```python
import sympy
from einsteinpy.symbolic import MetricTensor, ChristoffelSymbols, RiemannCurvatureTensor

sympy.init_printing()
```


```python
syms = sympy.symbols('r theta phi')
# define the metric
metric = [[0 for i in range(3)] for i in range(3)]
metric[0][0] = 1
metric[1][1] = syms[0]**2
metric[2][2] = (syms[0]**2)*(sympy.sin(syms[1])**2)
#create metric object
m_obj = MetricTensor(metric, syms)
m_obj.tensor()
```




$\displaystyle \left[\begin{matrix}1 & 0 & 0\\0 & r^{2} & 0\\0 & 0 & r^{2} \sin^{2}{\left(\theta \right)}\end{matrix}\right]$




```python
ch = ChristoffelSymbols.from_metric(m_obj)
ch.tensor()
```




$\displaystyle \left[\begin{matrix}\left[\begin{matrix}0 & 0 & 0\\0 & - r & 0\\0 & 0 & - r \sin^{2}{\left(\theta \right)}\end{matrix}\right] & \left[\begin{matrix}0 & \frac{1}{r} & 0\\\frac{1}{r} & 0 & 0\\0 & 0 & - \sin{\left(\theta \right)} \cos{\left(\theta \right)}\end{matrix}\right] & \left[\begin{matrix}0 & 0 & \frac{1}{r}\\0 & 0 & \frac{\cos{\left(\theta \right)}}{\sin{\left(\theta \right)}}\\\frac{1}{r} & \frac{\cos{\left(\theta \right)}}{\sin{\left(\theta \right)}} & 0\end{matrix}\right]\end{matrix}\right]$




```python
#Calculating Riemann Curvature Tensor
rm1 = RiemannCurvatureTensor.from_christoffels(ch)
rm1.tensor()
```




$\displaystyle \left[\begin{matrix}\left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right]\\\left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right]\\\left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right] & \left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right]\end{matrix}\right]$




```python

```

f74b6b3e7fddd84fd77adf589d33dea78d70b297
ipynb
Jupyter Notebook
Spherical Polars.ipynb
SheepWaitForWolf/General-Relativity
e9eb0f8cc65be9368c6648c8afaa1f8e631516a8
MIT
2021-06-04T11:01:54.000Z
2021-06-04T11:01:54.000Z
Spherical Polars.ipynb
SheepWaitForWolf/General-Relativity
e9eb0f8cc65be9368c6648c8afaa1f8e631516a8
MIT
Spherical Polars.ipynb
SheepWaitForWolf/General-Relativity
e9eb0f8cc65be9368c6648c8afaa1f8e631516a8
MIT
Qwen/Qwen-72B
1. YES
2. YES