The DifferentialGeometry Library package contains an extensive database of spacetime metrics and matter fields which give solutions to the Einstein equations of general relativity. The command MetricSearch allows the Maple user to search the database for metrics with specified properties.  The first calling sequence launches an easy to use Maplet. The second calling sequence provides the same search capabilities in a command line format.

The command MetricSearch() initializes a maplet which searches the DifferentialGeometry Library for metrics with user-specified properties. The current search criteria are summarized in the following table.

Once properties are selected by checking appropriate boxes, pressing the Search button will return all metrics in the DifferentialGeometry library which possess all of the indicated properties. The format of the result is a string representing the source reference and a sequence of lists indicating the equation numbers in the reference where the metrics appear. All the information in the DifferentialGeometry library for each metric can be obtained with the Retrieve command.

Information regarding the metric found by a search of the DifferentialGeometry library can be retrieved in one of two ways. One method is to enter the reference name (string), equation number, and the name of an initialized manifold (created in the calling worksheet using DGsetup) into the text boxes in the Retrieve section of the MetricSearch Maplet. Then pressing the Retrieve button will return a list of the spacetime fields defining the solution (e.g., metric, electromagnetic field, etc.) to the calling worksheet.  All the information in the DifferentialGeometry library for each metric can be obtained with the Retrieve command.

The Clear button resets all check boxes and clears all text boxes. The Close button will close the Maplet.

The second calling sequence accepts a list of desired properties, each specified by an equation $\mathrm{metricproperty} \= \mathrm{propertyvalue}$. The possibilities are:

Currently the DifferentialGeometry library contains selected metrics from:

 Stephani, H.; Kramer, D.; MacCallum, M.; Hoenselaers, C.; and Herlt, E. Exact Solutions to Einstein's Field Equations. 2nd ed. Cambridge Monographs on Mathematical Physics, 2003.

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{Tensor}\right)\:$$\mathrm{with}\left(\mathrm{LieAlgebras}\right)\:$$\mathrm{with}\left(\mathrm{Library}\right)\:$

$\mathrm{DGsetup}\left(\left[\mathrm{x1}\,\mathrm{x2}\,\mathrm{x3}\,\mathrm{x4}\right]\,M\right)$

$\mathrm{frame\; name:\; M}$

$F≔\mathrm{MetricSearch}\left(\right)\:$

$F$

$\mathrm{DGsetup}\left(\left[t\,x\,y\,\mathrm{\phi }\right]\,M\right)$

$\mathrm{frame\; name:\; M}$

$g≔\mathrm{evalDG}\left(\frac{1}{x^2}\left(\mathrm{dx}\&t\mathrm{dx}+\mathrm{dy}\&t\mathrm{dy}\right)+x^2\mathrm{dphi}\&t\mathrm{dphi}-\left(\mathrm{dt}-2y\mathrm{dphi}\right)\&t\left(\mathrm{dt}-2y\mathrm{dphi}\right)\right)$

$g:=-\mathrm{dt}\mathrm{dt}\+2y\mathrm{dt}\mathrm{dphi}\+\frac{\mathrm{dx}\mathrm{dx}}{x^2}\+\frac{\mathrm{dy}\mathrm{dy}}{x^2}\+2y\mathrm{dphi}\mathrm{dt}\+\left(-4y^2\+x^2\right)\mathrm{dphi}\mathrm{dphi}$

$\mathrm{RainichConditions}\left(g\right)$

$\mathrm{true}$

$\mathrm{KV}≔\mathrm{KillingVectors}\left(g\right)$

$\mathrm{KV}:=\left[\frac{1}{4}x\mathrm{D\_x}\+\frac{1}{4}y\mathrm{D\_y}-\frac{1}{4}\mathrm{\φ}\mathrm{D\_phi}\,\frac{1}{2}\mathrm{\φ}\mathrm{D\_t}\+\frac{1}{4}\mathrm{D\_y}\,-\frac{1}{4}\mathrm{D\_phi}\,\frac{1}{2}\mathrm{D\_t}\right]$

$\mathrm{nops}\left(\mathrm{KV}\right)$

$4$

$\mathrm{PetrovType}\left(g\right)$

$''I''$

$\mathrm{MetricSearch}\left(\left[''PrimaryDescription''=''EinsteinMaxwell''\,''PetrovType''=''I''\,''IsometryDimension''=4\right]\right)$

$\left[\left[''Stephani''\,1\,\left[12\,21\,1\right]\right]\right]$

$\mathrm{Retrieve}\left(''Stephani''\,1\,\left[12\,21\,1\right]\,\mathrm{manifoldname}=M\,\mathrm{output}=\left[''Metric''\right]\right)$

$\left[-\mathrm{dt}\mathrm{dt}\+2y\mathrm{dt}\mathrm{dphi}\+\frac{{\mathrm{\_a}}^2\mathrm{dx}\mathrm{dx}}{x^2}\+\frac{{\mathrm{\_a}}^2\mathrm{dy}\mathrm{dy}}{x^2}\+2y\mathrm{dphi}\mathrm{dt}\+\left(-4y^2\+x^2\right)\mathrm{dphi}\mathrm{dphi}\right]$

$S≔\mathrm{MetricSearch}\left(\left[''Keywords''=\left[''Goedel''\right]\right]\right)$

$S:=\left[\left[''Stephani''\,1\,\left[12\,26\,1\right]\right]\right]$

$g≔\mathrm{Retrieve}\left(\mathrm{op}\left(S\left[1\right]\right)\,\mathrm{manifoldname}=M\,\mathrm{output}=\left[''Metric''\right]\right)\left[1\right]$

$g:=-{\mathrm{\_a}}^2\mathrm{dt}\mathrm{dt}-{\mathrm{\_a}}^2{\ⅇ}^x\mathrm{dt}\mathrm{dphi}\+{\mathrm{\_a}}^2\mathrm{dx}\mathrm{dx}\+{\mathrm{\_a}}^2\mathrm{dy}\mathrm{dy}-{\mathrm{\_a}}^2{\ⅇ}^x\mathrm{dphi}\mathrm{dt}-\frac{1}{2}{\mathrm{\_a}}^2{\ⅇ}^{2x}\mathrm{dphi}\mathrm{dphi}$