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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectral geometry of cosmological and event horizons for Kerr-Newman-de Sitter metrics
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by Martin Engman and Gerardo A. Santana PDF
Proc. Amer. Math. Soc. 141 (2013), 3305-3311 Request permission

Abstract:

We study the Laplace spectra of the intrinsic instantaneous metrics on the event and cosmological horizons of a Kerr-Newman-de Sitter space-time and prove that the spectral data from these horizons uniquely determine the metric among all such space-times. This is accomplished by exhibiting formulae relating the parameters of the space-time metric to the traces of invariant and equivariant Green’s operators associated with these Laplacians. In particular, an interesting explicit formula for the cosmological constant is found.
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Additional Information
  • Martin Engman
  • Affiliation: Departamento de Ciencias y Tecnología, Universidad Metropolitana, San Juan, Puerto Rico 00928
  • Email: um_mengman@suagm.edu, mathengman@yahoo.com
  • Gerardo A. Santana
  • Affiliation: Departamento de Ciencias y Tecnología, Universidad Metropolitana, San Juan, Puerto Rico 00928
  • Email: gerardo.appmath@gmail.com
  • Received by editor(s): October 5, 2011
  • Received by editor(s) in revised form: December 10, 2011
  • Published electronically: June 10, 2013
  • Additional Notes: The second author thanks María del Rio for her support during the writing of this paper. This work was partially supported by the NSF grants Model Institutes for Excellence and AGMUS Institute of Mathematics at UMET

    • Dedicated: For Becky and Mom
  • Communicated by: Sergei K. Suslov
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 3305-3311
  • MSC (2010): Primary 58J50; Secondary 83C15, 83C57
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11600-X
  • MathSciNet review: 3068983