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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral geometry of cosmological and event horizons for Kerr-Newman-de Sitter metrics


Authors: Martin Engman and Gerardo A. Santana
Journal: Proc. Amer. Math. Soc. 141 (2013), 3305-3311
MSC (2010): Primary 58J50; Secondary 83C15, 83C57
Published electronically: June 10, 2013
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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{\textunderscore}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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11600-X
PII: S 0002-9939(2013)11600-X
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.