Bulletin of the American Physical Society
2007 APS April Meeting
Volume 52, Number 3
Saturday–Tuesday, April 14–17, 2007; Jacksonville, Florida
Session J12: Theoretical Gravitation |
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Sponsoring Units: GGR Chair: Bernard Whiting, University of Florida Room: Hyatt Regency Jacksonville Riverfront City Terrace 8 |
Sunday, April 15, 2007 10:30AM - 10:42AM |
J12.00001: Transition to matter dominance in expanding cosmological spacetimes containing gravitational waves Beverly K. Berger It has long been known that cosmological gravitational waves can play the role of an effective matter source to drive the dynamics of an average background spacetime. In vacuum, expanding, cosmological spacetimes, this effective gravitational-wave matter can yield surprising behavior. Examples include the new class of Gowdy $T^3$ solutions found by Ringstr\"{o}m and the unusual ``attractor" seen in generic $T^2$-symmetric spacetimes. However, it is also well known that ordinary matter, dark matter, and/or dark energy will quickly dominate the gravitational-wave-effective matter in the dynamics of the expansion. The question then arises of the interplay between the unusual gravitational-wave-driven dynamics and the transition to matter or cosmological constant dominance. Numerical studies of this interplay during the transition will be presented. [Preview Abstract] |
Sunday, April 15, 2007 10:42AM - 10:54AM |
J12.00002: Quasilocal Energy Inside the Event Horizon Andrew Lundgren, Bjoern Schmekel, James York Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy. The quasilocal energy (QLE) derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the singularity for a variety of types of black hole. The energy is typically concentrated just inside the horizon, not at the central singularity. [Preview Abstract] |
Sunday, April 15, 2007 10:54AM - 11:06AM |
J12.00003: On the Existence of Radiation Gauges in Petrov Type II Spacetimes Larry Price, Karthik Shankar, Bernard Whiting The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be over-specified. Their specification consists of five conditions: four (which we treat here as) ``gauge'' conditions plus an additional condition on the trace of the metric perturbation. In this work, we utilize a newly developed form of the perturbed Einstein equations to establish a condition --- on a particular tetrad component of the stress-energy tensor --- under which one can impose the full IRG/ORG. In a Petrov type II background, imposing the IRG/ORG requires (consistently) setting a particular component of the metric perturbation to zero ``by hand.'' By contrast, in a generic type D background, gauge freedom can generally be used to achieve this. As a specific example, we work through the process of imposing the IRG in a Schwarzschild background, using a more traditional approach. If time permits, implications for metric reconstruction using the Teukolsky curvature perturbations in type D spacetimes will be briefly discussed. [Preview Abstract] |
Sunday, April 15, 2007 11:06AM - 11:18AM |
J12.00004: Vector Theories with Spontaneous Lorentz Violation. Robert Bluhm, Alan Kostelecky Gravitational theories in which a vector field acquires a nonzero vacuum expectation value exhibit spontaneous breaking of Lorentz and diffeomorphism symmetry. The effects of this symmetry breaking include the generation of massless Nambu-Goldstone modes and additional couplings leading to modifications in the static limits of the gravitational and vector-field interactions. Under suitable circumstances, the class of such theories includes solutions equivalent to Einstein-Maxwell theory as well as a range of alternative solutions with modified gravitational interactions. [Preview Abstract] |
Sunday, April 15, 2007 11:18AM - 11:30AM |
J12.00005: Lambda-renormalized Einstein-Schrodinger theory - an alternative to Einstein-Maxwell theory James Shifflett The Einstein-Schrodinger theory is modified by including a quantization effect. The resulting theory closely approximates Einstein-Maxwell theory. In particular, the field equations match the ordinary Einstein and Maxwell equations except for additional terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. The theory predicts the exact Lorentz-force equation and avoids ghosts. Predictions of periastron advance, deflection of light, and time delay of light show fractional differences of $<10^{-56}$ compared to Einstein-Maxwell theory. Other fields can be added to the Lagrangian density in a matter term which may involve the symmetric metric and electromagnetic potential, just as in Einstein-Maxwell theory. When a spin-1/2 field is added we calculate fractional differences in Hydrogen atom energy levels of $<10^{-40}$ compared to Einstein-Maxwell theory. [Preview Abstract] |
Sunday, April 15, 2007 11:30AM - 11:42AM |
J12.00006: First-order generalized symmetries of spacetimes admitting two commuting Killing vector fields Balraj Menon A first-order generalized symmetry of a system of differential equations is an infinitesimal transformation constructed locally from the independent variables, the dependent variables and first derivatives of the dependent variables that maps any solution of the differential equations to a neighboring solution. By applying symmetry group methods, we determine all first-order generalized symmetries of the vacuum Einstein equations for spacetimes admitting two commuting Killing vector fields. Furthermore, as a direct consequence of Noether's theorems, local conservation laws associated with these first-order symmetries are determined. [Preview Abstract] |
Sunday, April 15, 2007 11:42AM - 11:54AM |
J12.00007: The periodic table of real geometric algebras, bits of space-time, and the Standard Model. Dennis Marks Real geometric algebras \textbf{R}$_{n;s}$ in $n$ dimensions with signature $s$ are isomorphic to algebras of real, complex, or quaternionic matrices ${\rm {\bf R}}(2^{\textstyle{{\rm {\bf n}} \over {\rm {\bf 2}}}})\mbox{, }{\rm {\bf C}}(2^{\textstyle{{n-1} \over 2}})\mbox{, or }{\rm {\bf H}}(2^{\textstyle{{n-2} \over 2}})\mbox{,}$ or of block diagonal matrices ${ }^2{\rm {\bf R}}(2^{\textstyle{{n-1} \over 2}})\mbox{ }$ or ${ }^2{\rm {\bf H}}(2^{\textstyle{{n-3} \over 2}}),\mbox{ }$ for $\left| {\left( {s+3} \right)_{\bmod 8} -4} \right|$~=~1, 2, 3, 0, or 4, respectively. Only for \textit{n~=~2~or~4} and \textit{s~=~0~or~2} is \textbf{R}$_{n;s}$ isomorphic to real $n\times n$ matrices \textbf{R}(n). \textbf{R}$_{2;2}$ and \textbf{R}$_{2;0}$ describe the Euclidean plane and the Minkowskian plane. Their direct product, \textbf{R}$_{4;2}$~=~\textbf{R}$_{2;0}$~$\otimes $~\textbf{R}$_{2;2}$, describes 4-d space-time with signature + + + -- and with dynamical elements (position, spin, momentum, and action) that satisfy the Heisenberg commutation relations. Quantum mechanics emerges naturally. Electromagnetism, described by $U(1)$~$\approx $~\textbf{C~}$\approx $~\textbf{R}$_{1;-1}$, has one time-like coordinate; the weak force, described by \textit{SU(2)~}$\approx $~\textit{SO(3)~}$\approx $~\textbf{R}$_{3;3}$, has three space-like coordinates. Thus the real algebra of the symmetry group of the electro-weak force is isomorphic to the real algebra of space-time. Finally, \textbf{R}$_{8;2}$~=~\textbf{R}$_{4;0}$~$\otimes $~\textbf{R}$_{4;2}$ is isomorphic to \textbf{R}(16), into which can be fit three generations of weakly interacting Fermi doublets and three generations of three colors of quarks. Every 8 dimensions thereafter, geometric algebras factor into direct products of \textbf{R}(16), interpreted as a 4-d hexadecimal space-time lattice with four additional internal coordinates for the Standard Model. [Preview Abstract] |
Sunday, April 15, 2007 11:54AM - 12:06PM |
J12.00008: Cosmological Variation of Gravitation in a Quantum Theory of Mass-Spacetime Dillon Scofield Quantum dynamical manifold theory (QDMT) is used to predict the single quasi-particle spin-1 boson manifold wave functions and the energy - excitation spectrum of a many-body mass-spacetime (MB-MST) assembly of such gravitrinos. This theory is used to calculate the small residual effective interaction between particles in the MB-MST after the full electroweak interaction is exactly removed. The interaction is mediated by the exchange of MST particle-hole excitations called xcitons that have a nominal energy of $5\times 10^{-8}$ MeV in the present epoch. The effective interaction, because of its magnitude, is identified with gravitation, giving a cosmological variation to Newton's gravitational parameter that is reported. The effective interaction leads to a superconducting, Bose- Einstein condensation (SC-BEC) at very high temperatures ($\sim$ 10$^{17}$ GeV). Moreover, cosmologically, from the first instant of the Big Bang, it evolves from initially strongly repulsive values, transitions through a resonance, becomes strongly attractive, then enters a cosmological epoch of slowly increasing value, ultimately becoming repulsive. Calculations of the effect of the MB-MST on the rotation curves of galaxies give a consistent picture that the presence of the gravitrinos is responsible for the anomalous rotation and for much, if not all, the (dark) mass- energy in a universe. [Preview Abstract] |
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