Symmetries of Geodesics for Homogeneous Gravitational Fields

ORAL

Abstract

In Einstein's general theory of relativity freely falling test particles follow geodesics of the spacetime geometry. Some geodesics have symmetries, known as affine collineations. Mathematically, these affine collineations are transformations that preserve the connection defined by the metric, without preserving the metric. Physically, they change the notion of lengths and angles, while preserving the notion of parallelism. Associated with each affine collineation are two conserved quantities. Previously these quantities were understood to be non-Noetherian, however we show that they can be derived from a direct application of Noether's theorem. We calculate all affine collineations and their corresponding conservation laws for all of the homogeneous solutions to the Einstein Field Equations in vacuum, with perfect fluid sources, and with homogeneous electromagnetic sources.

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Authors

  • David Maughan

    Utah State University

  • Colin Roberts

    High Precision Devices, Boulder, CO, Raytheon, Tucson, AZ, Seagate Technology, Minneapolis, MN, Ball Aerospace (retired), Bloomfield, CO, New Mexico State University, Brigham Young University, Colorado State University, Heinrich-Heine-Universitat Dusseldorf, National Security Technologies, Universidad de Buenos Aires, Colorado State Univ, Colorado College, Utah State University, Advisor, Material Physics Group, Utah State University, Box Elder Innovations, LLC, JILA and Department of Physics, CU Boulder, JILA and Department of Mathematics, CU Boulder, Colorado State University, Fort Collins, Colorado 80523, USA, JILA, NIST and the University of Colorado, Boulder, NIST, University of Colorado / NIST, University of Colorado/JILA, Colorado Sch of Mines, Colorado School of Mines, Southwestern Indian Polytechnic Institute, UC-Berkeley, Colorado State University, Fort Collins, CO, Wroclaw University of Science and Technology, Wroclaw, Poland, JILA, University of Colorado and NIST, Harvard University and Harvard-MIT Center for Ultracold Atoms, Univ of Colorado - Boulder, USAFA, Univ of Denver, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Utah Valley University, University of Colorado Boulder, Brigham Young Univ - Provo, Oak Ridge National Laboratory, University of Sherbrooke, NIST Boulder, Universidad Complutense de Madrid, Electrical and Computer Engineering Department, Colorado State University, Fort Collins, Co 80525, Lawrence Livermore National Lab. (United States), Physics Department, Colorado State University, Fort Collins, Co 80525, JILA, Department of Physics, University of Colorado Boulder, Los Alamos National Laboratory, University of Alabama, University of Wyoming, University of Guelph, University of Guelph, Canadian Light source