Bulletin of the American Physical Society
APS April Meeting 2017
Volume 62, Number 1
Saturday–Tuesday, January 28–31, 2017; Washington, DC
Session R6: Mathematical Aspects of General Relativity |
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Sponsoring Units: DGRAV Chair: Steven Carlip, University of California - Davis Room: Virginia C |
Monday, January 30, 2017 10:45AM - 10:57AM |
R6.00001: Blandford-Znajek without Plasma Maria Rodriguez, Theodore Jacobson We find vacuum solutions of Maxwell's equations describing energy extraction from cylindrical black holes and black holes in 2+1 spacetime dimensions. [Preview Abstract] |
Monday, January 30, 2017 10:57AM - 11:09AM |
R6.00002: Conserved currents for electromagnetic fields in the Kerr spacetime Alexander Grant, Eanna Flanagan For any classical linear Lagrangian field theory, the symplectic product provides a conserved current that is bilinear on the space of solutions. Given a linear mapping from the space of solutions into itself, a ``symmetry operator'', one can therefore generate quadratic conserved currents for any linear classical field theory. We apply this procedure to the case of electromagnetism on a Kerr background, showing that this procedure can generate the conserved currents given by Andersson, B\"ackdahl, and Blue, as well as two new conserved currents. These currents reduce to the sum of (positive powers of) the Carter constants of the photons in the geometric optics limit, and generalize the current for scalar fields discovered by Carter. We furthermore show that the fluxes of these new currents through null infinity and the horizon are finite. [Preview Abstract] |
Monday, January 30, 2017 11:09AM - 11:21AM |
R6.00003: Canonical energy and linear stability of Schwarzschild Kartik Prabhu, Robert Wald Consider linearised perturbations of the Schwarzschild black hole in 4 dimensions. Using the linearised Newman-Penrose curvature component, which satisfies the Teukolsky equation, as a Hertz potential we generate a 'new' metric perturbation satisfying the linearised Einstein equation. We show that the canonical energy, given by Hollands and Wald, of the 'new' metric perturbation is the conserved Regge-Wheeler-like energy used by Dafermos, Holzegel and Rodnianski to prove linear stability and decay of perturbations of Schwarzschild. We comment on a generalisation of this strategy to prove the linear stability of the Kerr black hole. [Preview Abstract] |
Monday, January 30, 2017 11:21AM - 11:33AM |
R6.00004: Horizon Instability of Extremal Charged Black Holes: Enhanced Growth for Charged Scalar Perturbations Peter Zimmerman We investigate the stability of highly charged Reissner-Nordström black holes to charged scalar perturbations. We show that the near-horizon region exhibits a transient instability which becomes the Aretakis instability in the extremal limit. The growth rates obtained match the enhanced rates of nonaxisymmetric perturbations to the near-extremal and extremal Kerr solutions. The agreement is shown to arise from a shared near-horizon symmetry of the two scenarios. [Preview Abstract] |
Monday, January 30, 2017 11:33AM - 11:45AM |
R6.00005: Nonlinear dynamics of near-extremal black holes Stephen Green, Samuel Gralla, Peter Zimmerman Near-extremal black holes possess a family of long lived quasinormal modes associated to the near-horizon throat geometry. For long lived modes, nonlinear interactions between the modes can potentially dominate over dissipation. We develop a framework for treating these interactions, and we study their dynamics. [Preview Abstract] |
Monday, January 30, 2017 11:45AM - 11:57AM |
R6.00006: Field Discontinuities and the Memory Effect Alexander Tolish, Robert Wald The "memory effect," a permanent change in the separation of test particles after the passage of a pulse of gravitational radiation, is a well-defined and fairly well-understood phenomenon in spacetimes with a notion of null infinity. However, many valid questions remain unanswered. For example, how do we define memory in the absence of null infinity? Or, does memory depend on the precise details of the radiation source or just on the source's asymptotic behavior? We believe that such questions are best answered using a simplified, distributional model of memory. If we consider linearized gravity on fixed background spacetimes, we can study the scattering of point particles, which radiate metric perturbations with sharp, step-function wave fronts. These steps correspond to derivative-of-delta-function discontinuities in the curvature, and according to the geodesic deviation equation, it is these discontinuities (and these alone) that contribute to permanent, finite changes in test particle separation--i.e., memory. Using this analysis of field discontinuities (as well as scalar and electromagnetic analogues of gravitational memory) we can isolate the physics of the memory effect from other, background phenomena. [Preview Abstract] |
Monday, January 30, 2017 11:57AM - 12:09PM |
R6.00007: Late-time quadrupolar gravitational wave power in de Sitter space Jeffrey Hazboun We have calculated the power emitted by a binary system in a cosmological context modeled by a stress energy source on a de~Sitter background. The calculation is based on the quadrupole formula for late-time gravitational waves in de~Sitter space put forward by Ashtekar, Bonga and Kesavan. There is little reason to expect, a priori, that the projection operator usually used to find the transverse-traceless components of a tensor in asymptotically flat spaces will accurately characterize the physical degrees of freedom in an asymptotically de~Sitter spacetime. Instead we use the differential recipe that is true in general, but cumbersome to solve explicitly. The solution presented is based on a conformally transformed version of the quadrupole moment from a Minkowski spacetime for a stable circular binary. A process for calculating the late time power is presented, which coincides with future null infinity. Progress on time dependent results will also be presented. We will discuss the physicality of these results and compare it to other results for gravitational waves in de~Sitter space, including recent results on gravitational wave memory. [Preview Abstract] |
Monday, January 30, 2017 12:09PM - 12:21PM |
R6.00008: Rain, Hail, and Drip frames of the Schwarzschild-de Sitter Geometry Tehani Finch Various families of coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry have been constructed by generalizing the Painleve-Gullstrand coordinates. Such observers have categorized as being in the rain frame, a hail frame, or a drip frame, by Taylor and Wheeler. This framework naturally progresses into a search for counterparts of these coordinate systems for the Schwarzschild-de Sitter (SdS) geometry. Consideration of local measurements made by a fiducial observer suggests that the conserved Killing quantity which best fits the designation of ``energy'' in the SdS geometry differs from the one which is typically denoted as such. This leads to Painleve-Gullstrand-style coordinate systems for the SdS geometry that differ from the naïve extrapolations of the Schwarzschild or de Sitter geometries. [Preview Abstract] |
Monday, January 30, 2017 12:21PM - 12:33PM |
R6.00009: Transverse traceless tensors in cosmology and gravitational wave theory Beatrice Bonga, Abhay Ashtekar There exists two distinct notions of transverse tracelessness tensors in the literature. In cosmology there exists a prefered time slicing because of spatial homogeneity and a transverse traceless tensor is a spatial tensor that is traceless and divergence-free with respect to the spatial metric. On the other hand, to study gravitational waves in asymptotically flat spacetimes, one often uses an algebraic projection operator in the asymptotic region to extract the transverse traceless piece of a tensor. A priori, these two notions have nothing to do with each other. The first notion is global in physical 3-space, whereas the second notion is local. Nonetheless, in the literature one often uses them interchangeably. This identification is incorrect. I will discuss the relation between the two notions. [Preview Abstract] |
Monday, January 30, 2017 12:33PM - 12:45PM |
R6.00010: An Example of Wang and Yau's Quasilocal Energy for Constant Radial Spacelike 2-Surfaces in a Maximally Rotating Black Hole Spacetime Shannon Ray, Warner Miller We present the first non-trivial illustration of Wang and Yau's quasilocal energy (WYQLE) for a maximally rotating Kerr spacetime. The surfaces for which we compute quasilocal energy (QLE) are axisymmetric closed space like 2-surfaces $\mathcal{S}$ with constant radii in Boyer-Lindquist coordinates. There exists a critical radius $r^*$ for which these 2-surfaces are isometrically embeddable in $\mathbb{R}^3$. For surfaces with $r \geq r^*$, the WYQLE trivially becomes the Brown and York QLE (BYQLE). To fully illustrate Wang and Yau's formulation, we compute the WYQLE for surfaces with $r < r^*$ that are not embeddable in $\mathbb{R}^3$. [Preview Abstract] |
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