Solving Einstein's field equations with Mathematica

ORAL

Abstract

We report an example using Mathematica to solve the semi-classical Einstein field equations in spherical coordinates. Metric variations resulting from the Casimir effect are calculated for an ideal massless superconducting sphere. Expressions for the change in scalar curvature inside the superconducting boundary are developed. We first consider the static case when the sphere is superconducting. Metric equations are then developed for the evolution of a scalar quantum field after the sphere transitions to the normal state.

–

Authors

  • Nilanjan Das

    Dept. of Physics, ESFM-IPN, Mexico City, Dept. of Physics, The University of Texas at El Paso, Texas A\&M University, Southeast Missouri State University, Departamento de Fisica, FCEN, Universidad de Buenos Aires, Nunez, Argentina, Cyclotron Institute, Texas A\&M University, University of Houston, Denison U., Advanced Space Propulsion Laboratory, AdAstra Rocket Company, Texas Tech University, Department of Chemistry and Biochemistry, Texas State Unv. - San Marcos, Department of Physics, Texas State Unv. - San Marcos, Rice U., Texas State University - San Marcos, Freescale Semiconductor, Inc., Varian Semiconductor Equipment Associates, Gloucester, MA, University of North Texas, Denton, TX, National Insitute of Standards \& Technology, Gaithersburg, MD, James Madison University, Harrisonburg, VA, Texas A\&M University, College Station, TX, Hong Kong University of Science and Technology; Texas Center for Superconductivity and Advanced Materials, University of Houston, Texas Center for Superconductivity at the University of Houston, University of Houston, University of Idaho, Department of Physics, Istanbul Technical University, University of California at Davis, Physics Department, University of South Florida, FL 33620, Physics Department, Texas A\&M University, TX 77843, Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, Rice University, TcSUH, University of Houston, Lawrence Berkeley National Laboratory, Hong Kong University of Science and Technology, Institute of Solid State Physics, Bulgarian Academy of Sciences, Hong Kong University of Science and Technology; Texas Center for Superconductivity, University of Houston; Lawrence Berkeley National Laboratory, Texas Center for Superconductivity, University of Houston

  • Rambis Chu

    Department of Physics Texas Southern University