Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hole

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.044051· OSTI ID:21432927

Fujita, Ryuichi; Iyer, Bala R ^[1]

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1. Raman Research Institute, Bangalore 560 080 (India)

Recent breakthroughs in numerical relativity enable one to examine the validity of the post-Newtonian expansion in the late stages of inspiral. For the comparison between post-Newtonian (PN) expansion and numerical simulations, the waveforms in terms of the spin-weighted spherical harmonics are more useful than the plus and cross polarizations, which are used for data analysis of gravitational waves. Factorized resummed waveforms achieve better agreement with numerical results than the conventional Taylor expanded post-Newtonian waveforms. In this paper, we revisit the post-Newtonian expansion of gravitational waves for a test particle of mass {mu} in circular orbit of radius r{sub 0} around a Schwarzschild black hole of mass M and derive the spherical harmonic components associated with the gravitational wave polarizations up to order v{sup 11} beyond Newtonian. Using the more accurate h{sub lm}'s computed in this work, we provide the more complete set of associated {rho}{sub lm}'s and {delta}{sub lm}'s that form important bricks in the factorized resummation of waveforms with potential applications for the construction of further improved waveforms for prototypical compact binary sources in the future. We also provide ready-to-use expressions of the 5.5PN gravitational waves polarizations h{sub +} and h{sub x} in the test-particle limit for gravitational waves data analysis applications. Additionally, we provide closed analytical expressions for 2.5PN h{sub lm}, 2PN {rho}{sub lm}, and 3PN {delta}{sub lm}, for general multipolar orders l and m in the test-particle limit. Finally, we also examine the implications of the present analysis for compact binary sources in Laser Interferometer Space Antenna.

• OSTI ID: 21432927
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevD.82.044051; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTENNAS
BLACK HOLES
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
DATA ANALYSIS
GRAVITATIONAL WAVES
INTERFEROMETERS
LASER RADIATION
MASS
ORBITS
PARTICLES
POLARIZATION
SCHWARZSCHILD METRIC
SPACE
SPHERICAL CONFIGURATION
SPHERICAL HARMONICS
SPIN
WAVE FORMS
ANGULAR MOMENTUM
CONFIGURATION
ELECTRICAL EQUIPMENT
ELECTROMAGNETIC RADIATION
EQUIPMENT
EVALUATION
FUNCTIONS
MEASURING INSTRUMENTS
METRICS
PARTICLE PROPERTIES
RADIATIONS
SIMULATION