Recent content by Confused Physicist

Hi! I have the following problem I don't really know where to start from: A bowl with axial symmetry is built in flat Euclidean space ##R^3##, and has a radial profile giveb by ##z(r)##, where ##z## is the axis of symmetry and ##r## is the radial distance from the axis. What radial profile...

I have the feeling the last step, where I integrate ##dt## and get the time the observer takes to fall into the black hole, is not quite correct. But I'm not really sure. Could someone help me out? Thanks, I really appreciate it.

Hi, I have the following problem: Given the 5-D generalization of the Schwarszschild solution with line element: ds^2=-\Bigg(1-\frac{r^2_+}{r^2}\Bigg)dt^2+\Bigg(1-\frac{r^2_+}{r^2}\Bigg)^{-1}dr^2+r^2[d\chi^2+\sin^2(\chi)(d\theta^2+\sin^2(\theta)d\phi^2)] where ##r_+## is a positive constant...

Hi, I'm the given the following line element: ds^2=\Big(1-\frac{2m}{r}\large)d\tau ^2+\Big(1-\frac{2m}{r}\large)^{-1}dr^2+r^2(d\theta ^2+\sin ^2 (\theta)d\phi ^2) And I'm asked to calculate the null geodesics. I know that in order to do that I have to solve the Euler-Lagrange equations. For...

What does it mean to treat ##\tau## as an angular coordinate? Is it a specific change of variable?

Thanks PeterDonis, I will post my future questions in the homework forum. I've been trying to squeeze my head around it, but I haven't posted my attempt because I literally don't have a decent one. Yes, the problem says ##r=0##, but you're right. I believe it's a mistake and it should say ##r=2m##.

Hi! I have the following problem I don't really know how to approach. Could someone give me a hand? The line element of a black hole is given by: ds^2=\Bigg(1-\frac{2m}{r}\Bigg)d\tau ^2+\Bigg(1-\frac{2m}{r}\Bigg)^{-1} dr^2+r^2\Big(d\theta ^2+\sin^2(\theta)d\phi ^2\Big) It has an apparent...

It was presented to me by its deffinition with Christoffel symbols. I was never explained the physical meaning behind it (geometrical meaning) to help me imagine it.

You mean when I multiply (2) by ##2x/y^2##? I'm repeating the process again, but I can't find the mistake... Ohhhhh okay I've seen the mistake now. The mistake is on equation (2). The ##2y^3\dot{y}^2## should be ##4y^3\dot{y}^2##. Oh no. That wasn't the mistake. I still can't see what you're...

Purely mathematical. Two years ago I took a course on differential geometry. It wasn't until this year I started studying General Relativity, but I'm learning it on my own.

Oh, why is my final equation for ##\ddot{y}## not correct? And what is that change of variables that simplifies the calculation? Is the solution I have obtained incorrect then?

No, not really. Could you illustrate it for me? Thank you!

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...

Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...