7.7. Components of the metric, MetricInBasis

MetricInBasis        Values for the components of the metric

Components of the metric

It is very common in General Relativity to start working from a known line element. Inded, the typical approach is to start from the components of a metric in a coordinated basis, which determine both the metric and the coordinate system unambiguously. xCoba` provides a specialised function to define the values for the components of a metric, which can be used on its own or as an option for DefBasis.

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? MetricInBasis

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$Metrics

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{metric}

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$CVVerbose = False ;

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MetricInBasis[metric, -polar, Table[i + j, {i, 3}, {j, 3}]]

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TensorValues[metric]

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An example with a diagonal metric

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DeleteTensorValues[metric]

Deleted values for tensor metric, derivatives {} and bases {{-polar, -polar}} .

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MetricInBasis[metric, -polar, {1, 2, 3}]

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And know with an orthonormal one

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? SignatureOfMetric

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SignatureOfMetric[metric]^={2, 1, 0}

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{2, 1, 0}

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MetricInBasis[metric, -cartesian, "OrthoNormal"]

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TensorValues[metric]

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