Recent content by grav-universe

Okay, so let's see. From what you said and from what little bit I can find on Wiki, if the energy density and isotropic pressure without the cosmological constant are ##\rho## and ##p##, then with the cosmological constant, these become just ##\rho_{(\Lambda)} = \rho + \Lambda / (\frac{8 \pi...

Given the metric $$c^2 d\tau^2 = B(r) c^2 dt^2 - A(r) dr^2 - C(r) r^2 d\Omega^2$$ how would the Einstein field equations be spelled out algebraicly for the energy density and radial and tangent pressures in terms of the unknown functions A, B, and C, while also including a cosmological constant...

Okay thank you. So from what you are saying, I gather that the assumption that the pressure is isotropic is my equation of state? That is, p = s for the radial and tangent pressures, thereby relating two aspects of the medium together?

Years ago I posted a thread where I solved for the exterior vacuum metric for a static spherical mass using only a single one of the unknown functions, A, B, or D, where D = C r^2, since they are inter-related. A moderator here graciously supplied the EFE's as A, B, and D relate to the energy...

Right okay, i thought about that. The only way to keep the forces linear is if some of it is transferred to tangential tidal force, right? So how do we find for that?

I was thinking about this today and have run into a conceptual problem. The idea of the measure of weight being linear so measured the same anywhere within a gravity well sounded good, nice and simple for calculations, just integrate for the mass times the acceleration of gravity at each height...

Okay cool :)

Right. I was referring to weight.

Well, I was working through some stuff with general relativity to begin with is all, and this topic popped up. I needed to know how a force measured locally would translate as measured at a different radii. Apparently it is invariant, but I didn't want to just assume it. Thanks :)

Wonderful :) thanks guys. It seemed too simple an assertion for general relativity so I wanted to be sure.

Well for free-fall it would be zero I suppose. Okay great, so we are saying that in general relativity, there is no transition of the measure of force acting upon different radii, that weight is invariant when the location of the mass remains the same?

It is weighing the same mass for the man in each case, right, but the acceleration of gravity for a mass placed upon the scale is different at each place. The mass of the man is the same at both places, so I want to be sure the reading upon the scale is due to the acceleration of gravity for...

I wasn't sure what to title it, I was thinking general relativity. I'm thinking the reading will be the same as when the scale was placed at the top of the pole, but I have no idea how to show that so I'm just guessing.

Let's say that a man standing on a scale on the surface of the Earth weighs 1000 Newtons. Now let's place the scale at the end of a very long pole extending far from the surface of earth, considering the Earth to be static. Let's say that the man on the scale now weighs 100 Newtons. If we were...

Yes of course I read it. I was trying to see what might be found without making any assumptions first however. Still am, I'm stubborn lol. I found a few simple relationships, but nothing yet that could be reduced much further to anything meaningful. Okay, sounds good for a start. I'll go ahead...