Timeline for Trying to confirm that the trace of the energy-momentum tensor divided by the energy density is NOT invariant
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2023 at 19:58 | vote | accept | perchlorious | ||
| Apr 26, 2023 at 18:41 | comment | added | KP99 | Just to clarify, in this question we are just considering the ratio $p/\mu$, and how it should change from one frame to another. OP denotes this ratio by $\omega$, which I've adopted in my answer. There may exist other definitions of $\omega$ (which I dont know), but it doesn't seem to be the point of the question | |
| Apr 26, 2023 at 18:18 | comment | added | KP99 | @A.V.S. $\omega$ is calculated wrt fluid's rest frame means it is frame dependent or observer dependent. Or, I'm not sure what you mean | |
| Apr 26, 2023 at 17:39 | comment | added | A.V.S. | ω is observer dependent Wrong. $ω$ is calculated w.r.t fluid's rest frame. In other words it is ratio of eigenvalues and not of components of SE tensors. | |
| Apr 26, 2023 at 13:15 | comment | added | KP99 | No problem, The way u can arrive at the above expressions is that first u write $T_{ab}$ in terms of $\hat{u}$ vector, then write $\hat{u}$ in terms of $u$ and $v$ and simply read the coeeficients. For instance, the coefficients of $u_au_b$ will be $\mu$ etc. So actually, it becomes a local comparison of these quantities | |
| Apr 26, 2023 at 13:11 | comment | added | perchlorious | I used the term timelike imprecisely. I see what you are saying now. | |
| Apr 26, 2023 at 12:56 | comment | added | KP99 | what is purely timelike ? All massive objects move in timelike trajectories, but we can define relative velocity b/w them..at least thats what we usually do in SR. Yes, when u take the difference, they will have space-like component which is encoded in $v$. This definition of relative velocity becomes ambiguous when we compare velocities b/w different tangent spaces in curved space-time | |
| Apr 26, 2023 at 12:41 | comment | added | perchlorious | I think I mostly understand your answer now. You are able to talk about relative velocity between the two timelike vectors because in this case they exist in the same tangent plane. What is unclear is this: if they are both purely timelike, how can they have a relative velocity? Wouldn't they each have a spacelike component relative to the other? | |
| Apr 26, 2023 at 11:59 | history | answered | KP99 | CC BY-SA 4.0 |