aurel.coreanalytic

Analytic version of AurelCore, using sympy for symbolic calculations.

This class is designed in a similar manner to the AurelCore class, but it takes in different inputs, has no cache management, and there are much fewer quantities available.

class aurel.coreanalytic.AurelCoreAnalytic(coords, g, verbose=True)

Bases: object

Analytic version of AurelCore, using sympy for symbolic calculations.

Parameters:

• coords (list of sympy symbols) – List of coordinates.

• g (sympy.Matrix) – Metric tensor in the down index form.

• verbose (bool, optional) – If True, print the calculation description. Default is True.

dim

(int) - Dimension of the metric tensor.

Type:

int

data

(dict) - Dictionary to store calculated quantities.

Type:

dict

Gamma_down()

Christoffel symbols in the down index form

Gamma_udd()

Christoffel symbols in the up-down-down index form

RicciS()

Ricci scalar

Ricci_down()

Ricci curvature tensor in the down index form

Riemann_down()

Riemann curvature tensor in the down index form

Riemann_uddd()

Riemann curvature tensor in the up-down-down-down index form

gup()

Metric tensor in the up index form