Bulletin of the American Physical Society
APS April Meeting 2015
Volume 60, Number 4
Saturday–Tuesday, April 11–14, 2015; Baltimore, Maryland
Session X13: Post-Newtonian Approximation in General Relativity |
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Sponsoring Units: GGR Chair: Samuel Gralla, Harvard University Room: Key 9 |
Tuesday, April 14, 2015 10:45AM - 10:57AM |
X13.00001: An analytic function expansion approach to computing perturbations from extreme-mass-ratio binaries with eccentric orbits Charles Evans, Erik Forseth, Seth Hopper Several groups (Fujita 2012; Shah, Friedman, and Whiting 2014; Shah 2014; Fujita 2014) have recently described results from computing gravitational perturbations and the self-force at extraordinarily high precision for binaries with circular orbits in the extreme-mass-ratio limit. These calculations have allowed comparison with post-Newtonian (PN) theory at the lowest order in the mass ratio and uncovered new terms and coefficients in the PN expansion for circular orbits. We describe a new means of extending this analytic function expansion approach to include binaries with eccentric orbits, thus allowing terms in the known 3PN order expansion to be verified and to discover new terms beyond 3PN. [Preview Abstract] |
Tuesday, April 14, 2015 10:57AM - 11:09AM |
X13.00002: High-precision gravitational wave fluxes from eccentric extreme-mass-ratio binaries and post-Newtonian comparison Erik Forseth, Charles Evans, Seth Hopper We describe use of a new arbitrarily high precision gravitational perturbation and self-force method to compute gravitational wave energy fluxes from eccentric extreme-mass-ratio binaries. Fluxes computed over a range of radii and eccentricity allow successive post-Newtonian (PN) terms to be isolated and eccentricity enhancement functions to be determined. For eccentric binaries, the approach can be used to extend PN theory (at lowest order in the mass ratio) to higher orders beyond the present state-of-the-art at 3PN order. We present current results and ongoing progress with these calculations, as well as prospects for future applications. [Preview Abstract] |
Tuesday, April 14, 2015 11:09AM - 11:21AM |
X13.00003: Hybrid self-force approach for calculating long term inspirals of highly eccentric EMRIs Thomas Osburn, Niels Warburton, Charles Evans, Seth Hopper Astrophysical models predict EMRIs to have eccentricities peaked around $e \sim 0.7$ and as high as $e \sim 0.8$. Such high eccentricities are a challenge to compute even with state-of-the-art frequency-domain-based self-force codes. Prospects of future eLISA observations dictate striving for cumulative theoretical phase errors less than $\delta\Phi \sim 10^{-2}$. This requires the orbit-averaged force to have fractional errors less than $\sim 10^{-8}$ and the oscillatory part of the self-force to have errors less than $\sim 10^{-3}$. In recent years a Lorenz gauge self-force code has been used to calculate long term inspirals of Schwarzschild EMRIs with $e \simeq 0.2$. We have developed a hybrid Lorenz gauge/Regge-Wheeler gauge self-force code that is capable of satisfying the error criterion even for astrophysically relevant high eccentricities. We describe the method and show progress in applying the approach to long term inspiral calculations of high eccentricity binaries. [Preview Abstract] |
Tuesday, April 14, 2015 11:21AM - 11:33AM |
X13.00004: Experimental mathematics meets gravitational self-force: Using a high-accuracy numerical computation to obtain analytic forms for the post-Newtonian expansion of the redshift invariant to 11.5PN and beyond Nathan Johnson-McDaniel, Abhay Shah, Bernard Whiting The redshift invariant of a point particle in a circular orbit about a black hole gives the linear-in-mass-ratio portion of the binding energy of a circular binary with arbitrary mass ratio. This binding energy, in turn, encodes the system's conservative dynamics. We demonstrate how one can obtain analytic forms for high-order post-Newtonian (PN) coefficients of the redshift invariant for a circular orbit in Schwarzschild from high-accuracy numerical self-force results (over 1000 digits). Using this method, we improve the analytic knowledge of these coefficients to at least 11.5PN from the previously known 8.5PN. At these high orders, an individual coefficient can have over 30 terms, including a wide variety of transcendental numbers, when written out in full. We are still able to obtain analytic forms for such coefficients from the numerical data through a careful study of the structure of the expansion. We also obtain numerical values for even higher-order coefficients. The additional terms in the expansion we obtain improve the accuracy of the PN series for the redshift observable, even in the very strong-field regime inside the innermost stable circular orbit. The structure we find also allows us to predict certain ``leading logarithm''-type contributions to all orders. [Preview Abstract] |
Tuesday, April 14, 2015 11:33AM - 11:45AM |
X13.00005: Inhomogeneous Galilei-invariant 4D variational principles for classically interacting point particles following from Poincar\'e-invariant ones Harry Woodcock In a previous paper, we established the most general four-dimensional, non-instantaneous, non-particle symmetric inhomogeneous Galilei-invariant variational principle (VP) for classically interacting point particles. For a particular time-asymmetric retarded (advanced) interaction, the Galilei-invariant equations of motion and ten conserved quantities were shown not to involve integrals over worldliness and to have a Newtonian-like initial value problem, even though they are non-instantaneous. These might provide an alternative slow-motion approximation to the usual Newtonian one for celestial mechanics. However, they had no apparent connection to either SRT or GRT. Here, the general inhomogeneous Galilei-invariant VP is shown to follow as the non-relativistic limit of a general Poincar\'e-invariant VP with its interaction-arguments constructed from specific combinations of Poincar\'e-invariant two-body algebraic expressions. The approximately relativistic VP follows by a Taylor expansion of the Poincar\'e-invariant one. [Preview Abstract] |
Tuesday, April 14, 2015 11:45AM - 11:57AM |
X13.00006: Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries David Savickas General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity.\footnote{D. Savickas, Am. J. Phys. 70, 798 (2002).} When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod.\footnote{D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).} This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. [Preview Abstract] |
Tuesday, April 14, 2015 11:57AM - 12:09PM |
X13.00007: ABSTRACT MOVED TO X7.00009 |
Tuesday, April 14, 2015 12:09PM - 12:21PM |
X13.00008: Testing numerically the null Cauchy horizon singularity inside Kerr black holes Lior Burko, Gaurav Khanna, Anil Zengino\v{g}lu The Cauchy horizon inside a Kerr black hole develops an instability that transforms it into a curvature singularity. Perturbative analyses are consistent with the picture arising from fully nonlinear simulations of spherical charged black holes: this singularity is deformational weak and null for early retarded times. Despite much interest in this long--standing problem, no numerical simulations of the interior of a perturbed Kerr black hole have been done to date. Here, we report on preliminary results obtained from a linear simulation of the evolution of the fields under the collapse of a test wave packet. We use recent developments to a Teukolsky equation solver, which use (event) horizon--penetrating, hyperboloidal coordinates, which compactify null infinity and penetrate through both horizons. This numerical technology allows us to penetrate through the event horizon, and probe the fields on the approach to the Cauchy horizon singularity. We study the behavior of the Weyl scalars $\psi_0$ and $\psi_4$ and of the curvature scalar $R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}$, and confront our results with those of perturbation analysis. Our results may be useful when planning fully nonlinear numerical studies of rotating black hole interiors. [Preview Abstract] |
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