Constraint-Preserving Boundary Conditions for the Linearized Baumgarte-Shapiro-Shibata-Nakamura Formulation
Alexander M. Alekseenko
Source: Abstr. Appl. Anal. Volume 2008 (2008), 21 pages.
Abstract
We derive two sets of explicit homogeneous algebraic constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system (which is first order in temporal and second order in spatial derivatives) are obtained. Generalizations to the case of nonhomogeneous boundary data are proposed.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969171
Digital Object Identifier: doi:10.1155/2008/742040
Mathematical Reviews number (MathSciNet):
MR2407284
Zentralblatt MATH identifier:
1148.83305
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Abstract and Applied Analysis
