Binary-black-hole initial data with nearly-extremal spins

Abstract: There is a significant possibility that astrophysical black holes with nearly-extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing binary-black-hole initial data, focusing on their ability to generate black holes with nearly-extremal spins: (i) Bowen-York initial data, including standard puncture data (based on conformal flatness and Bowen-York extrinsic curvature), (ii) standard quasi-equilibrium initial data (based on the extended-conformal-thin-sandwich equations, conformal flatness, and maximal slicing), and (iii) quasi-equilibrium data based on the superposition of Kerr-Schild metrics. We find that the two conformally-flat methods (i) and (ii) perform similarly, with spins up to about 0.99 obtainable at the initial time. However, in an evolution, we expect the spin to quickly relax to a significantly smaller value around 0.93 as the initial geometry relaxes. For quasi-equilibrium superposed Kerr-Schild (SKS) data [method (iii)], we construct initial data with \emph{initial} spins as large as 0.9997. We evolve SKS data sets with spins of 0.93 and 0.97 and find that the spin drops by only a few parts in 10^4 during the initial relaxation; therefore, we expect that SKS initial data will allow evolutions of binary black holes with relaxed spins above 0.99. [Abstract abbreviated; full abstract also mentions several secondary results.]

Summary of "Binary-black-hole initial data with nearly-extremal spins"

The paper "Binary-black-hole initial data with nearly-extremal spins" investigates the possibility of generating astrophysical black holes with spins approaching extremal values using different approaches to initial data construction for numerical simulations. The study is based on the hypothesis that black holes in the universe might exhibit nearly-extremal spin values due to processes such as accretion, and it examines three methods for constructing binary-black-hole initial data along these lines.

Methods of Data Construction

The authors compare three different methodologies for constructing initial data in numerical simulations to achieve nearly-extremal spins:

1. Bowen-York Initial Data: Utilizing standard puncture data based on conformal flatness and Bowen-York extrinsic curvature, this approach was initially unable to sustain spins above 0.93 during simulations, despite obtaining spins of up to 0.99 at the initial stage.

2. Standard Quasi-equilibrium Initial Data: This technique leverages extended-conformal-thin-sandwich equations with conformal flatness and maximal slicing, finding similar performance limitations as the Bowen-York method, with spins relaxing to about 0.93.

3. Quasi-equilibrium Superposed Kerr-Schild Initial Data (SKS): This approach involves superposing Kerr-Schild metrics and demonstrates an ability to achieve initial spin values as high as 0.9997, with spins relaxing significantly less than alternatives during evolutions.

Numerical Results and Implications

The research highlights several significant numerical findings:

• Spin Relaxation: Both conformally-flat methods (Bowen-York and standard quasi-equilibrium) exhibit substantial spin relaxation during numerical evolution, which limits their practical utility in simulating nearly-extremal spins. SKS data, conversely, suffers minimal spin relaxation, making it more robust for simulations requiring high spin fidelity.

• Secondary Observations: The study also presents secondary results, such as power-law coefficients for spin relaxation of puncture initial data and embedding diagrams for spinning black holes, offering insights into the geometric properties of these initial data sets.

The implications of these findings are substantial for both practical and theoretical explorations in astrophysics and numerical relativity. The capability to simulate black holes with spins closer to extremal values may improve the accuracy of gravitational wave predictions and allow researchers to better explore the effects of high-spin dynamics.

Theoretical and Practical Implications

From a theoretical perspective, achieving initial data sets that start close to the expected equilibrium spin state of astrophysical black holes opens avenues for more accurate modeling of phenomena such as gravitational wave emission during binary black hole mergers. Practically, the SKS approach could greatly enhance numerical simulations which use spectral methods due to their reduced transient effects and more stable evolution properties.

Future Directions

The results suggest several avenues for further research, including deeper exploration into the stability properties of SPK-based evolutions and extending simulations into full binary evolutions through merger and ringdown. The findings might catalyze advancements in measuring black hole spins directly from observational data, refining estimates related to cosmic events involving spinning black holes, and further unveiling mysteries tied to possible cosmic censorship scenarios.

In summary, the paper presents crucial insights into maximizing spin stability in numerical simulations for black holes, marking notable progress toward more accurate computational representations of these cosmic phenomena.