Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies

Abstract

The recently established formalism of a worldline quantum field theory, which describes the classical scattering of massive bodies in Einstein gravity, is generalized up to quadratic order in spin -- for a pair of Kerr black holes revealing a hidden ${\mathcal N}=2$ supersymmetry. The far-field time-domain waveform of the gravitational waves produced in such a spinning encounter is computed at leading order in the post-Minkowskian (weak field, but generic velocity) expansion, and exhibits this supersymmetry. From the waveform we extract the leading-order total radiated angular momentum in a generic reference frame, and the total radiated energy in the center-of-mass frame to leading order in a low-velocity approximation.

Figures (2)

• Figure 1: The four diagram topologies contributing to the 2PM Bremsstrahlung up to $\mathcal{O}(\mathcal{S}^2)$, where $\omega_i=k\cdot v_i$ by energy conservation at the worldline vertices. For diagrams (b)--(d) we also include the corresponding flipped topologies with massive bodies 1$\leftrightarrow$2; for diagram (d) (which includes the propagating fermion $\psi_2^{\prime\mu}$) we also include the graph with the arrow reversed.
• Figure 2: Total radiated angular momenta for the scattering of two Kerr-BHs with $v=0.2$ as a function of the angle between the total initial spins $\mathbf{a_{3}}=\mathbf{a_{1}} + \mathbf{a_{2}}$ and $\mathbf{b}$ (with $\mathbf{a_{i}}\cdot\mathbf{v_{i}}=0$) for a range of ratios $|\mathbf{a_{3}}|/|\mathbf{b}|$. We show the normalized ratio of angular momenta emitted orthogonal to the $\mathbf{b},\mathbf{v}$ plane (left plot) and in the $\mathbf{b}$ direction (right plot), normalization is w.r.t. angular momentum emitted in the spinless case.