Recent content by Matter_Matters

Hi there guys, I was wondering does anyone have a layman's explanation of the GCRS as defined in the title. I am confused as to whether this is an inertial or non inertial system. In text modern reference books such as this (chapter 10, section 10.3.2) they define rotating/non rotating...

Hmmm I am confused now! So, normally in GR we can set the Lagrangian = ##\pm c## depending on the signature of the line element. Is this only true when the geodesic is parametrised by an affine parameter also? Even using the ## L = \sqrt{ }##, I can't seem to manage to get the correct expression!

O wow! If this was the issue the whole time I will be very pleased but also annoyed at my ignorance!

Question Background: I'm considering the Eddington-Robertson-Schiff line element which is given by (ds)^2 = \left( 1 - 2 \left(\frac{\mu}{r}\right) + 2 \left(\frac{\mu^2}{r^2}\right) \right) dt^2 - \left( 1 + 2 \left( \frac{\mu}{r} \right) \right) (dr^2 + r^2 d\theta^2 + r^2 \sin^2{\theta}...

As far as I can tell the answer is actually quite non-trivial. Which is a shame because the coefficients looks like a generalisation of the isotopic and harmonic Schwarzschild line element just incorporating two potentials.

Did you read the question?

I was a bit hasty with my response there. You cannot parametrise a null geodesic with the proper time as it will assign the same value to all points along the geodesic. Just like you said :)

Can you illustrate that with an example? For example using \lambda over \tau as a parameter for the world line of a particle or satellite as it were.

This is brilliant. I enjoyed this a lot. Okay thanks mate. Now, you've opened up two different cans of worms... You can derive equations of motion for a null geodesic with the proper time as the "affine" parameter no problem I thought? Isn't it a standard calculation in undergrad GR...

Thanks Paul. However, the part I don't understand is the parametrisation of the spacetime coordinates. Normally, in GR they are parametrised by the proper time for the geodesic equation at least.

Excellent thanks for clearing that up for me. However, what I am struggling with is to grasp why the geocentric coordinate time is the affine parameter. So, let me try say it like this. Given a spacetime interval (In the GCRS) the line element of Minkowskian space is given by ds^2 = c^2 d...

Currently reading the following document which is a bit of a brain overload at the minute! Im considering Equation (4.61). It is the general relativistic correction due to the Schwarzschild field for a near Earth satellite when the parameters \beta, \;\gamma \equiv 1. However, as you will...

In coordinates given by x^\mu = (ct,x,y,z) the line element is given (ds)^2 = g_{00} (cdt)^2 + 2g_{oi}(cdt\;dx^i) + g_{ij}dx^idx^j, where the g_{\mu\nu} are the components of the metric tensor and latin indices run from 1-3. In the first post-Newtonian approximation the space time metric is...

You should note that the choice of sign for the potential energy is really down to convention. You could easily define it as the following: V(r) = \frac{GM}{r}, such that the force associated with the above potential may be given by the usual F = \nabla V(r), which gives the usual...

Thanks for the information. I'm trying to write it in terms of hamiltonian's specifically to later use symplectic integration schemes. However, this is proving to be quite the task! Well for my coding capabilities anyways.