Narrow Results

Recently, by the end of their second observing run, advanced LIGO and Virgo have detected some binary black hole mergers. In this paper, we show that the acceleration of black holes around each other causes the emergence of two Rindler space–times. The parameters of the black hole in each region change in opposite order to the parameters of the black hole in the other region. Also, the acceleration has a direct relation to the black hole entropies and their observed redshifts.

Over the last decade gravitational waveforms of binary black holes have been investigated using a variety of approaches like the Multipolar post-Minkowskian formalism, Numerical Relativity and the Effective-One-Body method. We review these complementary approaches and summarize the current status of these investigations of relevance to construct the best templates for the next generation Advanced gravitational wave detectors.

We discuss the merger process of binary black holes with Hawking radiation taken into account. Besides the redshifted radiation to infinity, binary black holes can exchange radiation between themselves, which is first redshifted and then blueshifted when it propagates from one hole to the other. The exchange rate should be large when the temperature-divergent horizons are penetrating each other to form a single horizon with unique temperature. This will cause nonnegligible mass and angular momentum transfer between the black holes during the merging process of the horizons. We further argue in the large mass ratio limit that the light hole whose local evaporation is enhanced by the competing redshift–blueshift effects will probably evaporate or decay completely before reaching the horizon of the heavy one. We also discuss the possibility of testing Hawking radiation and even exploring the information loss puzzle in gravitational wave observations.

The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into “fast and slow” degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlevé transcendents are a smoking gun of integrable structures, we propose the Painlevé-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward’s conjecture relating integrable and (anti-)self-dual solutions can provide the avenue to encode background binary black hole data in (nonlocal) twistor structures.

We performed a series of 1381 full numerical simulations of high energy collision of two black holes to search for the maximum recoil velocity after their merger. We studied equal mass binaries with opposite spins pointing along the orbital plane to maximize asymmetric gravitational radiation and performed a search of spin orientations in the plane, impact parameters, and initial linear momenta to find a maximum recoil velocity extrapolated to the extreme spinning case of $28,562\pm 342$km/s, thus tightly bounding recoil by $10\%$ the speed of light.

Gravitational waves from binary black-hole mergers can be used to provide distance and angular location information of these sources, which, upon comparison with galaxy catalogs, can be used to measure the Hubble Constant. For a given galaxy catalog, and binary merger rates associated with each galaxy, a Fisher information approach can be used to estimate the measurement error for the Hubble Constant from the dark siren approach. In this paper, we validate the predictions from the Fisher information approach by carrying out a series of Monte Carlo simulations. Except in situations with very low event rates, the Fisher information approach is shown to predict the statistical errors of the Bayesian approach with good accuracy.

We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to all orders in the black holes’ spins. Though the spins are treated nonperturbatively, surprisingly, the binding energy and the flux are given by simple analytical expressions which are finite (respectively third- and fifth-order) polynomials in the spins. Our final results are restricted to the important case of quasi-circular orbits with the black holes’ spins aligned with the orbital angular momentum.

The orbits of binary black hole systems shrink due to gravitational radiations. At the last stage of merger, the gravitational wave (GW) signals can be detected by the groundbased detectors, such as LIGO and Virgo. In the data analysis of GWs emitted from merging black hole binaries, the matched filtering method is employed in the detection pipeline to identify GW events. Once a detection is made, the parameter estimation seeks the physical parameters of the GW source. This pipeline repeatedly performs overlap computations by generating theoretical waveforms and matching those to the detector data based on Monte Carlo simulations. In this talk, we briefly review the search and the parameter estimation in GW data analysis, and introduce the Fisher matrix (FM) method that has been mainly used to predict the uncertainties in the parameter estimations analytically. The FM is very easy to compute and has very low computational cost compared to Monte Carlo simulations. Using the FM, we calculate the parameter estimation uncertainties for binary black hole systems.

The following sections are included:

• Introductory Remarks

• Cauchy Evolution

• Characteristic Extraction

• Binary Black Hole Evolution

• Acknowledgments

• References