Spin-squared Hamiltonian of next-to-leading order gravitational interaction

Journal Article · Sat Nov 15 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.101503· OSTI ID:21250863

Steinhoff, Jan; Hergt, Steven; Schaefer, Gerhard ^[1]

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1. Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet, Max-Wien-Platz 1, 07743 Jena (Germany)

The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a three-dimensional covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves.

• OSTI ID: 21250863
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 78; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
BLACK HOLES
COMPUTERIZED SIMULATION
EQUATIONS OF MOTION
GRAVITATIONAL INTERACTIONS
GRAVITATIONAL WAVES
HAMILTONIANS
LINEAR MOMENTUM
SPIN
THREE-DIMENSIONAL CALCULATIONS