Metric tensor Definition and 211 Threads

Hi, This might sound a very basic question to most of you all. But could you kindly give me some information on what eactly is a Metric Tensor and what is its significance in the higher dimension study? (Wiki or Google info seemed too cryptic. Thus...I ask you) Thank You

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}?