Session E6: Orbits, Spins & Tides: Analytic and Numerical Methods

Comparing the numerical redshift factor to analytic theory

The redshift factor $z$ is a quantity of fundamental interest in Post-Newtonian and self-force descriptions of binaries, allowing for interconnections between each theory. We have recently implemented a method for extracting the redshift factor from numerical simulations of binary black holes, and compared the redshift factor to analytic theory. I will present an update on our efforts to extend our analysis to high mass ratio simulations, in order to compare to self-force predictions.   

Modeling the Schwarzschild Green's function

At sufficiently late times, gravitational waveforms from extreme mass ratio inspirals consist of a sum of quasinormal modes, power law tails, and modes related to the matter source, such as the horizon mode (Zimmerman and Chen 2011). Due to the complexity of the exact curved spacetime Green function, making precise predictions about each component is difficult. We discuss the validity of a simple model for the scalar Schwarzschild Green's function. For observers at future null infinity, we model the Green's function as a simple function describing the direct radiation that matches to a single quasinormal mode at a retarded time related to the light ring location. As applications of the model, we describe the excitation process of the single quasinormal mode and the horizon mode, showing that waveform from the inspiralling object is in precise correspondence to the response of driven, damped harmonic oscillator.   

Dynamical Tidal Response of a Rotating Neutron Star

The gravitational wave phase of a neutron star (NS) binary is sensitive to the deformation of the NS that results from its companion's tidal influence. In a perturbative treatment, the tidal deformation can be characterized by a set of dimensionless constants, called Love numbers, which depend on the NS equation of state. For static NSs, one type of Love number encodes the response to gravitoelectric tidal fields (associated with mass multipole moments), while another does likewise for gravitomagnetic fields (associated with mass currents). A NS subject to a gravitomagnetic tidal field develops internal fluid motions through gravitomagnetic induction; the fluid motions are irrotational, provided the star is non-rotating. When the NS is allowed to rotate, the situation is complicated by couplings between the tidal field and the star's spin. The problem becomes tractable in the slow-rotation limit. In this case, the fluid motions induced by an external gravitomagnetic field are fully dynamical, even if the tidal field is stationary: interior metric and fluid variables are time-dependent, and vary on the timescale of the rotation period. Remarkably, the exterior geometry of the NS remains time-independent.   

Tidal deformability of compact boson stars

Gravitational waves can be used to probe the structure of compact objects in coalescing binary systems. This structure enters the pre-merger waveform through tidal interactions between the two bodies, characterized by each object's tidal deformability. We investigate whether these effects can differentiate binary black holes from systems containing compact boson stars. We compute the tidal deformability for various boson star models, including ultracompact non-topological solitonic solutions.   

Eccentric Inspirals with Self-Force and Spin-Force

Eccentric inspirals of a small mass about a more massive Schwarzschild black hole (EMRIs or IMRIs) are calculated using the gravitational self-force and the Mathisson-Papapetrou spin-force. These calculations include all dissipative and conservative effects that are first order in the mass ratio. We compute systems with initial eccentricities as high as e = 0.8, initial separations as large as 50 M, and arbitrary spin orientations. Including the spin-force causes the orbital plane to precess. Inspirals are calculated using an osculating-orbits scheme that is driven by self-force data from a hybrid self-force code and time-domain spin-force calculations. The hybrid approach uses both self-force data from a Lorenz gauge code and highly accurate flux data from a Regge-Wheeler-Zerilli code, allowing the hybrid model to track orbital phase of inspirals to within 0.1 radians or better over hundreds or thousands of orbits.   

Scalar self-force for generic bound orbits on Kerr

We perform scalar self-force calculations for inclined, eccentric orbits of a small, compact body in Kerr spacetime. To implement these calculations with arbitrary numerical precision, we generalize spectral source integration (SSI) techniques by introducing the Mino time parameter and extending mode decompositions to include a polar frequency for inclined motion. Calculations are conducted using a Mathematica code that implements these SSI techniques along with the Mano, Suzuki, and Takasugi (MST) formalism to determine the inhomogeneous wave function solutions to the Teukolsky equation. This allows us to improve the accuracy of previous calculations in the literature. We also probe the extended parameter space for various orbital inclinations. Further extension to the gravitational case is also considered.   

Progress toward post-adiabatic EMRI waveforms using the multiscale approximation

I present updates on an analytic approximation method for use in computing orbits and waveforms for Extreme Mass Ratio Inspirals (EMRIs). EMRIs are of particular interest for future space-based gravitational wave detectors, such as (e)LISA. Such gravitational wave detectors will depend on precise predictions of the waveform to take full advantage of the available data. The analytic approximation method for which I present new developments is based on second order self force methods, improved by use of the two-timescale approximation method. Once complete, this method will allow efficient computations of highly accurate EMRI waveforms.   

Charged Matter Tests of Cosmic Censorship for Extremal and Nearly-Extremal Black Holes

We investigate scenarios in which adding electrically charged matter to a black hole may cause it to become over-extremal, violating cosmic censorship. It has previously been shown that when the matter is localized as a point particle, no violation occurs for extremal black holes to lowest nonvanishing order in the particle's charge and mass. However, recent work has suggested that violations may be possible when the black hole deviates from extremality. We show that these potential violations always occur above lowest nonvanishing order, and conclude that no lowest-order violation can occur in the nearly-extremal case unless a violation also occurs in the extremal case. We also extend the previous results on point particles to show that no violations occur to second order in charge when an arbitrary charged matter configuration is added to an extremal Kerr black hole, provided only that the matter satisfies the null energy condition.