# How Do I Perform a Coordinate Transformation on a Metric Tensor?

I entered my coordinates like this:

```
M = Manifold(3, 'M', structure='Lorentzian')
X.<t,p,ph> = M.chart(r't p ph:\phi')
X
```

Then defined my metric-tensor like this:

```
g = M.metric()
g[0,0], g[1,1] = -1, 1
g[2,2] = (5*p^2+4*t^2)
g.display()
```

How to transform the metric under the coordinate change of `r=sqrt(5*p^2+4*t^2)`

? And once I do that, can the Christoffel symbols be calculated from the new metric instead of the old one, and in terms of t and r?