Bulletin of the American Physical Society
APS April Meeting 2014
Volume 59, Number 5
Saturday–Tuesday, April 5–8, 2014; Savannah, Georgia
Session X15: Approximations to General Relativity |
Hide Abstracts |
Chair: Bela Szilagyi, California Institute of Technology Room: 103 |
Tuesday, April 8, 2014 10:45AM - 10:57AM |
X15.00001: On incorporating post-Newtonian effects in N-body dynamics Clifford M. Will We show that the Newtonian energy of a test body orbiting a central body with a quadrupole moment is conserved over the relativistic pericenter precession timescale, if and only if relativistic, post-Newtonian cross terms between the mass monopole potential and the quadrupole potential are properly included in the equations of motion. We then argue that, for calculating the evolution of N-body systems with a central massive black hole over timescales comparable to the relativistic pericenter advance timescale, it is essential to include analogous ``cross terms'' in the equations of motion. These are post-Newtonian terms in the motion of a given body that represent a coupling between the potential of the central black hole and the potential due to other stars in the system. We display the post-Newtonian N-body equations of motion including a central black hole in a truncated form that includes all the relevant cross terms, in a format ready to use for numerical implementation. We do the same for hierarchical triple systems, and illustrate explicitly the effects of cross terms on the orbit-averaged equations of evolution for the orbit elements of the inner binary for the special case where the third body is on a circular orbit. [Preview Abstract] |
Tuesday, April 8, 2014 10:57AM - 11:09AM |
X15.00002: Radiation Reaction, Gravitational Self-Force and Higher-Order Perturbation Theory in General Relativity Steven Detweiler In General Relativity a small object of mass $m$ moves along a geodesic. This elementary fact implies that even under the influence of ``gravitational radiation reaction'' while the object orbits, say, a large black hole whose metric is $g_{ab}$, the motion of $m$ is geodesic---but not a geodesic of $g_{ab}$! The retarded metric perturbation $h^{\textrm{ret}}_{ab}$ caused by $m$ is determined using perturbation analysis. In a neighborhood of the small object, $h^{\textrm{ret}}_{ab}$ may be decomposed into two parts $h^{\textrm{ret}}_{ab} = h^S_{ab} + h^R_{ab}$ where the ``singular source term'' $h^S_{ab}$ appears, in coordinates local to the object, as the part of the Schwarzschild metric of mass $m$ which is linear in $m$ along with some other terms linear in $m$ that reflect the tidal distortion of the object. The ``regular remainder'' $h^{\textrm{R}}_{ab}$ is also linear in $m$ and is known to be differentiable in a neighborhood of the small object. The effect of radiation reaction and, more generally, the gravitational self-force then requires that the object move along a geodesic of $g_{ab} + h^{\textrm{R}}_{ab}$, which is a source free solution to the Einstein equations in a neighborhood of $m$. This description is extendable to include higher order perturbation analysis. [Preview Abstract] |
Tuesday, April 8, 2014 11:09AM - 11:21AM |
X15.00003: Second-Order Perturbations of Extreme Mass-Ratio Binary Schwarzschild Black Hole Systems Jonathan Thompson General advancement in perturbation theory usually involves pushing the perturbative analysis to higher orders. When examining the geodesic motion of a point particle in a circular orbit about a Schwarzschild mass, the full spacetime metric may be expanded in powers of the particle's mass, \(\mu\). Adhering to the standard formalism for self-force perturbations, one finds that by solving the first-order problem the particle no longer travels along a geodesic of the background metric, but rather a geodesic of the background plus an order \(\mathcal{O}(\mu)\) correction to the metric, typically written \(g_{\mu\nu}+h^{\mathrm{R}}_{\mu\nu}\). The field \(h^{\mathrm{R}}_{\mu\nu}\) is called the regular field. In advancing the perturbation to second-order, one must first calculate the first-order regular field, so as to account for the shift in the particle's worldline. Within this framework, second-order perturbative effects may be attained after solving the Einstein equations for a particle traveling along this regularly perturbed worldline, including as well the non-linear gravitational source terms arisng from the first-order metric perturbation. [Preview Abstract] |
Tuesday, April 8, 2014 11:21AM - 11:33AM |
X15.00004: Mode coupling mechanism for late--time Kerr tails Lior M. Burko, Gaurav Khanna We consider the decay rate for scalar fields in Kerr spacetime. We consider pure initial multipoles $\ell'$, and focus attention in the decay rate of the multipole $\ell$. We use an iterative method proposed by Gleiser, Price, and Pullin, and identify the mode coupling mechanism that gives rise to a decay rate formula recently proposed by Zengino\u{g}lu, Khanna, and Burko through the iterations in powers of the square of the Kerr black hole's specific angular momentum. We also show that one may identify the dominant channel of mode excitation, and obtain approximate results for the mode of interest by studying the dominant channel. The results of the dominant channel approximation approach the full--mode results at late times, and their difference approaches zero quadratically in inverse time. [Preview Abstract] |
Tuesday, April 8, 2014 11:33AM - 11:45AM |
X15.00005: A smoother effective source for scalar self-force simulations Peter Diener, Ian Vega, Barry Wardell In recent years the effective source approach to the self-force problem has had remarkable success culminating with the first self-consistent evolutions of a scalar charge around a Schwarzschild black hole. However, due primarily to the limited smoothness of the effective source used so far (it is continuous but not differentiable) the simulations have limited accuracy, significantly affecting their usefulness when comparing with other approaches. We will present new simulations with a smoother effective source (now twice differentiable) and contrast the accuracy and computational cost with the previous simulations. [Preview Abstract] |
Tuesday, April 8, 2014 11:45AM - 11:57AM |
X15.00006: Self-force in nonvacuum spacetimes Eric Poisson The gravitational self-force has thus far been formulated and computed in vacuum spacetimes. This is adequate for many applications, including the modelling of extreme mass-ratio inspirals around black holes. In other applications, however, such as the incorporation of the self-force in Hubeny's overcharging scenario (in which a Reissner-Nordstrom black hole may become overextreme by the absorption of a charged particle), the self-force must be formulated in a nonvacuum spacetime. In this talk I describe ongoing work with Peter Zimmerman on the formulation of the self-force when the background metric is not a solution to the vacuum field equations. We consider two types of situations, one involving a background spacetime with a background scalar field, which gives rise to a coupled scalar and gravitational self-force, and another involving a background electromagnetic field, which gives rise to a coupled electromagnetic and gravitational self-force. [Preview Abstract] |
Tuesday, April 8, 2014 11:57AM - 12:09PM |
X15.00007: Gravitational Self-Torque and Spin Precession in Compact Binaries Alexandre Le Tiec, Sam Dolan, Niels Warburton, Abraham Harte, Barry Wardell, Leor Barack We calculate the effect of self-interaction on the ``geodetic'' spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle $\psi$ per radian of orbital revolution for a particle carrying mass $\mu$ and spin $s \ll (G/c) \, \mu^2$ in a circular orbit around a Schwarzschild black hole of mass $M \gg \mu$. We compute $\psi$ through $\cal{O}(\mu/M)$ in perturbation theory, i.e, including the correction $\delta\psi$ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for $\delta\psi$, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semi-analytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches. [Preview Abstract] |
Tuesday, April 8, 2014 12:09PM - 12:21PM |
X15.00008: Compact Binaries and Supermassive Black Holes Shane Larson, Eric Addison, Pablo Laguna Given the stellar density near the galactic center, close encounters between compact object (CO) binaries and the supermassive black hole (SMBH) are plausible. Tidal disruptions resulting from such encounters have been proposed as possible sources of extreme-mass-ratio inspirals (EMRIs) and hyper velocity stars (HVS) in the galaxy, however the surviving binaries merit attention as they will suffer perturbations to their orbital parameters. We show the conditions under which CO binaries are able to survive the tidal field of supermassive black holes during a parabolic encounter, as well as the distribution of orbital parameters post-encounter. The effect of the tidal field on binaries that remain unbound from the SMBH is to de-circularize and shrink them, thus accelerating merger due gravitational radiation emission and affecting the predicted compact binary coalescence (CBC) rates. For disrupted binaries we show that the component of the compact object binary becoming bound to the supermassive black hole have initial eccentricities $\approx 1 - \mathcal{O}$(10$^{-2}$) but circularize dramatically by the time they enter the LISA band, consistent with previous studies. [Preview Abstract] |
Tuesday, April 8, 2014 12:21PM - 12:33PM |
X15.00009: Differential rotation of the unstable nonlinear r-mode John Friedman, Lee Lindblom, Keith Lockitch To second order in perturbation theory, the r-modes of uniformly rotating stars include an axisymmetric part that can be identified with a growing differential rotation of the background star. If one does not include radiation-reaction, the differential rotation is constant in time and has been computed by S\'a. It has a gauge dependence associated with a choice of equilibrium configuration: Adding to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders: $\delta\Omega = \delta\Omega(\varpi)$. For the radiation-reaction driven r-mode, however, the differential rotation includes an exponentially growing part that is unique, gauge-independent, and vorticity-conserving. We compute this differential rotation for slowly rotating Newtonian models, acted on by the radiation-reaction force of the unstable mode. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2019 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700