Hello
I have been going through the cosmology chapter in Choquet Bruhats GR and Einstein equations and in definition 3.1 of chapter 5 she defines the sectional curvature with a Riemann( X, Y;X, Y) (X and Y two vectors)
I don't understand this notation, regarding the use of the semi colon, is it...
I need to find all the non-zero components of the Riemann Tensor in a two-dimensional geometry knowing that the only two non-zero components of the Christoffel symbols are:
\Gamma^x_{xx}=\frac{1}{x} and \Gamma^y_{yy}=\frac{2}{y}
knowing that: R^\alpha_{\beta\gamma\delta}=\partial_\gamma...
1. Homework Statement
Show that
\int_{A} 1 = \int_{T(A)} 1
given A is an arbitrary region in R^n (not necessarily a rectangle) and T is a translation in R^n.
2. Homework Equations
Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero...
http://arxiv.org/abs/1202.2115
I know Arxiv isn't a real journal, but this caught my eye.
Is this a meaningful physical interpretation of the Riemann hypothesis?
From what I understand, the zeta function can be modeled as a wave, but attempting to solve for the real part requires infinite...
Using Ray D'Inverno's Introducing Einstein's Relativity. Ex 6.31 Pg 90.
I am trying to calculate the purely covariant Riemann Tensor, Rabcd, for the metric
gab=diag(ev,-eλ,-r2,-r2sin2θ)
where v=v(t,r) and λ=λ(t,r).
I have calculated the Christoffel Symbols and I am now attempting the...
Hello, I am currently in my first year of college, and I already took calculus in high school. I was able to solve all the problems, but I feel like I didn't understand everything conceptually.
When integrating dy/dx=x you get,
∫x dx=1/2x2.
But what exactly happened to the dx, why did it...
Hello,
Since it was mentioned in my textbook, I've been trying to find Riemann's proof of the existence of definite integrals (that is, the proof of the theorem stating that all continuous functions are integrable). If anyone knows where to find it or could point me in the right direction, I...
Is anyone familiar with Atlas 2 for mathematica to calculate the Riemann Tensor, Ricci Tensor, and scalar I have a metric that I need to calculate these things for. Can anyone help? I'm not too up on Mathematica either.
Hi
It's just that last step I'm not getting, so you have:
[1 / Kz] - [1 / (2K)z]
= [ (2K)z - Kz ] / [(2K)z * Kz]
= [ (2)z - 1 ] / [(2K)z*]
Then what?
Thanks