Recent content by Igorr

I agree, SR space-time is flat and the shapes of worldlines are understood modulo Poincare transform, while in GR the worldlines and metric are modulo diffeomorphisms; that's why it's more difficult to interpret them. I just try to adopt a practical point of view, common in celestial mechanics...

Correction: ##p^{\mu}## above are not completely independent variables. They are restricted by continuity condition ##p^{\mu}_{,\ \mu}=0##, where comma denotes derivative w.r.t. ##x^{\mu}##. This condition is denoted by Dirac as "conservation of matter" and it is not identical with continuity...

Please tell me am I right: In Newtonian mechnics as well as in special relativity one can perform observations of a body motion from a distant point, then reconstruct the motion in the form of worldline x(t). In GR one can reconstruct a worldline only upto diffeomorphisms of surrounding...

For those who has doubts on using delta functions in PDEs, the above cited Dirac's lectures have an expression for the action of continuously distributed matter coupled to gravitation: ##\Delta A = -\int d^{4}x \sqrt{p^{\mu}p_{\mu}}## where ##p^{\mu}=\rho v^{\mu}\sqrt{-det~g}##, ##\rho## is...

OK, this is a good example, a binary pulsar, whose trajectories are studied by an observer from a large distance. The purpose is to compare GR solution with the observed trajectory and also with Newtonian approximation to the same problem. GR solution is defined upto arbitrary diffeomorphisms...

I have a generic question on solution procedure. Suppose I consider a system of several point-like bodies interacting only via gravitation. I formulate PDE+ODE system, containing EFE and geodesic motion of the bodies. Since EFE do not define metric uniquely, I need to impose a particular...

@dextercioby: ##\sqrt{a^{2}+b^{2}}##, thank you!

@PeterDonis: First, I said what x is. Second, it seems now that you don't understand the matter, saying that there is only one variable with respect to which the action is being varied, the metric. At least, in Dirac's lectures the action is varied w.r.t. all variables entering in it. Third, I...

It sounds like you are not permitting me doing this :) OK, look: ΔA=∫ dτ √(x'μ gμν x'ν), x=c0+c1τ I have fixed the worldline to a straight line. The result is still a functional of metric, which I can variate to find stationary point of action (w.r.t. metric). So I'm puzzled why I cannot do...

There is a proof in P.A.M.Dirac, General Theory Of Relativity, Florida State University 1975, Chap.25 that continuity equation on stress-energy tensor is equivalent to (1) conservation of mass and (2) motion of matter along geodesics. Of course, this is for the case when the matter is involved...

Action depends on the metric (g) and the worldline (x). Normally one finds stationary point w.r.t. both, variation w.r.t. g gives EFE, variation w.r.t. x gives the shape of the worldline. One can also, for the purpose of mathematical exercise, fix g and find the shape of the worldline in the...

Thank you, guys! @PeterDonis: Physically, one cannot fix the worldline without adding external force and corresponding material term into eqs. Mathematically, one can fix the worldline in the action and ask what is the stationary point of this functional. The purpose is to understand the role...

Hello, can somebody please help me understanding the following. Action of general relativity consists of two terms: action of gravitation, dependent on metric tensor and its derivatives; action of matter, say one freely moving point mass particle, dependent on particle coordinates and metric...