Bulletin of the American Physical Society
APS April Meeting 2016
Volume 61, Number 6
Saturday–Tuesday, April 16–19, 2016; Salt Lake City, Utah
Session C15: Mathematical Aspects of Relativity IInvited

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Sponsoring Units: GGR Chair: David Garfinkle, Oakland University Room: 251C 
Saturday, April 16, 2016 1:30PM  1:42PM 
C15.00001: A new conserved current 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 generates the conserved currents given in Andersson, B\"ackdahl, and Blue, as well as a new conserved current. These currents reduce to the sum of the Carter constants of the photons in the geometric optics limit, and generalize the current for scalar fields discovered by Carter. [Preview Abstract] 
Saturday, April 16, 2016 1:42PM  1:54PM 
C15.00002: Physics near Rapidly Spinning Black Holes Samuel Gralla, Alexandru Lupsasca, Scott Hughes, Achilleas Porfyriadis, Andrew Strominger, Niels Warburton The nearhorizon region of a nearextreme Kerr black hole possesses additional emergent symmetries and can be thought of as a spacetime in its own right. I will discuss the dynamics of particles and fields in this region, the constraints imposed by symmetry, and observational consequences for astrophysical black holes. [Preview Abstract] 
Saturday, April 16, 2016 1:54PM  2:06PM 
C15.00003: New charge for BMS symmetries Aruna Kesavan, Abhay Ashtekar Conservation laws of asymptotic symmetries are essential to quantify the amount of energymomentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the BondiMetznerSachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding twodimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984). [Preview Abstract] 
Saturday, April 16, 2016 2:06PM  2:18PM 
C15.00004: Methods for measuring and transporting angular momentum in general relativity David Nichols, Eanna Flanagan, Leo Stein, Justin Vines For an observer in a curved spacetime, elements of the dual space of the set of linearized Poincare transformations from the observer's tangent space to itself can naturally be interpreted as local linear and angular momenta. We give an operational procedure by which the observer can measure such local linear and angular momenta from the local spacetime geometry. These momenta can be interpreted as approximate versions of the linear and angular momenta of the spacetime about the observer's location. The measurement algorithm allows for a more accurate determination of the linear and angular momentum of stationary, asymptotically flat systems than previous proposals do. We also describe a prescription by which observers at different locations can compare values of their measured linear and angular momentum by using a specific transport equation, which refines previous proposals. These operational definitions may also prove useful for clarifying the physical interpretation of BondiMetznerSachs asymptotic charges in asymptotically flat spacetimes. [Preview Abstract] 
Saturday, April 16, 2016 2:18PM  2:30PM 
C15.00005: Gravitational wave memory in an expanding universe Alexander Tolish, Robert Wald We investigate the gravitational wave memory effect in an expanding FLRW spacetime. We find that if the gravitational field is decomposed into gaugeinvariant scalar, vector, and tensor modes after the fashion of Bardeen, only the tensor mode gives rise to memory, and this memory can be calculated using the retarded Green's function associated with the tensor wave equation. If locally similar radiation source events occur on flat and FLRW backgrounds, we find that the resulting memories will differ only by a redshift factor, and we explore whether or not this factor depends on the expansion history of the FLRW universe. We compare our results to related work by Bieri, Garfinkle, and Yau. [Preview Abstract] 
Saturday, April 16, 2016 2:30PM  2:42PM 
C15.00006: First Law for fields with Internal Gauge Freedom Kartik Prabhu We extend the analysis of Iyer and Wald to derive the First Law of blackhole mechanics in the presence of fields charged under an 'internal gauge group'. We treat diffeomorphisms and gauge transformations in a unified way by formulating the theory on a principal bundle. The first law then relates the energy and angular momentum at infinity to a potential times charge term at the horizon. The gravitational potential and charge give a notion of temperature and entropy respectively. [Preview Abstract] 
Saturday, April 16, 2016 2:42PM  2:54PM 
C15.00007: Nonlinear evolution and final fate of (charged) superradiant instability Stephen Green, Pablo Bosch, Luis Lehner We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a ReissnerNordstromAdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeateadly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes. [Preview Abstract] 
Saturday, April 16, 2016 2:54PM  3:06PM 
C15.00008: Gauge invariant perturbations of Petrov type D spacetimes Bernard Whiting, Abhay Shah The ReggeWheeler and Zerilli equations are satisfied by gauge invariant perturbations of the Schwarzschild black hole geometry. Both the perturbation of the imaginary part of $\Psi_2$ (a component of the Weyl curvature), and its time derivative, are gauge invariant and solve the ReggeWheeler equation with different sources. The $\Psi_0$ and $\Psi_4$ perturbations of the Weyl curvature are not only gauge, but also tetrad, invariant. We explore the framework in which these results hold, and consider what generalizations may extend to the Kerr geometry, and presumably to Petrov type D spacetimes in general. [Preview Abstract] 
Saturday, April 16, 2016 3:06PM  3:18PM 
C15.00009: A Fanfare of Trumpet Black Holes Jolyon Bloomfield The trumpet slicing of a black hole spacetime has a number of interesting properties: the slicing is horizon penetrating but never enters an ``alternative universe'' and the central singularity is automatically excised without the need for any boundary conditions. These properties have been exploited in movingpuncture numerical relativity codes. Analytic solutions for trumpet coordinates in the Schwarzschild geometry are well known. We present the analytic solution for the extremal trumpet slicing of the ReissnerNordstrom geometry, and use an unexpected structure present in this solution to derive new insights into the Schwarzschild trumpet coordinates. A new method for obtaining the limiting surface of a trumpet slicing is exploited to obtain the limiting surface for the Kerr geometry order by order in $a^2$. These results are then combined to construct the leadingorder extremal trumpet solution for the Kerr geometry. [Preview Abstract] 
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