Recent content by rolling stone

And thanks also for this suggestion of yours. I will try to work it out

OK Dale Unfortunately this is not obvious to me, therefore I understand that I have still a lot to learn about the Schwartschild metric.

This problem is really tough, but I think it may be overcome, first by remembering that spacecraft s are moving along a geodetic path in a “curved" space, and then by resorting to the definition of speed as the fraction between the space that has been traveled (not the space that will be...

In the scenario seen by spaceman ##S_1## he may legitimately consider himself - on board of his spacecraft that moves by inertia along a geodetic path (if ##R=GM/v^2##) - at rest with respect to the mass ##M## (if ##M## is a homogeneous sphere). So ##S_1##’s metric is the Schwarzschild metric...

Consider a mass ##M## that generates a curvature of the space-time and an observer ##O##, fixed and positioned at such a great distance from ##M## that the time ##t## of its clock is not affected by ##M##. Suppose that the observer ##O##, in his polar coordinates reference system centred at...

to Vahnees71 I just wanted to deduce the Friedmann equations keeping track of the “c” term, i.e. without setting equal to one the velocity of light. I never understood the utility of the natural units. By natural units it is not possible to appreciate, for instance, the difference in the...

Sorry I made a mistake in the signs of eq. 6. The right equation is: (6) ##T^{ij}##=##(ρ + p/c^2)## ##u^{0}## ##u^{0}## ##- p ## ##g^{ij}##

Thanks Pervect for the suggestion. I try it again by Latex The starting point is the fully contravariant energy-stress tensor of a perfect fluid in a Local Inertial Frame: (1) ##T^{ij}##= \begin{bmatrix} + ρ c^2& 0 & 0 & 0 \\ 0 & +p& 0 & 0 \\ 0 & 0 & +p & 0 \\ 0 & 0 & 0 & +p \\...

Hi everyone! The foregoing discussion about the metric tensor of a perfect fluid in its rest frame has helped me very much in solving the problem from which my doubt arose: the deduction of the Friedmann equations from the Einstein field equations, keeping track of the “c” term. If someone is...

High to everybody! With just one and half year delay (sorry), here is a way to derive the Friedmann equations keeping track of the “c” term. Starting point is the fully contravariant energy-stress tensor of a perfect fluid in a Local Inertial Frame: (1) T_Hij = diag[ ρ * c^2, p, p, p...

PeterDonis Thanks a lot: now I understand where I was wrong. Actually eq.(1) has been deduced (as I see in Physicspages) in a local orthonormal inertial frame, where gij = ηij, so that it makes no sense to look for the solution of eq.(2) with Tij as stated in eq.(1). It does make sense with...

The stress-energy tensor of a perfect fluid in its rest frame is: (1) Tij= diag [ρc2, P, P, P] where ρc2 is the energy density and P the pressure of the fluid. If Tij is as stated in eq.(1), the metric tensor gij of the system composed by an indefinitely extended perfect fluid in...