Sourced metric perturbations of Kerr spacetime in Lorenz gauge

Abstract

We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of six scalars, with two of spin-weight $\pm 2$, two of spin-weight $\pm 1$, and two of spin-weight $0$. We derive the sourced Teukolsky equations satisfied by these scalars, with the sources given in terms of differential operators acting on the stress-energy tensor. The method can be used to obtain both linear and higher order nonlinear metric perturbations, and it fully determines the metric perturbation up to a time integral, omitting only static contributions which must be handled separately.

References in corpus (12)

• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• xPerm: fast index canonicalization for tensor computer algebra
• Gravitational waveforms for compact binaries from second-order self-force theory
• Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric
• Numerical computation of second order vacuum perturbations of Kerr black holes
• Gravitational perturbations of rotating black holes in Lorenz gauge
• On the Existence of Radiation Gauges in Petrov type II spacetimes
• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
• Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations
• Separable electromagnetic perturbations of rotating black holes

Cited by in corpus (6)

• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Constants of motion in gravitational self-force theory
• Frequency-domain self-force calculations using Gegenbauer reconstruction
• Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
• Relativistic frequency shifts in gravitational waves from axion clouds
• Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime