Schwarzschild Embedding Module¶
Class for Utility functions for Schwarzschild Embedding surface to implement gravitational lensing:
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class
einsteinpy.hypersurface.schwarzschildembedding.
SchwarzschildEmbedding
(M)¶ Class for Utility functions for Schwarzschild Embedding surface to implement gravitational lensing
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r_init
¶ - Type
m
Constructor Initialize mass and embedding initial radial coordinate in appropiate units in order to render the plots of the surface in finite grid. The initial r is taken to be just greater than schwarzschild radius but it is important to note that the embedding breaks at r < 9m/4.
- Parameters
M (kg) – Mass of the body
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gradient
(r)¶ Calculate gradient of Z coordinate w.r.t r to update the value of r and thereby get value of spherical radial coordinate R.
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radial_coord
(r)¶ Returns spherical radial coordinate (of the embedding) from given schwarzschild coordinate.
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get_values
(alpha)¶ Obtain the Z coordinate values and corrosponding R values for range of r as 9m/4 < r < 9m.
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get_values_surface
(alpha)¶ Obtain the same values as of the get_values function but reshapes them to obtain values for all points on the solid of revolution about Z axis (as the embedding is symmetric in angular coordinates).
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plot_hypersurface
(plot_type='wireframe', alpha=100)¶ Plots the surface thus obtained for the embedding.
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show
()¶ Show the plot made by plot_hypersurface()
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