Bulletin of the American Physical Society
APS April Meeting 2014
Volume 59, Number 5
Saturday–Tuesday, April 5–8, 2014; Savannah, Georgia
Session C16: Mathematical Aspects of General Relativity I |
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Chair: Ivan Booth Room: 104 |
Saturday, April 5, 2014 1:30PM - 1:42PM |
C16.00001: Universality in the collapse of rotating gravitational waves Tony Chu Choptuik's discovery of critical phenomena in the collapse of a spherically symmetric massless scalar field has spurred much interest over the years to explore critical collapse in more general settings. By evolving one-parameter families of initial data, it was found that spacetimes near the threshold of collapse or dispersion exhibited type II critical phenomena, with the properties of universality, scaling, and self-similarity. Shortly afterwards, similar results were obtained by Abrahams and Evans (and more recently by Sorkin) for the critical collapse of axisymmetric non-rotating gravitational waves. Despite many investigations into the critical collapse of other spherically symmetric or axisymmetric configurations, there has been relatively little headway on studying the critical collapse of non-axisymmetric configurations, which may carry angular momentum. In this talk, I will report on progress in simulating the critical collapse of non-axisymmetric rotating gravitational waves, which instead exhibit signs of type I critical phenomena, and comment on evidence for universality. [Preview Abstract] |
Saturday, April 5, 2014 1:42PM - 1:54PM |
C16.00002: Thermodynamic and Dynamic Stability of Asymptotically Anti-de Sitter Black Holes Stephen Green, Stefan Hollands, Akihiro Ishibashi, Robert Wald Hollands and Wald previously established a criterion for dynamic stability of asymptotically flat black holes with respect to linearized axisymmetric perturbations. They showed that stability is equivalent to positivity of a canonical energy on a certain class of these perturbations. We adapt this work to the asymptotically anti-de Sitter case, and find that the restriction to axisymmetric perturbations is lifted as a consequence of the reflecting nature of spatial infinity. The consideration of non-axisymmetric perturbations allows us to address phenomena such as superradiant instabilities. As in the previous work, the canonical energy can be expressed in terms of second order variations of thermodynamic quantities, thereby establishing a connection between thermodynamic and dynamic stability. We discuss the relationship between negative canonical energy configurations and the presence of a generalized ergosphere. [Preview Abstract] |
Saturday, April 5, 2014 1:54PM - 2:06PM |
C16.00003: Positive energy and stability of black holes Kartik Prabhu, Robert Wald Hollands and Wald showed that dynamic stability of stationary axisymmetric black holes is equivalent to positivity of canonical energy on a space of linearised axisymmetric perturbations satisfying certain boundary and gauge conditions. We show that the ``kinetic energy'' --- the energy of the perturbations that are odd under reflection in \( t \) and \(\phi \) --- is positive. We discuss implications of having a positive kinetic energy for proving exponential growth in the case where the ``potential energy'' can be made negative. [Preview Abstract] |
Saturday, April 5, 2014 2:06PM - 2:18PM |
C16.00004: Turning Point Instabilities for Relativistic Stars and Black Holes Joshua Schiffrin, Robert Wald In the light of recent results relating dynamic and thermodynamic stability of relativistic stars and black holes, we re-examine the relationship between ``turning points''---i.e., extrema of thermodynamic variables along a one-parameter family of solutions---and instabilities. We give a proof of Sorkin's general result---showing the existence of a thermodynamic instability on one side of a turning point---that does not rely on heuristic arguments involving infinite dimensional manifold structure. We use the turning point results to prove the existence of a dynamic instability of black rings in $5$ spacetime dimensions in the region where $c_J > 0$, in agreement with a result of Figueras, Murata, and Reall. [Preview Abstract] |
Saturday, April 5, 2014 2:18PM - 2:30PM |
C16.00005: Retarded Fields of Null Particles and the Memory Effect Alexander Tolish, Robert Wald We consider the scalar, electromagnetic and linearized gravitational fields produced by a particle moving on a null geodesic. We cut off the null source at a finite time $t_0$ and then consider two limits: (i) the limit as the observation point goes to null infinity at fixed $t_0$, and (ii) the limit $t_0\to-\infty$ at fixed observation point. Limit (i) gives rise to a velocity kick on distant test particles in the scalar and electromagnetic cases, and a memory effect (permanent change in relative separation of test particles) in the gravitational case, in agreement with past analyses. Limit (ii) does not exist in the scalar case or for the Lorenz gauge potential and metric perturbation in the electromagnetic and gravitational cases. However, we find well defined distributional limits for the electromagnetic field strength and Riemann tensors. In the gravitational case, there is no memory effect associated with this limit. This suggests that the memory effect should not be interpreted as arising simply from the passage of null stress energy to null infinity but rather as arising from a burst of radiation associated with the creation of the null stress-energy (as in case (i)) or, more generally, with radiation present that was not produced by the null stress-energy. [Preview Abstract] |
Saturday, April 5, 2014 2:30PM - 2:42PM |
C16.00006: Spacetime Approach to Force-free Magnetospheres Samuel Gralla, Ted Jacobson Force-Free Electrodynamics (FFE) describes a magnetically dominated relativistic plasma, as expected to exist near pulsars and (some) supermassive black holes. Despite being fully covariant, FFE has primarily been studied in $3+1$ frameworks. We have instead taken a spacetime approach, focusing on observer-independent properties. In this talk I will describe some of the progress we have made with this approach, both new results and improved understanding of previous results. I will focus particularly on energy extraction from spinning conductors and black holes. [Preview Abstract] |
Saturday, April 5, 2014 2:42PM - 2:54PM |
C16.00007: Magnetohydrodynamical Analogue of a Black Hole Nelson Zamorano, Felipe Asenjo We study the conditions that a plasma fluid and its container should meet to generate a magneto-acoustic horizon. This effect becomes an alternative to the analogue black hole found in a transonic fluid flow setting. In this context we use the magnetohydrodynamic formalism (MHD) to analyze the evolution of an irrotational plasma fluid interacting with an external constant magnetic field. Under certain plausible approximations, the dynamic of the field perturbations is described by a scalar field potential that follows a second order differential equation. As we prove here, this equation corresponds to the wave equation associated to a scalar field in a curved space-time. This horizon emerges when the local speed of the medium grows larger than the sound velocity. The magnetic field generates an effective pressure which contributes to the magneto-acoustic speed. We compare these results with the known physics of analogue black holes. We will also refer to our ongoing experiment that, in its first stage, attempts to reproduce the wave horizons found in an open channel with an obstacle: PRL 106, 021302(2011). [Preview Abstract] |
Saturday, April 5, 2014 2:54PM - 3:06PM |
C16.00008: The Quasinormal Modes of the Kerr-Newman Spacetime in the Small Charge Limit Zachary Mark, Huan Yang, Aaron Zimmerman, Yanbei Chen The quasinormal modes (QNM) solutions of the linearized Einstein equations are important tools for calculating gravitational waveforms from astrophysical systems and for considering the stability of the background spacetime. The equations governing perturbing fields on a Kerr-Newman background fail to separate or decouple, making an exact calculation of the QNM frequencies currently intractable. In this study we circumvent this issue by looking at the limit \(Q \ll M\). In this regime, we can apply perturbation theory a second time to the small charge parameter \(q = Q^2/M^2\) and semi-analytically arrive at the QNM frequencies to first order in q. [Preview Abstract] |
Saturday, April 5, 2014 3:06PM - 3:18PM |
C16.00009: Eikonal Green function of the Kerr spacetime Aaron Zimmerman, Huan Yang, Fan Zhang, Yanbei Chen The Green function of a black hole spacetime determines its response to small perturbations. The Green function can be used to calculate the self-force correction to the motion of a small mass about the black hole. We have constructed the part of the Green function arising from perturbations which are partially trapped at the light ring, in the eikonal (high-frequency) limit. This ``quasinormal mode'' part of the Green function is important at early and intermediate response times. In the eikonal limit, it diverges where null geodesics connect a response point to the source point, and it exhibits a four-fold singularity structure. I will discuss our results, future applications of our work, and open questions. [Preview Abstract] |
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