Bulletin of the American Physical Society
APS April Meeting 2012
Volume 57, Number 3
Saturday–Tuesday, March 31–April 3 2012; Atlanta, Georgia
Session R8: Approximations in General Relativity |
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Sponsoring Units: GGR Chair: Samuel Gralla, University of Maryland College Park Room: Embassy B |
Monday, April 2, 2012 1:30PM - 1:42PM |
R8.00001: How to Compute the Motion of a Body Samuel Gralla Previous work established a universal form for the equation of motion of bodies in theories of a metric and other tensor fields that have second-order field equations following from a covariant Lagrangian in four spacetime dimensions. Differences in the motion of the ``same'' body in two different theories are entirely accounted for by differences in the body's effective mass and charges in those different theories. In previous work the process of computing the mass and charges for a particular body was left implicit. I now obtain explicit expressions for the mass and charges of a body as surface integrals of the body fields at infinity, where the integrand is constructed from the symplectic current for that theory. This allows the entire prescription for computing the motion of a body to be written down in a few lines, in a manner universal across bodies and theories. [Preview Abstract] |
Monday, April 2, 2012 1:42PM - 1:54PM |
R8.00002: Self-forced motion of a scalar particle around a Schwarzschild black hole Ian Vega, Peter Diener, Barry Wardell, Steven Detweiler Motivated by the prospect of detecting low-frequency gravitational waves from the inspirals of compact objects onto massive black holes, much effort has gone into computing backreacting self-forces and investigating their effects on the motion of a point mass in black hole spacetimes. However, none of the work done to date has been able to look at what happens when you evolve the field and particle self-consistently. With newly-developed code, we have been able to accomplish just this, for the case of a scalar charge. In this talk we present the self-consistent motion of a scalar charge in the vicinity of a Schwarzschild black hole. These results are the first of its kind in the self-force community. [Preview Abstract] |
Monday, April 2, 2012 1:54PM - 2:06PM |
R8.00003: Self-consistent waveforms from a scalar charge in orbit around a Schwarzschild blak hole Peter Diener, Ian Vega, Barry Wardell, Steven Detweiler Extreme Mass Ratio In-spirals of compact objects into super massive black holes are expected to be a very important source of gravitational waves for future space based gravitational wave detectors. For the detection and analysis of gravitational waves from such events, it is necessary to know the waveforms to exquisite precision. Here we report on recent progress on using the effective source approach to the self-force problem to perform self-consistent evolutions of a scalar charge in orbit around a Schwarzschild black hole. The effective source approach allow us to cheaply extract the self-force acting on the scalar charge at every timestep and thereby evolve both the scalar field produced by the particle and the orbit of the particle at the same time in a self-consistent manner. We present the first waveforms generated using this method. [Preview Abstract] |
Monday, April 2, 2012 2:06PM - 2:18PM |
R8.00004: Inspiralling compact binaries in scalar-tensor theories of gravity: Equations of motion to 2.5 post-Newtonian order Saeed Mirshekari, Clifford Will We derive the scalar-tensor equations of motion for non-spinning compact objects, including black holes and neutron stars, to order $(v/c)^5$ beyond Newtonian order. We use the DIRE (Direct Integration of the Relaxed Einstein Equations) formalism [1] adapted to scalar- tensor theory, coupled with Eardley's scheme [2] for incorporating compact, quasi- stationary, self-gravitating bodies. We find that to this order of the PN approximation, binary black hole behavior in this class of theories is indistinguishable from that predicted by general relativity. Supported in part by the NSF, PHY 09-65133.\\[4pt] [1] A. G. Wiseman and C. M. Will, Phys. Rev. D 54, 4813 (1996); M. E. Pati and C. M. Will, Phys. Rev. D 62, 124015 (2000); ibid. 65, 104008 (2002).\\[0pt] [2] D. M. Eardley, Astrophys. J. Lett. 196, L59 (1975). [Preview Abstract] |
Monday, April 2, 2012 2:18PM - 2:30PM |
R8.00005: Tendex and Vortex Lines of Black Hole Spacetimes Aaron Zimmerman, David Nichols, Rob Owen, Fan Zhang, Jeandrew Brink, Yanbei Chen, Jeffrey Kaplan, Geoffrey Lovelace, Keith Matthews, Mark Scheel, Kip Thorne In a 3+1 split of spacetime, the Riemann curvature tensor is completely characterized by two symmetric, trace-free tensors: the tidal field and the frame-drag field. The eigenvalues and eigenvectors of these tensors characterize them completely, and the streamlines of the eigenvector fields provide a set of six field lines, called the tendex and vortex lines of the spacetime. These lines are directly analogous to the more familiar electric and magnetic field lines, and they provide a visual representation of the preferred directions of stress and frame dragging in a spacetime. I will review the theory of vortex and tendex lines, and discuss their application to the study of black hole spacetimes. In particular, I compare the tendex and vortex lines of a Kerr black hole in several gauges. [Preview Abstract] |
Monday, April 2, 2012 2:30PM - 2:42PM |
R8.00006: Tendex and Vortex Lines of Perturbed Schwarzschild and Kerr Black Holes David Nichols, Jeandrew Brink, Yanbei Chen, Jeffrey Kaplan, Geoffrey Lovelace, Keith Matthews, Robert Owen, Mark Scheel, Kip Thorne, Fan Zhang, Aaron Zimmerman As part of a program to use tendex and vortex lines to visualize binary-black-hole spacetimes and to provide simplified models of their dynamics, we focus in this talk on the late stages of binary-black-hole coalescence, when the post-merger black hole can be treated as a stationary black hole plus small gravitational perturbations. Specifically, we calculate the complete perturbative Riemann tensor of both Schwarzschild and Kerr black holes, which have been perturbed by the least-damped $l=2$, $m=2$ quasinormal modes of even and odd parities. From this perturbative curvature tensor, we compute its electric and magnetic parts, and then its vortex and tendex lines. We perform our analysis in an outgoing-radiation gauge, first found by Chrzanowski, which allows us to compare Schwarzschild and Kerr perturbations in similar gauges and to highlight the qualitative differences produced by the spin of the black hole. To investigate the slicing dependence of the vortex and tendex lines, we compare the results of our analytical calculations with those of the end stages of a numerical-relativity simulation. The qualitative agreement is good between these very different calculations. [Preview Abstract] |
Monday, April 2, 2012 2:42PM - 2:54PM |
R8.00007: Quasinormal modes of Kerr black holes in the eikonal limit Huan Yang, David Nichols, Fan Zhang, Aaron Zimmerman, Zhongyang Zhang, Yanbei Chen Quasinormal-mode frequencies of Kerr black holes with l=$\vert $m$\vert $ and l=0 relate simply to equatorial and polar unstable spherical photon orbits (orbits restricted on spherical shells), respectively, in the eikonal limit (l $>>$1). The real part of a mode's frequency corresponds to the photon's orbital frequency, and the imaginary part of the mode's frequency relates to the Lyapunov exponent of the photon's orbit. Although a similar correspondence between non-polar and non-equatorial photon orbits and quasinormal modes with large l and $\vert $m$\vert $!=l or 0 has been predicted before, an explicit calculation comparing null geodesics to these more general modes (in the eikonal limit) has not been performed. In this article, we use a WKB analysis to reveal the connection between general spherical photon orbits and the least damped quasinormal modes in the eikonal limit. With our result, we find that for any black-hole spin parameter, there are pairs of quasinormal modes that have different l,m but the same real-part of their frequencies; furthermore, for values of black-hole spin parameter with this mode degeneracy, the corresponding spherical photon orbits are closed. In addition to revealing more about the structure of the quasinormal-mode spectrum of Kerr black holes, this relationship between closed orbits and degenerate modes bears an interesting similarity with the onnection between degeneracy in the spectrum of the hydrogen atom in quantum mechanics and closed orbits of a classical particle in a Coulomb potential. [Preview Abstract] |
Monday, April 2, 2012 2:54PM - 3:06PM |
R8.00008: Relativistic effects in the tidal interaction between a white dwarf and a massive black hole in Fermi normal coordinates Roseanne M. Cheng, Charles R. Evans We present a new numerical code constructed to obtain accurate simulations of encounters between a star and a massive black hole. We assume Newtonian hydrodynamics and self-gravity for the star. The three-dimensional parallel code includes a PPMLR hydrodynamics module to treat the gas dynamics and a Fourier transform-based method to calculate the self-gravity. The formalism for calculating the relativistic tidal interaction in Fermi normal coordinates (FNC) allows the addition of an arbitrary number of terms in the tidal expansion. We present the relevant post-Newtonian terms for this code. Results are given for an $n=1.5$ polytrope with comparisons between simulations and predictions from the linear theory of tidal encounters. It is shown that the inclusion of the $l=3$ tidal term will cause the center of mass of the star to deviate from the origin of the FNC. We compare relativistic and Newtonian simulations for three different mass ratios, $\mu \sim 10^{-3}, 10^{-4}, 10^{-5}$. We find that for relativistic encounters, the dimensionless parameter, $T_2 (\eta)$, (which characterizes the energy deposited into non-radial oscillations) must not only be a function of the dimensionless disruption parameter, $\eta$, but also of a dimensionless relativistic parameter $\Phi_p$. [Preview Abstract] |
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