grwiki.physics.ncsu.edu

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Covariant and Lie Derivatives. Christoffel Symbols, Riemann Tensor, etc. Variations of Christoffel, Riemann, etc. Tetrad Formalism, Weyl Scalars, etc. Differential Forms, Integration and Stokes' Theorem. Splitting Spacetime into Space and Time. Formulations of the Einstein Equations. Generalized Harmonic (second order). Generalized Harmonic (first order). Conformal Thin Sandwich Decomposition. To try out edits. Retrieved from " http:/ grwiki.physics.ncsu.edu/wiki/Main Page. Log in / create account.

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Covariant and Lie Derivatives. Christoffel Symbols, Riemann Tensor, etc. Variations of Christoffel, Riemann, etc. Tetrad Formalism, Weyl Scalars, etc. Differential Forms, Integration and Stokes' Theorem. Splitting Spacetime into Space and Time. Formulations of the Einstein Equations. Generalized Harmonic (second order). Generalized Harmonic (first order). Conformal Thin Sandwich Decomposition. To try out edits. Retrieved from http:/ grwiki.physics.ncsu.edu/wiki/Main Page. Log in / create account.

<META> KEYWORDS

1 Main Page

2 Anti-deSitter

3 BSSN

4 Bowen-York Solution

5 Conformal Thin Sandwich Decomposition

6 Conformal Transverse-Traceless Decomposition

7 DeSitter

8 Derivative Rules

9 Einstein Equations

10 Forms

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main page,from grwiki,jump to navigation,about grwiki,hamiltonian adm,gdot kdot,bssn,generalized bssn,gauge conditions,slicing conditions,shift conditions,initial value problem,bowen york solution,misner data,exact solutions,schwarzschild black hole,flrw

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GRwiki | grwiki.physics.ncsu.edu Reviews

https://grwiki.physics.ncsu.edu

Covariant and Lie Derivatives. Christoffel Symbols, Riemann Tensor, etc. Variations of Christoffel, Riemann, etc. Tetrad Formalism, Weyl Scalars, etc. Differential Forms, Integration and Stokes' Theorem. Splitting Spacetime into Space and Time. Formulations of the Einstein Equations. Generalized Harmonic (second order). Generalized Harmonic (first order). Conformal Thin Sandwich Decomposition. To try out edits. Retrieved from " http:/ grwiki.physics.ncsu.edu/wiki/Main Page. Log in / create account.

INTERNAL PAGES

grwiki.physics.ncsu.edu

1

BSSN - GRwiki

http://grwiki.physics.ncsu.edu/wiki/BSSN

The BSSN variables are the conformal metric. The trace of the extrinsic curvature. The trace-free part of the extrinsic curvature. And the conformal connection functions. The conformal metric has unit determinant,. Are defined in terms of the physical spatial metric. And physical extrinsic curvature. Is the determinant of the physical metric. Note that. Is a type 0-2 tensor density of weight -2/3,. Is the logarithm of a scalar density of weight 1/6,. Is a scalar, and. The lapse function is.

2

Forms - GRwiki

http://grwiki.physics.ncsu.edu/wiki/Forms

Stokes' Theorem in Two Dimensions. Test edit, again, and again. A p-form is a totally antisymmetic type (0,p) tensor:. Often the indices are dropped. The exterior product (wedge product) of a p-form and a q-form is a p q form:. Are both 1-forms,. The exterior derivative of a p-form. Is a p 1 form. Any derivative operator can be used in place of the coordinate derivative. Is a p-form and. Is a q-form,. Where the plus sign applies if p is even, the minus sign applies if p is odd. In the coordinate basis:.

3

Variations - GRwiki

http://grwiki.physics.ncsu.edu/wiki/Variations

Variations of the Christoffel symbols, Riemann tensor, Ricci tensor, curvature scalar, and inverse metric:. Is the covariant derivative compatible with the metric. Are general. They can be replaced by, say, coordinate derivatives or time derivatives. Bryce DeWitt's favorite identity is. Is a matrix and. Denotes the trace. Other useful relations, where. Denotes a scalar, include. A term that appears in modified gravity theories is. Retrieved from " http:/ grwiki.physics.ncsu.edu/wiki/Variations.

4

Conformal Transverse-Traceless Decomposition - GRwiki

http://grwiki.physics.ncsu.edu/wiki/Conformal_Transverse-Traceless_Decomposition

The energy density is. And the momentum density is. Freely specify the following:. Denote the covariant derivative and Ricci tensor built from the conformal metric. Indices on. Are raised with the inverse conformal metric. Solve the following equations for. Are lowered with the conformal metric. The physical metric and extrinsic curvature are. The equations above are written compactly with the operators. Is the covariant derivative built from the physical metric. Let. And any symmetric trace-free tensor.

5

Conformal Thin Sandwich Decomposition - GRwiki

http://grwiki.physics.ncsu.edu/wiki/Conformal_Thin_Sandwich_Decomposition

Conformal Thin Sandwich Decomposition. The matter energy density is. The momentum density is. Is the trace of the spatial stress. Original Thin Sandwich Decomposition. Freely specify the following:. Is the trace-free part of the time derivative of the conformal metric. Is related to the scalar lapse function. Is the determinant of the physical spatial metric. Denote the covariant derivative and Ricci tensor built from the conformal metric. Indices on. Solve the following equations for a scalar.

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Covariant and Lie Derivatives. Christoffel Symbols, Riemann Tensor, etc. Variations of Christoffel, Riemann, etc. Tetrad Formalism, Weyl Scalars, etc. Differential Forms, Integration and Stokes' Theorem. Splitting Spacetime into Space and Time. Formulations of the Einstein Equations. Generalized Harmonic (second order). Generalized Harmonic (first order). Conformal Thin Sandwich Decomposition. To try out edits. Retrieved from " http:/ grwiki.physics.ncsu.edu/wiki/Main Page. Log in / create account.

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