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In this short Note, I answer the titular question: yes, a radiation gauge can be horizon-locking. Radiation gauges are very common in black hole perturbation theory. It’s also very convenient if a gauge choice is horizon-locking, i.e. the location of the horizon is not moved by a linear metric perturbation. Therefore it is doubly convenient that a radiation gauge can be horizon-locking, when some simple criteria are satisfied. Though the calculation is straightforward, it seemed useful enough to warrant writing this Note. Finally I show an example: the$\ell$vector of the Hartle–Hawking tetrad in Kerr satisfies all the conditions for ingoing radiation gauge to keep the future horizon fixed.

 

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe.

 

The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black hole (BBH) Hamiltonian system has proven to be evasive for a long time since the introduction of the system in 1966. Solutions of the PN BBH systems with arbitrary parameters (masses, spins, eccentricity) are required for modeling the gravitational waves emitted by them. Accurate models of gravitational waves are crucial for their detection by LIGO/Virgo and LISA. Only recently, two solution methods for solving the BBH dynamics were proposed in Ref. [G. Cho and H. M. Lee, Phys. Rev. D 100, 044046 (2019)] (without using action-angle variables), and Refs. [S. Tanay et al., Phys. Rev. D 103, 064066 (2021), S. Tanay et al., Phys. Rev. D 107, 103040 (2023)] (action-angle based). This paper combines the ideas laid out in the above articles, fills the missing gaps and compiles the two solutions which are fully 1.5PN accurate. We also present a public Mathematica package bbhpntoolkit which implements these two solutions and compares them with the result of numerical integration of the evolution equations. The level of agreement between these solutions provides a numerical verification for all the five action variables constructed in Refs. [S. Tanay et al., Phys. Rev. D 103, 064066 (2021), S. Tanay et al., Phys. Rev. D 107, 103040 (2023)]. This paper hence serves as a stepping stone for pushing the action-angle-based solution to 2PN order via canonical perturbation theory. 

One of the important targets for the future space-based gravitational wave observatory Laser Interferometer Space Antenna is extreme mass ratio inspirals (EMRIs), where long and accurate waveform modeling is necessary for detection and characterization. Modeling EMRI dynamics requires accounting for effects such as the ones induced by an external tidal field, which can break integrability at resonances and cause significant dephasing. In this paper, we use a Newtonian analogue of a Kerr black hole to study the effect of an external tidal field on the dynamics and the gravitational waveform. We have developed a numerical framework that takes advantage of the integrability of the background system to evolve it with a symplectic splitting integrator, and compute approximate gravitational waveforms to estimate the timescale over which the perturbation affects the dynamics. Comparing this timescale with the characteristic time under radiation reaction at resonance, we introduce a tool for quantifying the regime in which tidal effects might be included when modeling EMRI gravitational waves. As an application of this framework, we perform a detailed analysis of the dynamics at one resonance to show how different entry points into the resonance in phase-space can produce substantially different dynamics, and how one can estimate bounds for the parameter space where tidal effects may become dominant. Such bounds will scale as$\epsilon \gtrsim Cq$, whereɛmeasures the strength of the external tidal field,qis the mass ratio, andCis a number which depends on the resonance and the shape of the tide. We demonstrate how to estimateCusing our framework for the 2:3 radial to polar frequency resonance in our model system. This framework can serve as a proxy for proper modeling of the tidal perturbation in the fully relativistic case.