Tagged Questions
0
votes
0answers
37 views
Curved space to flat space calculation
When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?
0
votes
1answer
310 views
How to get the gradient potential in polar coordinate
In polar coordinate,
$$\nabla U = \frac{\partial U}{\partial r}\hat{\mathbf{r}} + \frac{1}{r}\frac{\partial U}{\partial \theta}\hat{\mathbf{\theta}} .$$
Can anyone show me how to get this result?
2
votes
1answer
103 views
What is the physical intepretation of harmonic coordinates?
When I see harmonic coordinates used somewhere, what should my association be?
Is there some general use or need to consider the harmonic cooridnate condition?
I don't really see what's ...
4
votes
1answer
625 views
Why is light described by a null geodesic?
I'm trying to wrap my head around how geodesics describe trajectories at the moment.
I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
0
votes
1answer
1k views
Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?
I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
0
votes
3answers
271 views
Need some basic help with notation and the Christoffel symbols
Apologies in advance if some of the questions below seem overly simple.
In an introductory GR book, I find the following expression for the autoparallel of the affine connection (the upper bound of ...
6
votes
3answers
129 views
From Manifold to Manifold?
Tensor equations are supposed to stay invariant in form wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor ...
