Bulletin of the American Physical Society
APS April Meeting 2015
Volume 60, Number 4
Saturday–Tuesday, April 11–14, 2015; Baltimore, Maryland
Session H13: Statics and Dynamics in Spacetimes |
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Sponsoring Units: GGR Chair: Javier Olmedo, Louisiana State University Room: Key 9 |
Sunday, April 12, 2015 8:30AM - 8:42AM |
H13.00001: Simulation of Black Hole Collisions in Asymptotically anti-de Sitter Spacetimes Hans Bantilan, Paul Romatschke The main purpose of this talk is to describe, in detail, the necessary ingredients for achieving stable Cauchy evolution of black hole collisions in asymptotically anti-de Sitter (AdS) spacetimes. I will begin by motivating this program in terms of the heavy-ion physics it is intended to clarify. I will then give an overview of asymptotically AdS spacetimes, the mapping to the dual conformal field theory on the AdS boundary, and the method we use to numerically solve the fully non-linear Einstein field equations with AdS boundary conditions. As a concrete example of these ideas, I will describe the first proof of principle simulation of stable AdS black hole mergers in 5 dimensions. [Preview Abstract] |
Sunday, April 12, 2015 8:42AM - 8:54AM |
H13.00002: Conserved quantities and dual turbulent cascades in Anti--de Sitter spacetime Stephen Green, Alex Buchel, Luis Lehner, Steven Liebling We consider the dynamics of a spherically symmetric massless scalar field coupled to general relativity in Anti--de Sitter spacetime in the small-amplitude limit. Within the context of our previously developed two time framework (TTF) to study the leading self-gravitating effects, we demonstrate the existence of two new conserved quantities in addition to the known total energy $E$ of the modes: The particle number $N$ and Hamiltonian $H$ of our TTF system. $H$ represents the next-order contribution after $E$ to the total ADM mass $M$. Simultaneous conservation of $E$ and $N$ implies that weak turbulent processes undergo dual cascades (direct cascade of $E$ and inverse cascade of $N$ or vice versa). This partially explains the observed dynamics of 2-mode initial data. In addition, conservation of $E$ and $N$ limits the region of phase space that can be explored within the TTF approximation and in particular rules out equipartion of energy among the modes for general initial data. Finally, we discuss possible effects of conservation of $N$ and $E$ on late time dynamics. [Preview Abstract] |
Sunday, April 12, 2015 8:54AM - 9:06AM |
H13.00003: Reflection Symmetry in Higher Dimensional Black Hole Spacetimes Robert Wald, Joshua Schiffrin It is well known that for any 4-dimensional asymptotically flat, stationary, and axisymmetric vaccum solution of Einstein's equation, there exists a $t$-$\phi$ reflection isometry that reverses the direction of the timelike Killing vector field and the direction of the axial Killing vector field. However the proof of this result does not generalize to higher spacetime dimensions. Here we consider asymptotically flat, stationary, and axisymmetric (i.e., having one or more commuting rotational isometries) black hole spacetimes in vacuum general relativity in $d \geq 4$ spacetime dimensions such that the action of the isometry group is trivial. We prove that there exists a $t$-$\phi$ reflection isometry that reverses the direction of the timelike Killing vector field and the direction of each axial Killing vector field. The proof relies in an essential way on the first law of black hole mechanics. [Preview Abstract] |
Sunday, April 12, 2015 9:06AM - 9:18AM |
H13.00004: Growth rate for blackhole instabilities 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. Using a reflection isometry of the background, we split the energy into kinetic and potential parts. We show that the kinetic energy is positive. In the case that potential energy is negative, we show existence of exponentially growing perturbations and further obtain a variational formula for the growth rate. [Preview Abstract] |
Sunday, April 12, 2015 9:18AM - 9:30AM |
H13.00005: Numerical Tests of the Cosmic Censorship Conjecture via Event-Horizon Finding Maria Okounkova, Christian Ott, Mark Scheel, Bela Szilagyi We present the current state of our research on the possibility of naked singularity formation in gravitational collapse, numerically testing both the cosmic censorship conjecture and the hoop conjecture. The former of these posits that all singularities lie behind an event horizon, while the later conjectures that this is true if collapse occurs from an initial configuration with all circumferences $C \leq 4\pi M$. We reconsider the classical Shapiro \& Teukolsky (1991) prolate spheroid naked singularity scenario. Using the exponentially error-convergent Spectral Einstein Code (SpEC) we simulate the collapse of collisionless matter and probe for apparent horizons. We propose a new method to probe for the existence of an event horizon by following characteristic from regions near the singularity, using methods commonly employed in Cauchy characteristic extraction. [Preview Abstract] |
Sunday, April 12, 2015 9:30AM - 9:42AM |
H13.00006: Numerical simulations of null singularities David Garfinkle Numerical simulations of the formation of singularities are performed in double null coordinates. Vacuum axisymmetric spacetimes are simulated with the initial data given on two intersecting null hypersurfaces. The properties of the singularity are found from the behavior of the metric functions at large advanced time. [Preview Abstract] |
Sunday, April 12, 2015 9:42AM - 9:54AM |
H13.00007: Stationarity of Extremum Entropy Stars and Black Holes Joshua Schiffrin For axisymmetric perfect-fluid stars in general relativity, we show that extrema of total entropy at fixed mass, angular momentum, and particle number are stationary. For axisymmetric vacuum black holes, we show that extrema of apparent-horizon area at fixed mass and angular momentum are stationary. [Preview Abstract] |
Sunday, April 12, 2015 9:54AM - 10:06AM |
H13.00008: Novel Solutions for Nonminimally Coupled D-Stars Graham Reid D-Stars are a composite system consisting of a boson star and global monopole coupled together through gravity. As shown by Marunovic and Murkovic, when this system is modified by the presence of non-minimal coupling to gravity, the resulting solutions are able to achieve large central densities. We performed detailed simulations of this model and discovered unusual families of solutions characterized by the abrupt formation of mater shells far from the origin. For these families, the asymptotic mass of the system is no longer a smooth function of the central density as is typical of boson stars. Current work involves investigating the stability properties of these solutions through dynamical simulation. [Preview Abstract] |
Sunday, April 12, 2015 10:06AM - 10:18AM |
H13.00009: Examination of a simple case of gravitational wave memory Alexander Tolish, Lydia Bieri, David Garfinkle, Robert Wald We examine a simple case of gravitational wave memory due to the decay of a point particle into two point particles. In the case where one of the decay products is null, there are two types of memory: a null memory due to the null particle and an ordinary memory due to the recoiling timelike particle. In the case where both decay products are timelike, there is only ordinary memory. However, this ordinary memory can mimic the null memory in the limit where one of the decay products has a large velocity. [Preview Abstract] |
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