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 J15: Mathematical Aspects of Relativity II |
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Sponsoring Units: GGR Chair: Lior Burko, Georgia Gwinnett College Room: 251C |
Sunday, April 17, 2016 10:45AM - 10:57AM |
J15.00001: The properties of spikes in spacetime singularities David Garfinkle When a spacetime singularity forms, narrow features called spikes form and become ever narrower as the singularity is approached. This talk reports on a combination of analytical and numerical work that yields a complete description of the properties of the spikes. I also report on work on the possible effects of quantum gravity on spikes. [Preview Abstract] |
Sunday, April 17, 2016 10:57AM - 11:09AM |
J15.00002: New numerical evidence for asymptotics in $\mathbb T^2$-symmetric cosmologies on $\mathbb T^3$ Adam Layne, Beverly K Berger, James Isenberg In two papers from 2005 and 2009, Ringström has shown that the Strong Cosmic Censorship conjecture (SCC) holds for the class of Gowdy symmetric cosmologies with $\mathbb T^3$ spatial topology. This is currently the least symmetric class of cosmologies in which SCC is known to hold. Recently, multiple authors have made progress describing the future asymptotics of cosmologies with weaker $\mathbb T^2$-symmetry. In these cases, however, either small data or boundedness of certain operators is assumed. We describe novel numerical and heuristic arguments for asymptotics in the $\mathbb T^2$-symmetric case without either of these assumptions. [Preview Abstract] |
Sunday, April 17, 2016 11:09AM - 11:21AM |
J15.00003: Numerical Tests of the Cosmic Censorship Conjecture with Collisionless Matter Collapse Maria Okounkova, Daniel Hemberger, Mark Scheel We present our results of numerical tests of the weak cosmic censorship conjecture (CCC), which states that generically, singularities of gravitational collapse are hidden within black holes, and the hoop conjecture, which states that black holes form when and only when a mass $M$ gets compacted into a region whose circumference in every direction is $C \leq 4\pi M$. We built a smooth particle methods module in SpEC, the Spectral Einstein Code, to simultaneously evolve spacetime and collisionless matter configurations. We monitor $R_{abcd}R^{abcd}$ for singularity formation, and probe for the existence of apparent horizons. We include in our simulations the prolate spheroid configurations considered in Shapiro and Teukolsky's 1991 numerical study of the CCC. [Preview Abstract] |
Sunday, April 17, 2016 11:21AM - 11:33AM |
J15.00004: Critical Phenomena in the Aspherical Collapse of Radiation Fluids Thomas Baumgarte We study critical phenomena in the gravitational collapse of radiation fluids. We perform numerical simulations in both spherical symmetry and axisymmetry, and observe critical scaling in both supercritical evolutions, which lead to the formation of a black hole, and subcritical evolutions, in which case the fluid disperses to infinity and leaves behind flat space. We identify the critical solution in spherically symmetric collapse, and study the approach to this critical solution in the absence of spherical symmetry. Our simulations are preformed with an unconstrained evolution code, implemented in spherical polar coordinates, and adopting "moving-puncture" coordinates. [Preview Abstract] |
Sunday, April 17, 2016 11:33AM - 11:45AM |
J15.00005: Application of covariant analytic mechanics to gravity with Dirac field Satoshi Nakajima We applied the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as the basis variables. A significant feature of the covariant analytic mechanics is that the canonical equations, in addition to the Euler-Lagrange equation, are not only manifestly general coordinate covariant but also gauge covariant. Combining our study and the previous works (the scalar field, the abelian and non-abelian gauge fields and the gravity without the Dirac field), the applicability of the covariant analytic mechanics was checked for all fundamental fields. We studied both the first and second order formalism of the gravitational field coupled with matters including the Dirac field. It was suggested that gravitation theories including higher order curvatures cannot be treated by the second order formalism in the covariant analytic mechanics. In addition, we showed that the covariant analytic mechanics is equivalent to corrected De Donder-Weyl theory. [Preview Abstract] |
Sunday, April 17, 2016 11:45AM - 11:57AM |
J15.00006: Stress-Energy Tensor in Einstein-Cartan Theory Eugene Kur We present a proof connecting the Noether stress-energy tensor with the Hilbert stress-energy tensor for theories coupled to an arbitrary background metric. In particular, we show how applying Noether's theorem to spacetime diffeomorphisms leads to Hilbert's formula $T^{\mu\nu}\propto\frac{\delta S}{\delta g_{\mu\nu}}$. The proof immediately yields the symmetry of the stress-energy tensor as well as the vanishing of its covariant divergence. In the case that the theory is coupled to a background tetrad and a background connection, we show that the stress-energy tensor receives contributions from the torsion of the background connection and the spin current of the matter. We discuss the applications of these results to fermions coupled to Einstein-Cartan gravity and to theories of gravity with no matter coupling. [Preview Abstract] |
Sunday, April 17, 2016 11:57AM - 12:09PM |
J15.00007: Geometrization conditions for perfect fluids, scalar fields, and electromagnetic fields Charles Torre, Dionisios Krongos The classical Rainich conditions are a system of geometric conditions, expressed purely in terms of the spacetime metric, which are necessary and sufficient for the metric to define a solution to the Einstein-Maxwell equations with a non-null electromagnetic field. We obtain analogous ``geometrization'' conditions for other matter sources. Specifically, we find geometric conditions which are necessary and sufficient for a metric to define a solution to the Einstein equations with a perfect fluid source, and to define a solution to the Einstein-scalar field equations. These conditions work in any dimension, allow for a cosmological constant, and allow for an arbitrary self-interaction potential in the scalar field case. We also generalize the classical Rainich conditions to include a cosmological constant and we obtain geometrization conditions which are applicable to the case of null electromagnetic fields. [Preview Abstract] |
Sunday, April 17, 2016 12:09PM - 12:21PM |
J15.00008: Rainich geometrization extended to electromagnetic fields in (2 + 1)-dimensional gravity. Dionisios Krongos, Charles Torre In four spacetime dimensions the Rainich conditions are a set of equations equivalent to the Einstein-Maxwell equations, but are expressed soley in terms of the metric tensor. We have found the analogous conditions in (2 + 1)-dimensional gravity such that a metric tensor defines a non-null solution to the Einstein-Maxwell equations. These conditions can be extended to other theories of (2 + 1)-dimensional gravity. These conditions are obtained by reducing the problem to that of a scalar field, which we have treated elsewhere. We illlustrate these results using the charged BTZ solution. [Preview Abstract] |
Sunday, April 17, 2016 12:21PM - 12:33PM |
J15.00009: ABSTRACT WITHDRAWN |
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