# Weyl Tensor calculations using Symbolic module¶

[1]:

import sympy
from sympy import cos, sin, sinh
from einsteinpy.symbolic import MetricTensor, WeylTensor

sympy.init_printing()


## Defining the Anti-de Sitter spacetime Metric¶

[2]:

syms = sympy.symbols("t chi theta phi")
t, ch, th, ph = syms
m = sympy.diag(-1, cos(t) ** 2, cos(t) ** 2 * sinh(ch) ** 2, cos(t) ** 2 * sinh(ch) ** 2 * sin(th) ** 2).tolist()
metric = MetricTensor(m, syms)


## Calculating the Weyl Tensor (with all indices covariant)¶

[3]:

weyl = WeylTensor.from_metric(metric)
weyl.tensor()

[3]:

$\displaystyle \left[\begin{matrix}\left[\begin{matrix}0 & 0 & 0 & 0\\0 & - \cos^{2}{\left(t \right)} & 0 & 0\\0 & 0 & - \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)} & 0\\0 & 0 & 0 & - \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\end{matrix}\right] & \left[\begin{matrix}0 & - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)}}{6} - 2 \cos^{2}{\left(t \right)} & 0 & 0\\\frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)}}{6} + 3 \cos^{2}{\left(t \right)} & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0\\0 & 0 & 0 & 0\\- \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{5 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0 & 0\\0 & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2}\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\- \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{5 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0 & 0\end{matrix}\right]\\\left[\begin{matrix}0 & \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)}}{6} + 3 \cos^{2}{\left(t \right)} & 0 & 0\\- \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)}}{6} - 2 \cos^{2}{\left(t \right)} & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}- \cos^{2}{\left(t \right)} & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)} & 0\\0 & 0 & 0 & \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{\cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0\\0 & \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0\\0 & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{\sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2}\\0 & 0 & 0 & 0\\0 & \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0\end{matrix}\right]\\\left[\begin{matrix}0 & 0 & - \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{5 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0\\0 & 0 & 0 & 0\\\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0 & 0\\0 & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0\\0 & - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{\cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0\\0 & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}- \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)} & 0 & 0 & 0\\0 & \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)} & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & - \left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{4}{\left(\chi \right)}\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} + \left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{4}{\left(\chi \right)} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{4}{\left(\chi \right)}}{6}\\0 & 0 & \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} + \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{4}{\left(\chi \right)}}{6} & 0\end{matrix}\right]\\\left[\begin{matrix}0 & 0 & 0 & - \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{5 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2}\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} - \frac{3 \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2}\\0 & 0 & 0 & 0\\0 & - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)}}{2} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{6} + \frac{\sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} + \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{4}{\left(\chi \right)}}{6}\\0 & 0 & - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} - \frac{\left(\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}\right) \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{2} + \left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{4}{\left(\chi \right)} + \frac{\left(\frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sinh^{2}{\left(\chi \right)} - 2 \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} + \frac{\left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \sinh^{2}{\left(\chi \right)} - 2 \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}}{\sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)}} - 6\right) \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{4}{\left(\chi \right)}}{6} & 0\end{matrix}\right] & \left[\begin{matrix}- \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{2}{\left(\chi \right)} & 0 & 0 & 0\\0 & \sin^{2}{\left(\theta \right)} \cos^{4}{\left(t \right)} \sinh^{2}{\left(\chi \right)} & 0 & 0\\0 & 0 & - \left(\sin^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(\theta \right)} \cos^{2}{\left(t \right)} \sinh^{4}{\left(\chi \right)} & 0\\0 & 0 & 0 & 0\end{matrix}\right]\end{matrix}\right]$
[4]:

weyl.config

[4]:

'llll'