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Energy versus angular momentum in black hole binaries
Thibault Damour1, Alessandro Nagar, Denis Pollney
1Institut des Hautes Etudes Scientifiques, 91440 Bures-sur-Yvette, France.
Physical Review Letters
|May 1, 2012
Summary
The binding energy (E) and angular momentum (j) relation accurately diagnoses black-hole binary dynamics. The effective one body formalism closely matches numerical relativity simulations, unlike post-Newtonian expansions.
Area of Science:
- Astrophysics
- General Relativity
- Computational Physics
Background:
- Black-hole binaries are key systems for testing general relativity.
- Understanding their dynamics requires accurate theoretical models.
Purpose of the Study:
- To compute the gauge-invariant binding energy (E) versus angular momentum (j) relation for black-hole binaries.
- To assess the accuracy of analytic approximation schemes against numerical relativity.
Main Methods:
- Performed accurate numerical-relativity simulations for nonspinning black-hole binaries with mass ratios 1:1, 2:1, and 3:1.
- Computed the E(j) relation from simulation data.
- Compared numerical relativity results (E(NR)(j)) with analytic predictions (e.g., post-Newtonian, effective one body).
Main Results:
- The E(j) relation serves as a precise diagnostic for black-hole binary dynamics in the highly relativistic regime.
- Post-Newtonian expansions show significant deviations from numerical relativity results.
- The effective one body formalism accurately predicts the E(NR)(j) curve without numerical relativity calibration.
Conclusions:
- The effective one body formalism provides a highly accurate description of black-hole binary dynamics.
- Numerical relativity simulations are crucial for validating and improving analytic models in strong gravity regimes.
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