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Space-time collocation method: Loop quantum Hamiltonian constraints

Author

Listed:
  • A. Yonika

    (Department of Physics & Center for Scientific Computing and Visualization Research, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747, USA)

  • A. Heryudono

    (Department of Mathematics & Center for Scientific Computing and Visualization Research, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747, USA)

  • G. Khanna

    (Department of Physics & Center for Scientific Computing and Visualization Research, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747, USA)

Abstract

A space-time collocation method (STCM) using asymptotically-constant basis functions is proposed and applied to the quantum Hamiltonian constraint for a loop-quantized treatment of the Schwarzschild interior. Canonically, these descriptions take the form of a partial difference equation (PDE). The space-time collocation approach presents a computationally efficient, convergent, and easily parallelizable method for solving this class of equations, which is the main novelty of this study. Results of the numerical simulations will demonstrate the benefit from a parallel computing approach; and show general flexibility of the framework to handle arbitrarily-sized domains. Computed solutions will be compared, when applicable, to a solution computed in the conventional method via iteratively stepping through a predefined grid of discrete values, computing the solution via a recursive relationship.

Suggested Citation

  • A. Yonika & A. Heryudono & G. Khanna, 2020. "Space-time collocation method: Loop quantum Hamiltonian constraints," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(11), pages 1-17, November.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:11:n:s0129183120501661
    DOI: 10.1142/S0129183120501661
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