Example 1
We find examples of metrics which are Einstein metrics of Petrov type III. First initialize a manifold with coordinates
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Start the MetricSearch Maplet.
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Check the Einstein box in the PhysicalProperties-Primary Description section and type III in the Algebraic Properties-Petrov Type section.
The result is "Stephani": [12, 35, 1].
Enter "Stephani" into the Reference textbox, enter [12, 35,1] into the equation number textbox, and enter M into the manifold textbox. Hit Retrieve. The fields for this library entry are assigned to
Example 2
We calculate some properties of a given metric and identify the metrics with the same properties in the library database.
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We use the command RainichConditions to see if the space-time is an Einstein-Maxwell space-time.
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We use the command KillingVectors to determine the dimension of the group of isometries.
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Next we find the Petrov type of the metric.
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Start the MetricSearch Maplet, check the Einstein-Maxwell box, the Petrov Type I box, and the Isometry Dimension 4 box. We find that this is the metric in Stephani, Kramer et al. equation [12, 21, 1].
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