Maximizing properties of extremal surfaces in general relativity

Details Maximizing properties of extremal surfaces in general relativity Maximizing properties of extremal surfaces in general relativity

May 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978anihp..28..335b&link_type=abstract

Institut Henri Poincare, Annales, Section A - Physique Theorique, vol. 28, Apr. 1-May 15, 1978, p. 335-347.

Mathematics

18

Cosmology, Extremum Values, Relativity, Space-Time Functions, Surfaces, Curvature, Einstein Equations, Functionals, Maxima, Operators (Mathematics)

Scientific paper

A previous paper discussed the uniqueness and local maximizing properties of maximal surfaces. This study is continued to include surfaces of constant mean curvature in spaces of nonvanishing matter content and with arbitrary cosmological constant. The nature of the extremum is characterized by means of the eigenvalues of an elliptic differential operator defined on the surface. To illustrate the different possibilities, a universe of the Taub type with cosmological constant is constructed, and this example suggests a conjecture that the index of these surfaces is less than 2.

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