Timeline for Validity of relativistic hydrodynamic equations
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 19, 2018 at 22:38 | history | bounty ended | Mathews24 | ||
| May 15, 2018 at 2:47 | vote | accept | Mathews24 | ||
| May 12, 2018 at 22:24 | comment | added | Mathews24 | It appears to be a limit comparing the wavevector to the Christoffel symbol. $g/c^2 \gg 2/\lambda \implies g/(\lambda/\tau)^2 \gg 2/\lambda \implies \frac{1}{2}g\tau^2 \gg \lambda$ where $\tau$ is the period for a causal response over the perturbation wavelength, $\lambda$. The limit essentially indicates the displacement due to gravity is much greater than the perturbation (i.e. "strong acceleration"). | |
| May 12, 2018 at 20:32 | comment | added | John Donne | I don't know exactly. I guess it's some sort of "size of the system". For a Newtonian body with zero energy $v^2/g\approx R$ | |
| May 12, 2018 at 19:52 | comment | added | Mathews24 | I agree; I suppose the assumptions you stated above appear almost exactly those assumed in the Newtonian limit except for the possibility of $p > \rho_o c^2$ and I was attempting to clarify any additional differences. I agree that "strong acceleration" can be viewed as a limit on wavelengths, but what does comparing $k$ to $g/c^2$ physically represent? Is the latter quantity of any significance in any contexts? | |
| May 12, 2018 at 19:47 | comment | added | John Donne | @Mathews24 In the Newtonian limit, there shouldn't be any factors of $c$, so this is not the usual Newtonian limit, but rather something ad hoc. As to the strong gravity thing, you can interpret that statement as saying something about $k$ rather than $g$: it would be the limit of long wavelengths | |
| May 12, 2018 at 13:53 | comment | added | Mathews24 | To clarify: how do the assumptions you've taken differ from the classical Newtonian limit? Also, Allen & Hughes consider the situation of strong acceleration (i.e. $g \gg kc^2$)—is not the usage of weak gravity invalid in the above derivation? | |
| May 12, 2018 at 9:59 | history | answered | John Donne | CC BY-SA 4.0 |