Post-Newtonian Expansion Of Gravitational Waves Research Articles

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

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 $\m$ in circular orbit of radius $r_0$ around a Schwarzschild black hole of mass $M$ and derive the spherical harmonic components associated with the gravitational wave polarizations up to order $v^{11}$ beyond Newtonian. Using the more accurate $h_{\ell m}$'s computed in this work, we provide the more complete set of associated $\rho_{\ell m}$'s and $\delta_{\ell m}$'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 $h_+$ and $h_\times$ in the test-particle limit for gravitational wave data analysis applications. Additionally, we provide closed analytical expressions for 2.5PN $h_{\ell m}$, 2PN $\rho_{\ell m}$ and 3PN $\delta_{\ell m}$, for general multipolar orders $\ell$ 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.

Post-Newtonian Expansion of Gravitational Waves from a Particle in Slightly Eccentric Orbit around a Rotating Black Hole

5) beyond the quadrupole formula. We find that circular orbit is stable up through the order O(v 5 ) even if the spin of a black hole exists. Using the results, we argue the total phase of gravitational waves from coalescing compact binaries. We find that the eccentricity is important at O(v 5 ) order if the initial eccentricity in the LIGO's band is greater than 0.4. There are possibilities that binaries which have a non-negligible eccentricity will be observed by laser interferometers and our results will be useful to analyze gravitational waves from such binaries.

Analytic Black Hole Perturbation Approach to Gravitational Radiation.

We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently, the Teukolsky equation is used directly in its original form. The former’s advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter’s advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.

Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole: Effects of Black Hole Absorption

Coalescing compact binaries are the most promising candidates for detection by near-future, ground based laser interferometric detectors. It is very important to investigate detailed wave forms from coalescing compact binaries. When one (or two) of the stars is a black hole, some of those waves are absorbed by the black hole. Here, we consider a case when a test particle moves circular orbit on the equatorial plane around a Kerr black hole, and calculate the the energy absorption rate by the black hole. We adopt an analytic techniques for the Teukolsky equation which was found by Mano, Suzuki, and Takasugi (1996). We calculated the energy absorption rate to O((v/c)13) beyond the Newtonian-quadrupole formula of gravitational waves radiated to infinity, assuming v/c ≪ 1. Here v is the velocity of the particle. We find that, when a black hole is rotating, the black hole absorption appear at O((v/c)5) beyond the Newtonian-quadrapole formula. These effects become more important as the mass of the black hole becomes larger. We also found that the black hole absorption is more important when a particle moves to the same direction of the black hole rotation. All the details of this paper is presented in Tagoshi et al. (1997).

Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole: Effects of Black Hole Absorption

When a particle moves around a Kerr black hole, it radiates gravitational waves.Some of these waves are absorbed by the black hole. We calculate such absorption of gravitational waves induced by a particle of mass mu in a circular orbit on an equatorial plane around a Kerr black hole of mass M. We assume that the velocity of the particle v is much smaller than the speed of light c and calculate the energy absorption rate analytically. We adopt an analytic technique for the Teukolsky equation developed by Mano, Suzuki and Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to the lowest order. We find that the black hole absorption occurs at O((v/c)^5) beyond the Newtonian-quadrapole luminosity at infinity in the case when the black hole is rotating, which is O((v/c)^3) lower than the non-rotating case. Using the energy absorption rate, we investigate its effects on the orbital evolution of coalescing compact binaries.

Post-Newtonian Expansion of Gravitational Waves from a Compact Star Orbiting a Rotating Black Hole in Brans-Dicke Theory: Circular Orbit Case

5) beyond the leading, Newtonian-dipole formula. The calculation is based on a method developed recently by Sasaki in the Schwarzschild case in the context of general relativity. The orbit of a compact star is restricted on the equatorial plane. Then we estimate the post-Newtonian effect of scalar radiation to the orbital evolution of coalescing compact binaries. We find that the post· Newtonian effect of scalar radiation is small in the LIGO band if we take into account the experimental bound of the Brans·Dicke parameter (/)8D>500. On the other hand, we find that the post· Newtonian effect of the scalar radiation is not negligible for the LISA experiment.

Post-Newtonian expansion of gravitational waves from a particle in circular orbit around a rotating black hole: Up to O(v8) beyond the quadrupole formula.

Extending a method developed by Sasaki in the Schwarzschild case and by Shibata, Sasaki, Tagoshi, and Tanaka in the Kerr case, we calculate the post-Newtonian expansion of the gravitational wave luminosities from a test particle in circular orbit around a rotating black hole up to $O(v^8)$ beyond the quadrupole formula. The orbit of a test particle is restricted on the equatorial plane. We find that spin dependent terms appear in each post-Newtonian order, and that at $O(v^6)$ they have a significant effect on the orbital phase evolution of coalescing compact binaries. By comparing the post-Newtonian formula of the luminosity with numerical results we find that, for $30M\lesssim r \lesssim 100M$, the spin dependent terms at $O(v^6)$ and $O(v^7)$ improve the accuracy of the post-Newtonian formula significantly, but those at $O(v^8)$ do not improve.

Post-Newtonian Expansion of Gravitational Waves from a Particle in Slightly Eccentric Orbit around a Rotating Black Hole

Using the Teukolsky and Sasaki-Nakamura equations, we calculate the post-Newtonian expansion of the energy and angular momentum luminosities of gravitational waves from a test particle with slightly eccentric orbit around a rotating black hole up to O(v5) beyond the quadrupole formula. We find that circular orbit is stable up through the order O(v5) even if the spin of a black hole exists. Using the results, we argue the total phase of gravitational waves from coalescing compact binaries. We find that the eccentricity is important at O(v5) order if the initial eccentricity in the LIGO's band is greater than 0.4. There are possibilities that binaries which have a non-negligible eccentricity will be observed by laser interferometers and our results will be useful to analyze gravitational waves from such binaries.

Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbit around a Schwarzschild Black Hole

Based upon the formalism recently developed by one of us (MS), we analytically perform the post-Newtonian expansion of gravitational w;;tves from a test particle in circular orbit of radius ro around a Schwarzschild black hole of mass M. We calculate gravitational wave forms and luminos­ ity up to v 8 order beyond Newtonian, where v=(M/ro) 112 • In particular, we give the exact analytical values of the coefficients of In v terms at v 6 and v 8 orders in the luminosity and confirm the numerical values obtained previously by one of us (HT) and Nakamura. Our result is valid in the small mass limit of one body and gives an important guideline for the .gravitational wave physics of coalescing compact binaries.

Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbit around a Schwarzschild Black Hole

Based upon the formalism recently developed by one of us (MS), we analytically perform the post-Newtonian expansion of gravitational waves from a test particle in circular orbit of radius r0 around a Schwarzschild black hole of mass M. We calculate gravitational wave forms and luminosity up to v8 order beyond Newtonian, where v = (M/r0)1/2. In particular, we give the exact analytical values of the coefficients of ln v terms at v6 and v8 orders in the luminosity and confirm the numerical values obtained previously by one of us (HT) and Nakamura. Our result is valid in the small mass limit of one body and gives an important guideline for the gravitational wave physics of coalescing compact binaries.