Bulletin of the American Physical Society
APS April Meeting 2015
Volume 60, Number 4
Saturday–Tuesday, April 11–14, 2015; Baltimore, Maryland
Session K7: Spacetime Geometry and Cosmology |
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Sponsoring Units: GGR Chair: Kartik Prabhu, University of Chicago Room: Key 3 |
Sunday, April 12, 2015 1:30PM - 1:42PM |
K7.00001: Analytical Trumpet Slices in Schwarzschild and Kerr Spacetimes Thomas Baumgarte, Kenneth Dennison, Pedro Montero We will start by presenting a new family of coordinate systems for the Schwarzschild spacetime. These remarkably simple coordinates have some other remarkable properties as well, including the fact that slices of constant time feature a trumpet geometry. Moreover, these coordinates can be generalized for rotating black holes, resulting in a new family of coordinate systems for Kerr spacetimes. We will then introduce a 2+1+1 formalism to characterize trumpet geometries in the absence of spherical symmetry. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes. [Preview Abstract] |
Sunday, April 12, 2015 1:42PM - 1:54PM |
K7.00002: Searching for Toroidal Event Horizons in Binary Black Hole Mergers Andy Bohn We find event horizons of binary black hole (BBH) mergers, produced using the Spectral Einstein Code (SpEC), and explore their topologies. When the BBH merger does not exhibit certain spatial symmetries, we expect the spatial slices of the event horizon to go through a toroidal topology. However, we find no evidence of a toroidal phase using the spatial slicing of the SpEC simulations, generalized harmonic gauge, to the accuracy of our event horizon finder. To further explore the $2+1$ dimensional event horizon hypersurface, we re-slice the event horizons in an affine slicing to look for a toroidal phase. [Preview Abstract] |
Sunday, April 12, 2015 1:54PM - 2:06PM |
K7.00003: Monte Carlo Studies of Transitions in Interacting Spacetimes and Scalar Fields Kendall Mallory We present some numerical studies of simple interactive spacetimes with scalar energy fields by Metropolis Monte Carlo simulations. These studies focus on transitions between phases involving collapsing, expanding and inflating states of spacetime interacting with non-zero ground states of the scalar field. Motivation for these studies arises from theories of cosmic inflation driven by phase transitions and higher dimensional spacetime models in string theory with collapsed dimensions. [Preview Abstract] |
Sunday, April 12, 2015 2:06PM - 2:18PM |
K7.00004: Asymptotics with a positive cosmological constant: Illustration with linear fields on de Sitter space-time Beatrice Bonga, Abhay Ashtekar, Aruna Kesavan The framework that allows the study of isolated systems is well-developed for space-times with a vanishing cosmological constant $\Lambda$ and it lies at the foundation of research in diverse areas in gravitational physics. The standard extension of this framework to space-times with a positive $\Lambda$ fails for non-stationary space-times as there is no physically useful notion of conserved quantities. I will outline a new physically meaningful proposal and illustrate it by applying it to linearized gravity. The conserved quantities constructed are shown to be equivalent to those derived by using the symplectic formulation. This linear analysis provides a first step to study the errors one makes by assuming $\Lambda = 0$ when studying general relativistic gravitating systems. [Preview Abstract] |
Sunday, April 12, 2015 2:18PM - 2:30PM |
K7.00005: Asymptotics with a positive cosmological constant II Aruna Kesavan, Abhay Ashtekar, Beatrice Bonga The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. This means that presently there is no fundamental understanding of gravitational waves in our own universe. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. In particular, I will discuss the quadrupole formula for gravitational radiation and its implications. [Preview Abstract] |
Sunday, April 12, 2015 2:30PM - 2:42PM |
K7.00006: Closed Timelike Loops in Homogeneous Rotating $\Lambda$-dust Cosmologies David Lindsay We first describes what a ``rotating'' $\Lambda$-dust universe is in general relativity: basically, our universe plus a small amount of rotation. We then mention the Canonical example, the G\"odel solution, which would add one rotation to our universe in about 200 billion years. Then we describe what we believe to be all known homogeneous rotating $\Lambda$-dust cosmologies. A plot of their characteristics shows that they cannot comprise all such solutions, though the literature claims (in several places) that all rotating solutions with a non-zero $\Lambda$ term have been discovered. Our research has investigated these solutions for closed timelike loops (CTLs), i.e., time-machines, and concluded that exactly those with $\Lambda<0$ possess CTLs. This observation calls into question the standard bias in GR that ``too much'' rotation leads to non-causal behavior; instead, it appears that a negative cosmological constant is the culprit. [Preview Abstract] |
Sunday, April 12, 2015 2:42PM - 2:54PM |
K7.00007: Spacetime Topology from Cosmic Strings and Foliations Christopher Duston One of the major difficulties in the mathematical representation of the gravitational field is that it is not generally possible to determine when two spacetime models are unique - this is known as the exotic smoothness problem. In this talk I will discuss how to completely enumerate the differentiable structures of a closed four-manifold using a branched covering of the four-sphere. This will allow us to avoid the problem of exotic smoothness, and construct a formally complete semiclassical partition function. This construction naturally includes cosmic strings and a unique specification of the topology of a codimension two foliation of the four-manifold via a redefinition of the geometric degrees of freedom. As a result of this construction, we propose that spacetime topology emerges as a result of symmetry breaking of the fundamental fields in the early universe. [Preview Abstract] |
Sunday, April 12, 2015 2:54PM - 3:06PM |
K7.00008: Tracking the Degrees of Freedom in the AdS/CFT Correspondence with Cartan Geometry Jeffrey Hazboun The explicit correspondence of the degrees of freedom in an $\left(n+1\right)$-dimensional anti-de Sitter space with those of an n-dimensional conformal gravitational theory are shown. While the degrees of freedom on both sides of the correspondence originate from gravitational ones, the equations for various biconformal curvatures have the form of the Yang-Mills field strength. Using the quotient method first pioneered by Ne'eman and Regge allows us to construct both sides of the correspondence as different quotients of the same group, $SO\left(n,2\right)$. As a result, there is a direct correspondence in the degrees of freedom of the two connections. The flat case in AdS space is then shown to correspond to a biconformal space that is flat with respect to the Cartan curvature, however possessing a number of torsion terms that are interpreted as the field strengths of a unitary group. The latter structure is strongly dependent on the fact that biconformal space has $2n$-dimensions. This allows us to interpret $n$ of the dimensions as non-gravitational fields. In the more general curved case, the simplest action linear in the curvature is constructed for both spaces. Connections to a number of simple examples of the AdS/CFT correspondence are then shown. [Preview Abstract] |
Sunday, April 12, 2015 3:06PM - 3:18PM |
K7.00009: Boundary Terms of Noether Currents for Gravity from Multisymplectic Geometry Eugene Kur Recent developments in multisymplectic geometry have clarified the connection between conserved Noether currents and symmetry transformations in field theories. In particular, the diffeomorphism invariance of the Einstein-Hilbert action has an associated collection of Noether currents, given by the Einstein tensor. We consider a space+time decomposition of the theory with the spatial slice having non-trivial boundary conditions. Using the multisymplectic formalism to simplify the transition to the space+time framework, we show how easy it is to obtain the ``boundary terms'' for the Noether currents. This is the first known incorporation of surfaces with non-trivial boundary conditions into this particular type of multisymplectic formalism. For asymptotically flat spacetimes, these boundary terms, in turn, have a clear, transparent, connection to the conserved quantities at spatial infinity, such as the ADM mass and ADM momentum. [Preview Abstract] |
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