Bulletin of the American Physical Society
APS April Meeting 2010
Volume 55, Number 1
Saturday–Tuesday, February 13–16, 2010; Washington, DC
Session X14: Foundational Aspects of General Relativity |
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Sponsoring Units: GGR Chair: Steven Detweiler, University of Florida Room: Washington 4 |
Tuesday, February 16, 2010 10:45AM - 10:57AM |
X14.00001: How does a black hole horizon start? Dieter Brill When a black hole is created by gravitational collapse, there is a region of spacetime before the collapse where there is no horizon. Before the matter can fall through the horizon and create a black hole, the horizon has to start and expand to meet the matter. The starting point or points is where the generators enter the horizon. This set is a lower-dimensional, connected subset of a spacelike surface. By way of examples we will discuss the early configuration of the horizon to the time that matter enters. [Preview Abstract] |
Tuesday, February 16, 2010 10:57AM - 11:09AM |
X14.00002: A Classical and Quantum Two-Sphere Singularity Deborah Konkowski, Thomas Helliwell The two-sphere singularity in the maximal extension of the Florides exact solution is analyzed. The classical structure shows inextendible null geodesics (complete timelike geodesics) along with curvature invariants that diverge as the two-sphere is approached. The spacetime of this classical timelike scalar curvature singularity is classified as to its Petrov and Segre types. Its energy conditions together with the strength of the singularity are analyzed to determine the physical relevance of the spacetime. Whether the singularity persists in a quantum sense is considered next. A review of the definition of quantum singularity is given in terms of the essential self-adjoitness of the Klein-Gordon operator using Weyl's limit circle/limit point procedure. The singularity is then shown to remain robust and persist under a quantum wave probe. [Preview Abstract] |
Tuesday, February 16, 2010 11:09AM - 11:21AM |
X14.00003: Quasilocal Energy in FRW Cosmology Marcus Afshar The quasilocal energy (QLE) of a generic FRW model of the universe is calculated. The calculation is performed using several different formulations of QLE and the results are compared. The non-stationary nature of this example serves to differentiate competing formulations of QLE. Certain formulations are shown to have incorrect classical limits. Also, the QLE is used to calculate the entropy of several specific FRW models, providing a check on other methods of entropy calculation. [Preview Abstract] |
Tuesday, February 16, 2010 11:21AM - 11:33AM |
X14.00004: Initial Data for the Gravity Dual in an AdS/CFT Correspondence Hans Bantilan, Frans Pretorius The AdS/CFT correspondence conjectures that a gauge theory admits a dual gravity description in a negatively curved spacetime. In particular, it has been conjectured that aspects of heavy-ion collisions described by QCD are dual to black hole collisions in 5-dimensional anti-de Sitter (AdS) space. BH-BH collisions have received a lot of attention in the field of numerical relativity, in the context of the gravitational waves generated in their inspiral phase and upon merger. By taking advantage of techniques in numerical relativity to simulate 5-dimensional AdS, it is hoped that we can learn a bit more about heavy-ion physics, and perhaps more about the AdS/CFT correspondence in the process. I will describe steps that are being taken in this direction, first focusing on motivations, then on results, with an emphasis on the initial data we generate for preliminary simulations of the gravity dual. [Preview Abstract] |
Tuesday, February 16, 2010 11:33AM - 11:45AM |
X14.00005: Asymptotically AdS spacetimes in 2+1 dimensions Arif Mohd, Luca Bombelli We revisit the asymptotically AdS spacetimes in 2+1 dimensions. Using conformal techniques we formulate the boundary conditions in a covariant fashion and construct the global charges associated to the asymptotic symmetries. We calculate the Trace Anomaly which is same as the Central Charge of the algebra of asymptotic symmetries first obtained by Brown and Henneaux. The motivation for this work is to understand why the central extension or the trace anomaly arises and how one can extend these techniques to formulate the boundary conditions specifying the presence of a black hole. [Preview Abstract] |
Tuesday, February 16, 2010 11:45AM - 11:57AM |
X14.00006: Gravity from Thermodynamics: Going beyond Einstein equation of state Sudipta Sarkar, Maulik Parikh, Ted Jacobson We will discuss the possibility of deriving the classical equation of motion of any diffeomorphism-invariant theory of gravity from the thermodynamic relation $T\delta S = \delta Q$, applied to a local Rindler horizon with $S$ as the Wald entropy. The approach generalizes an earlier result for General Relativity and thereby suggests a thermodynamic origin of any metric theory of gravity. [Preview Abstract] |
Tuesday, February 16, 2010 11:57AM - 12:09PM |
X14.00007: Einsteinian Relativity in the Tangent Bundle of Spacetime Howard Brandt The tangent bundle of spacetime consists of spacetime in the base manifold and four-velocity space in the fiber [1]. The coordinates of a point in the spacetime tangent bundle are the spacetime and four-velocity coordinates of the observer. Einsteinian relativity plays a central role in the formulation of possible differential geometric structures and embedded fields in the spacetime tangent bundle. The covariant four-acceleration of Einstein's theory of general relativity plays a particularly important role. The quantum mechanics of the vacuum suggests the existence of a limiting proper acceleration, thereby placing restrictions on the differential geometric structure of the spacetime tangent bundle, and also on the structure of embedded classical and quantum fields [2-4]. In the present work, examples are addressed emphasizing the roles of both special-relativistic Lorentz invariance and general relativistic covariance in the theory of the spacetime tangent bundle. \\[4pt] [1] H. E. Brandt, Contemp. Math. \textbf{196}, 273 (1996). \\[0pt] [2] H. E. Brandt, Rep. Math. Phys. \textbf{45}, 389 (2000). \\[0pt] [3] H. E. Brandt, J. Mod. Optics \textbf{50}, 2455 (2003) \\[0pt] [4] H. E. Brandt, Internat. J. Math. and Math. Sci. \textbf{2003}, 1529 (2003). \\[0pt] [4] H. E. Brandt, Nonlinear Analysis \textbf{63}, 119 (2005). [Preview Abstract] |
Tuesday, February 16, 2010 12:09PM - 12:21PM |
X14.00008: The GSL implies the ANEC on Null Lines Aron Wall A null line is a lightlike geodesic which is complete (i.e. infinite in both directions) and achronal (i.e. it goes from point to point faster than any timelike curve). I describe work showing that the averaged null energy condition (ANEC) holds on null lines as a consequence of the generalized second law (GSL) of thermodynamics in semiclassical gravity, given certain auxilliary assumptions. This is done by thinking of the null geodesic itself as being an ``observer'' lying on its own past and future horizons. If the future horizon obeys the GSL and the past horizon obeys the time-reverse of the GSL, then the ANEC must hold on the null line. In curved spacetimes, the ANEC can be violated on general geodesics. But even if the ANEC only holds on null lines, theorems by Sorkin, Penrose and Woolgar, and by Graham and Olum imply that semiclassical gravity should satisfy positivity of energy, topological censorship, and should not admit closed timelike curves. These results can thus be seen as consequences of the GSL. However, these theorems break down when gravitational fluctuations are taken into account. I will suggest a generalization of the ANEC for use in this case. [Preview Abstract] |
Tuesday, February 16, 2010 12:21PM - 12:33PM |
X14.00009: Advance in the Foundations of Quantum Mechanics Juliana Brooks An advance has occurred in the foundations of quantum mechanics. Examination of a seemingly minor mathematical irregularity in Max Planck's work led to the discovery of previously hidden quantum variables and constants. A richer and more realistic interpretation of quantum mechanics is suggested. (Brooks, J., ``Hidden Variables: The Elementary Quantum of Light'', Proc. of SPIE Vol. 7421, 74210T-3, 2009.) Planck's quantum formula, E = h$\nu $, is missing the variable for measurement time. Planck included the missing time variable in his earlier work, but omitted it in his famous quantum paper. Restoring time (``t'') to Planck's quantum formula produces E = h$^{\sim }\nu $ t, where ``h$^{\sim }$'' is Planck's \textit{energy} constant, the mean energy of a single oscillation of light, namely 6.626 X 10$^{-34}$ J/osc. Light's mean oscillation energy is \textit{constant}, and invariant with frequency or wavelength. The ``photon'' is a time dependent (one second) packet of energy, and thus cannot be a truly indivisible and elementary particle of nature. The true elementary particle of light, with its invariant and universal energy constant, is the single EM oscillation. Many of the quantum mechanical paradoxes - uncertainty, wave-particle duality, normalization of wave functions, the fine structure constant, and problems of quantum gravity - are simplified or eliminated by a re-interpretation of quantum mechanics using Planck's complete quantum formula, with its time variable and energy constant, E = h$^{\sim }\nu $ t. [Preview Abstract] |
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