Thanks Snoopy... that help but the problem is that a numerical solution bring to a singularity somewhere for t=t* (finite value). I wonder if somebody has analyzed that kind of eq. to identify what are (if any) the conditions for it's integrability.
Sorry Snoopy I guess I was unclear. The eq. to solve is: y''(t)+C_{1}(y(t))\; y'(t)= C_{2}(y(t)). I thought that kind of eq. received some attention in literature and I wonder if somebody can help me in finding papers that analyze that type of DE. Thanks
Thanks Snoopy. Actualli I know the D1(y)=A1*(B1-ye)/ye+1/2 and D2(y)=A2(1-ye)(B2-ye)/y2e-1... (Ai, Bi, e are costants) but the problems is that when i try to solve that equation numerically y->0 for a finite value of t and that has no physical meaning (the metric degenerates at a finite (>0)...
If we change the x with x=exp(-t) we have the following diff. eq.:
d2y/dt2+(1-2D1)dy/dt+D2=0
where 0<=t<=\infty.
Any hint? Do you know where this kind of eq. has been analyzed?
Ty
Solving the Einstein eq. i found the following differential eq. that would descrive the metric inside a body:
x2d2y(x)/dx2+2xD1(y)dy(x)/dx+D2(y)=0
where D1(y) and D2(y) are known function of y and 0<=x<=1.
I try to solve numerically but looks like there is a cusp; any suggestion how to...
Well "freeze time" is a) not well defined, b) impossible to test... so the answer can be "yes" or "no" and you can't verify if is right or not. So no dense.
gijeqkeij
Nope, the "why" questions can't be answered in physics. We know "how": space-time curvature generate what we feel as gravity.
gijeqkeij
Universe principles are so simple that it's almost impossible for us to understand them
Nope, the "why" questions can't be answered in physics. We know "how": space-time curvature generate what we feel as gravity.
gijeqkeij
Universe principles are so simple that it's almost impossible for us to understand them
yes, but the universe seems not to follow this way. Don't ask me why...
gijeqkeij
Universe it's so simple that it's almost impossible for us to understand it
Space and time are just 1 thing in SR and GR. If both can say "you are more distant from me" and being both right why both can't say "you are older than me" and being both right?
gijeqkeij
Universe it's so simple that it's almost impossible for us to understand it
Consider coins glued just in one point over a balloon; if you inflate the balloon what you see is the bi-dimensional view of how the universe is behaving. At least @ my understanding.
gijeqkeij
Universe it's so simple that it's almost impossible for us to understand it
Few thoughts
* mass in GR is not actually defined and mass density is an invariant but not a conserved quantity
* in SR you can imagine a frame of ref. like a grid with no limit in the extension but in SR you can't consider mass
* in GR, where heavy objects are present, you can't consider a...
Probably we say the same things in different words. Let me rephrase: you can't actually distinguish in GR between mass, energy, energy of gravitational fields. That why you can't have in GR a proper energy conservation law... so mass and energy can't be well defined in GR.
gijeqkeij
Probably I was unclear: in GR you can only speak of energy conservation and not mass conservation...and also energy conservation in my opinion is not well defined.
Yes I do have MTW; pls check page 466ff: in GR you can't localize the energy of gravitational fields... that means in general...
Pete, first of all we are now talking of energy and not only mass anymore; second Tuv;u = 0 is not a proper conservation law (that the reason for the energy pseudo-tensor and all the relevant discussion).
gijeqkeij