tensor[displayGR] - display the nonzero components of a specific general relativity tensor
tensor[display_allGR] - display the nonzero components of all of the general relativity tensors and quantities calculated by tensor[tensorsGR]
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Calling Sequence
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displayGR(GR_name, object)
display_allGR(coord, cov_metric, con_metric, det_met, C1, C2, Rm, Rc, R, G, C)
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Parameters
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GR_name
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name of a specific GR-related object where the name is one of coordinates, cov_metric, contra_metric, detmetric, Christoffel1, Christoffel2, Riemann, Ricci, Ricciscalar, Einstein, or Weyl
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object
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object to display
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coord
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list of coordinate variable names (for example, [t, x, y, z])
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cov_metric
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covariant metric tensor (index_char=[-1,-1])
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con_metric
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contravariant metric tensor (index_char=[1,1])
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det_met
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determinant of metric tensor components
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C1, C2
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Christoffel symbols of first and second kind
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Rm, Rc, R
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Riemann tensor, Ricci tensor, Ricci scalar
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G, C
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Einstein and Weyl tensors
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Description
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The function displayGR(Einstein, G) displays the nonzero components and the index character of the tensor_type G using the symmetries of the Einstein tensor to reduce the number of components shown. G is expected to be a tensor of rank 2 with the proper symmetries. It can be calculated using tensor[Einstein].
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The function display_allGR(coord, cov_met, cont_met, det_met, C1, C2, Rm, Rc, R, G, C) displays all of the GR-related objects passed in the parameter list. They must be passed in the following order: the coordinates list, the covariant metric tensor ([-1,-1]), the contravariant metric tensor ([1,1]), the determinant of the metric tensor components (algebraic type), the Christoffel symbols of the 1st kind ([-1,-1,-1]), the Christoffel symbols of the 2nd kind ([1,-1,-1]), the Riemann tensor, the Ricci tensor, the Ricciscalar ([]), the Einstein tensor, the Weyl tensor. Each of the quantities is displayed by making the appropriate call to tensor[displayGR]. See tensor[tensorsGR] for the calculation of these quantities.
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For displaying general tensor_type objects not listed above, use the 'display' option of tensor[act].
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These functions are part of the tensor package, and so can be used in the form displayGR(..) / display_allGR(..) only after performing the command with(tensor), or with(tensor, displayGR) / with(tensor, display_allGR).
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Examples
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Define the coordinates and covariant metric for the Schwarzschild metric:
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Compute the curvature (without the print option)
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Use displayGR to show that it is a vacuum solution of the Einstein field equations:
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Use displayGR to show the nonzero Christoffel symbols of the first kind:
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Display everything using display_allGR:
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