Recent content by dwellexity

Homework Statement A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x3+2x2y+2xy2+y3. What is the average potential energy, calculated over a long time? Homework EquationsThe Attempt at a Solution I think that this can be solved using Virial Theorem...

I am currently doing a experimental project work on superconductors. I am supposed to study properties of FeTeSe. I am having trouble understanding the difference between Zero-Field Cooling and Field Cooling. In both cases, I am measuring magnetization with varying temperature (from lower to...

I don't understand how this would affect anything. Even if Ricci tensor and Ricci Scalar have second derivatives, what ultimately matters is this particular sum.

I have got ##G_{tt} = - \frac{2(-1+2\phi)(\phi + 2 \phi^2 +r \phi')}{(r+2r\phi)^2}## How do I proceed from here? I am getting a first derivative of ##\phi## instead of second derivative.

If I am asked to show that the tt-component of the Einstein equation for the static metric ##ds^2 = (1-2\phi(r)) dt^2 - (1+2\phi(r)) dr^2 - r^2(d\theta^2 + sin^2(\theta) d\phi^2)##, where ##|\phi(r)| \ll1## reduces to the Newton's equation, what exactly am I supposed to prove?

It's a question in an assignment I have to do.

@PeterDonis Did you delete the last post? I can't see it anymore. Anyway, I tried what you suggested and it didn't get me anywhere. Maybe I am doing something wrong. Could you please show me a few steps?

I do not know of any symmetry involving swapping two middle indices of the Riemann tensor. The symmetries I know involve first two or last two or pair of first two and last two.

Just raising the ##\alpha## index doesn't solve the problem. There is still the minus sign and the order of ##\mu## and ##\nu## indices is wrong.

I need to prove that $$D_\mu D_\nu \xi^\alpha = - R^\alpha_{\mu\nu\beta} \xi^\beta$$ where D is covariant derivative and R is Riemann tensor. ##\xi## is a Killing vector. I have proved that $$D_\mu D_\nu \xi_\alpha = R_{\alpha\nu\mu\beta} \xi^\beta$$ I can't figure out a way to get the required...

I put the above mentioned Lagrangian $$ L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$ in the EL equation $$\frac{d}{dt}\frac{\partial L}{\partial \dot x^l} = \frac{\partial L}{\partial x^l }$$ and solved to get this. Please see the attached images. I hope it is legible.

I am just a beginner in these things. Can you guide me on how to proceed from the equation I have to get the geodesic equation?

I didn't understand it. You are differentiating ##\dot \gamma## wrt ##\dot \gamma##? Also ##g(\dot\gamma,\dot \gamma)##? Having found the equation I have given above, how do I proceed to do this reparametrisation?

I am trying to derive the geodesic equation using variational principle. My Lagrangian is $$ L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$ Using the Euler-Lagrange equation, I have got this. $$ \frac{d^2 x^u}{dt^2} + \Gamma^u_{mk} \frac{dx^m}{dt} \frac{dx^k}{dt} =...

I think I will talk to him about this. He is not that kind of guy. Anyways, thanks for the help.