Christoffel¶

einsteinpy.utils.christoffel.riemann_curvature_tensor(list2d, syms)¶

Function to calculate Riemann Curvature Tensor of a given metric

Parameters

list2d (list) – d list (Matrix) representing metric, containing ~sympy expressions
syms (list) – 1d list containing representaion of [x0,x1,x2…] in ~sympy expressions

Returns

4d list of ~sympy expressions containing components of Riemann Tensor

Return type

list

einsteinpy.utils.christoffel.christoffels(list2d, syms)¶

Function to calculate christoffel symbols of a given metric

Parameters

list2d (list) – 2d list (Matrix) representing metric, containing ~sympy expressions
syms (list) – 1d list containing representaion of [x0,x1,x2…] in ~sympy expressions

Returns

3d list of ~sympy expressions containing christoffel symbols

Return type

list

einsteinpy.utils.christoffel.simplify_christoffels(list3d, dims=4)¶

Returns a 3d list of simplified christoffel symbols.

Parameters

Returns

3d list containing simplified christoffel symbols

Return type

list

einsteinpy.utils.christoffel.schwarzschild_christoffels(symbolstr='t r theta phi')¶

Returns the 3d list of christoffel symbols of Schwarzschild Metric.

Parameters: symbolstr (string) – symbols to be used to define schwarzschild space, defaults to ‘t r theta phi’
Returns: 3d list of christoffel symbols for schwarzschild metric
Return type: list

einsteinpy.utils.christoffel.kerr_christoffels(symbolstr='t r theta phi')¶

Returns the 3d list of christoffel symbols of Kerr metric(BL coordinates) in Plank units : G=1, c=1.

Parameters: symbolstr (string) – symbols to be used to define kerr space in BL coordinates, defaults to ‘t r theta phi’
Returns: 3d list of christoffel symbols for kerr metric
Return type: list

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