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Keywords
(4)
Einstein Equation
Hyperbolic System
Minkowski Space
First Order
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Fixing Einstein's Equations
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New firstorder formulation for the Einstein equations
New firstorder formulation for the Einstein equations,10.1103/PhysRevD.68.064013,Physical Review D,Alexander M. Alekseenko,Douglas N. Arnold
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New firstorder formulation for the Einstein equations
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Citations: 4
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Alexander M. Alekseenko
,
Douglas N. Arnold
We derive a new firstorder formulation for Einstein's equations which involves fewer unknowns than other firstorder formulations that have been proposed. The new formulation is based on the 3+1 decomposition with arbitrary lapse and shift. In the reduction to
first order
form only 8 particular combinations of the 18 first derivatives of the spatial metric are introduced. In the case of linearization about Minkowski space, the new formulation consists of symmetric
hyperbolic system
in 14 unknowns, namely the components of the extrinsic curvature perturbation and the 8 new variables, from whose solution the metric perturbation can be computed by integration.
Journal:
Physical Review D  PHYS REV D
, vol. 68, no. 6, 2003
DOI:
10.1103/PhysRevD.68.064013
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Citation Context
(3)
...of Einstein’s equations introduced by Alekseenko and Arnold in [
3
]...
Nicolae Tarfulea
.
Constraint Preserving Boundary Conditions for Hyperbolic Formulations ...
...of Einstein’s equations introduced by Alekseenko and Arnold in [
3
]...
NICOLAE TARFULEA
,
et al.
and have found that is is complete and satisfactory in all respects, a...
...Second order formulations in general relativity, in particular, the generalized harmonic (e.g., [29, 1, 20]) and the BSSN formulations [54, 12], have an important advantage of being several times smaller in size compared to the complete first order reductions (e.g., [31, 17, 39,
6
])...
Alexander M. Alekseenko
.
Research Statement of Alexander M. Alekseenko
References
(1)
Partial Differential Equations
(
Citations: 690
)
L. C. Evans
Published in 1997.
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Citations
(4)
Wellposed constraintpreserving boundary conditions for the AA formulation of Einstein's equations
Nicolae Tarfulea
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 359, no. 2, pp. 711721, 2009
Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein's Equations
(
Citations: 4
)
Nicolae Tarfulea
Published in 2005.
and have found that is is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made
NICOLAE TARFULEA
,
DOUGLAS N. ARNOLD
Research Statement of Alexander M. Alekseenko
Alexander M. Alekseenko