Fully-constrained formulation of Einstein's field equations using ...

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Constrained formulation of Einstein equations Jérôme Novak Introduction Constraints Motivations Formulation Conformal decomposition Equations Strategy Simulations Gravitational Waves Neutron stars Summary Outline 1 Introduction Constraints issues in 3+1 formalism Motivation for a fully-constrained scheme 2 Description of the formulation and strategy Covariant 3+1 conformal decomposition Einstein equations in Dirac gauge and maximal slicing Integration strategy 3 Numerical implementation and results Evolution of gravitational wave spacetimes Models of rotating neutron stars
Constrained formulation of Einstein equations Jérôme Novak Introduction Constraints Motivations Formulation Conformal decomposition Equations Strategy Simulations Gravitational Waves Neutron stars Summary 3+1 formalism Decomposition of spacetime and of Einstein equations Evolution equations: ∂Kij ∂t − LβKij = −DiDjN + NRij − 2NKikK k j + N [KKij + 4π((S − E)γij − 2Sij)] K ij = 1 „ ij ∂γ 2N ∂t + Diβ j + D j β i « . Constraint equations: R + K 2 − KijK ij = 16πE, DjK ij − D i K = 8πJ i . gµν dx µ dx ν = −N 2 dt 2 + γij (dx i + β i dt) (dx j + β j dt)
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Fully-constrained formulation of Einstein's field equations using ...

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