Recent content by Ulrich

If the matter density is a function of the radius alone, that is, if it is constant everywhere at the same distance from the gravity center of a mass distribution, the entire mass can be considered as a point mass. We made an exercise on that in classical mechanics in the second year. h=10km is...

Since this is the difference from the mean radius, the polar radius must have about 10km less such that the difference between equatorial and polar radius is 20km. So there must something be wrong with my calculation of the shape since it yields 10km for this last difference, but what?

You are right, this could explain the flow showed in the documentary.

The basic calculation is in the first attachement, the Mathematica code in the second as pdf file. Yeah, this is right, I didn't think to that but for slow rotation I think it's a good approximation. That for such cases my calculation is correct can also be seen in another way: if the Earth is...

I recently saw a documentary, which claimed that if the Earth rotation slows down the water of the oceans will flood to the north and south because the centripetal force at the equator diminishes. In fact, earth’s radius is about 20 km longer at the equator than at the poles. However, I doubt...

Definitions are based on such assumptions, so call it what ever you want. You are mixing up coordinate invariance with Lorentz invariance. The first implies a change from one coordinate system into another from the point of view of the same observer staying at the same place wheras the second...

Exactly, it is a definition. And because it is a definition, one cannot derive it from anything else. ##ρ=-p## follows from that definition and not the other way around. Definitions come first, derivations thereafter. The Friedmann equation is not Newtonian mechanics. It is derived from the...

From what do you infer this? What you are referring to is the general perfect fluid stress-energy tensor. General means that it applies to any density and pressure in a perfect fluid. Also matter and radiation densities have no preferred direction in a FRW-model. So according to your...

A disagree here because if you say that a cosmological constant has an equation of state of ##w = -1## you still have to explain why this is the case and what is the physical reasoning behind it. The general form of the equation of state is w=\frac{p}{ρ} where p is a pressure and ρ the...

Sorry Chronos, I edited my post too late, I meant of course if \dot{a} goes to 0 not to ∞

Well there is this term \frac{k c^2+\dot{a}^2}{a^2} in the Einstein curvature tensor, where k is -1,0 or 1 for hyperbolic, flat or spherical universe. In all cases this term becomes infinite if ##a## goes to zero, unless \dot{a} also goes to zero, which would yield un undetermined limit. Hartle...

Thanks Marcus for your search. However, I think that we cannot really crasp what happened at the big bang so research on that subject will always stay speculative in my humble opinion. What is more interesting me at the moment are other questions like how pressures of radiation and vacuum...

It may be small but small does not signify zero. What the zero-energy-universe-cosmologists are trying to establish is a theory that explains how the universe came out of nothing. However, nothing really signifies zero in the strict mathematical sense. Something around 10^-29 grams per cubic...

Can you explain this further? Here is my understanding: The equation you give is the first law of thermodynamics for cosmology for a general density. It is supposed that the vacuum energy density is independent of time so ## \dot \rho = 0## and correspondingly ##p = - \rho##. If now I want to...

Something that I cannot understand in this "zero energy universe" is that only gravitational and mass energy is taken into account. What about dark energy that represents over 70% of cosmological density? And isn't there also kinetic energy of all the mass moving? And not to forget the...