Metric tensor Definition and 210 Threads

How do we derive the metric tensor?

That's a crucial point of GR ! And I have always problems with that. Back to the basics, with your help. Thanks Michel

What is the metric tensor on a spherical surface?

I read some books and see that the definition of covariant tensor and contravariant tensor. Covariant tensor(rank 2) A'_ab=(&x_u/&x'_a)(&x_v/&x'_b)A_uv Where A_uv=(&x_u/&x_p)(&x_u/&x_p) Where p is a scalar Contravariant tensor(rank 2) A'^uv=(&x'^u/&x^a)(&x'^v/&x^b)A^ab Where A^ab=dx_a...

Wiki says it's 1 0 0 sin^2\theta My book says it's cos²\theta 0 0 1 I calculate 1 0 0 cos^2\theta ?! which is it?

Q1 If given a 2D Riemannian space, ds^2 = dx^2 + x^2dy^2, do the componets of the metric tensor are these: g_11 = 1, g_12 = 0 g_21 = o, g_22 = x^2 ? In addition, I got a question from my lecturer: Q2. 2 metrics, defined in a Riemannian space, are given by ds^2 = g_ijdx^idy^j and ds'^2 =...

My cosmology textbook tells me that if I raise the indicies on the metric tensor (from subscript to superscript), then all I have to do is divide one by each element. But from what I know about inverting matricies, the process is quite a bit more involved. When I raise the indicies on the...

I was wonder if some can explain to me what exactly are the 10 parameters for the metric tensors. I know the reason for getting 10 parameters, 3^2=9 + 1, you get three for every spatial dimensions plus one for time. But why exactly three parameters for each spatial dimension? And what exactly...

Hi I'm new here and I hope that you will be able to give me a lot of help. My english is far to be perfect but sufficiant to asks you a lot of questions... (i hope so :wink:). First question : I'm looking for a complete proof (with all steps) of : \partial _h g = gg_{ij} \partial _h...

If the cosmological constant, \Lambda has units of reciprocal time squared then what is the unit for the metric tensor, g_{ij}?