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location United Kingdom
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visits member for 3 years, 11 months
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Studied physics and maths at school many years ago.


May
5
comment Zero divergence of energy-momentum tensor and gravitational energy
in some way from the rhs, hence my confusion. I didn't know that (as you say) “the curvature of spacetime is ONLY dictated by the density of the non-gravitational energy density T or EMT”. So, thankfully, all the calculations I've struggled through re Schwarzschild and cosmology are still valid because only the EMT (and not gravitational energy) curves spacetime? I'm still puzzled about why zero divergence of the rhs (the EMT) doesn't imply the conservation of energy and momentum. If you put the Einstein tensor on the rhs (ie, the lhs equals zero), would the zero divergence
May
5
comment Zero divergence of energy-momentum tensor and gravitational energy
Oh dear. I think I've got this seriously wrong. Please bear with me. I thought the rhs of the field equations (ie the EMT) described the total energy-momentum of a system (which I think is correct). I thought the lhs was a description of the curvature of spacetime caused by the rhs (which I think also is correct). But I never thought of the lhs as describing gravitational energy. (Thinking about it, both sides must of course have the same units, so if the rhs describes energy so must the lhs). I thought that the “additional source of energy”, ie gravitational energy, was missing
May
5
comment Zero divergence of energy-momentum tensor and gravitational energy
thanks. I did try to read the link but it was a little over my head (my level - I've no idea what Hamiltonians or Lagrangians are!). I've been trying to understand the Schwarzshild metric and relativistic cosmology both of which are based on a particular energy-momentum tensor (zero and perfect fluid). I still don't see how that can be valid if the EMT doesn't include gravitational energy. I sense you answering my question in your final paragraph ("very-long-distance effective description") but, sorry, don't understand. Please don't worry about making your answer too simple!
May
5
asked Zero divergence of energy-momentum tensor and gravitational energy
Apr
26
accepted Confusion regarding geodesic of thrown ball - curved or Cartesian coordinates?
Apr
26
comment Confusion regarding geodesic of thrown ball - curved or Cartesian coordinates?
Thank you, though I find your first sentence a little ambiguous. Are you saying it's a valid approximation to plot the ball's path using Cartesian coordinates because (1) it's moving relatively slowly and/or (2) is in a weak gravitational field and/or (3) is not being thrown very far? So if I was throwing the ball at a velocity near the speed of light on the surface of a neutron star, for example, I couldn't plot its path using Cartesian coordinates but would need to take into account spacetime curvature and use curved coordinates - whatever they are?
Apr
25
asked Confusion regarding geodesic of thrown ball - curved or Cartesian coordinates?
Apr
25
comment Why do objects follow geodesics in spacetime?
Thanks for the replies, though I'm afraid they are way over my head. I still don't get it.
Apr
24
comment Why do objects follow geodesics in spacetime?
@David Zaslavsky Both, but of course I can't promise I'll understand the mathematical one.
Apr
24
asked Why do objects follow geodesics in spacetime?
Apr
8
accepted Hubble time, the age of the Universe and expansion rate
Apr
8
comment Hubble time, the age of the Universe and expansion rate
thanks very much.
Apr
7
asked Hubble time, the age of the Universe and expansion rate
Apr
7
comment How does the critical density decide the fate of the Universe?
of course! Funny how some things are obvious when they're pointed out. I was getting the strangest results trying to feed my equation into the WolframAlpha differential equation calculator. Thanks.
Apr
7
accepted How does the critical density decide the fate of the Universe?
Apr
6
comment How does the critical density decide the fate of the Universe?
thanks. Ryden uses parametric equations to get her big bang to big crunch graph of a matter only universe on p87. Just out of interest, do you know why I can't set the first term on the rhs of the Friedmann equation to a constant $C$, $k=+1$, $c=1$ to obtain $$\left[\frac{1}{R}\frac{dR}{dt}\right]^{2}=C-\frac{1}{R^{2}}$$ $$\frac{dR}{dt}=\left(R^{2}-1\right)^{1/2}$$ but when I try to solve this, I don't get the nice Big Bang to Big Crunch graph that Ryden does?
Apr
5
asked How does the critical density decide the fate of the Universe?
Apr
3
comment Very basic question about empty universe
Thanks for that. I looked at the paper - superluminal galaxies are not travelling faster than light in our or any other observer's inertial frame so don't contradict STR. That is amazing.
Apr
3
accepted Very basic question about empty universe
Apr
2
revised Very basic question about empty universe
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