The partition function of a massless scalar field on a Euclidean spacetime manifold ℝ^d−1 × 𝕋² and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝ^p × 𝕋^q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋^d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.