ydoaPs Posted May 28, 2005 Share Posted May 28, 2005 i am having a difficult time locating the GR equations for gravity with x amount of mass energy. could someone post them please? Link to comment Share on other sites More sharing options...
Johnny5 Posted May 28, 2005 Share Posted May 28, 2005 i am having a difficult time locating the GR equations for gravity with x amount of mass energy. could someone post them please? All i remember is this: [math] G_{\mu}_{\nu} = \frac{8 \pi G}{c^4} T_{\mu}_{\nu} [/math] The LHS is the einstein tensor, and the RHS is a constant (whose units are inverse force) and T is the stress-energy tensor. Also, the Einstein tensor can be written in terms of the Ricci tensor and the Ricci scalar, as follows: [math] G_{\mu}_{\nu} = R_{\mu}_{\nu} - \frac{R}{4}g_{\mu}_{\nu} [/math] R mu nu is the Ricci tensor, R is the Ricci scalar, and g mu nu is the metric tensor. Someone else can be more specific. But the answer lies in the meaning of the stress tensor. And I don't understand it yet. But at least this post might get an answer for you started. Regards Link to comment Share on other sites More sharing options...
□h=-16πT Posted May 29, 2005 Share Posted May 29, 2005 See above for equation. The stress-energy tensor is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity. Google Einstein's field equations. Sorry about the accidental mass posting. Link to comment Share on other sites More sharing options...
□h=-16πT Posted May 29, 2005 Share Posted May 29, 2005 'Damn 'tex. Here's Einstein's field equations in component form <html>G<sub>αβ</sub>=8πT<sub>αβ</sub></html> The stress-energy tensor is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity. Link to comment Share on other sites More sharing options...
□h=-16πT Posted May 29, 2005 Share Posted May 29, 2005 'Damn 'tex. G=8G(pi)T The stress-energy tensor (T) is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity. Link to comment Share on other sites More sharing options...
□h=-16πT Posted May 29, 2005 Share Posted May 29, 2005 'Damn 'tex. G=8G(pi)T The stress-energy tensor (T) is a frame invariant form of representing the dynamics of a system: energy density, energy flux, momentum flux and momentum density. In GR the whole of the stress energy tensor is responsible for causing the field, rather than just the mass density as it is in Newtonian gravity. Just do a google search for einstein's field equations. Link to comment Share on other sites More sharing options...
□h=-16πT Posted May 30, 2005 Share Posted May 30, 2005 Johnny5, the Einstein tensor has the coefficient of the ricci scalar and metric as a half not a quarter. [math] G^{\alpha\beta}=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R[/math] Link to comment Share on other sites More sharing options...
Johnny5 Posted May 31, 2005 Share Posted May 31, 2005 Johnny5' date=' the Einstein tensor has the coefficient of the ricci scalar and metric as a half not a quarter. [math'] G^{\alpha\beta}=R^{\alpha\beta}-\frac{1}{2}g^{\alpha\beta}R[/math] Ok thank you. We can get back to working on GR whenever you'd like. I'd like to learn it, regardless of whether or not i think its correct, because I now find myself wanting to learn tensor calculus for reasons that have nothing to do with GR. Specifically, i am trying to learn about quaternions, and how to use them to derive rotation matrices. I am also trying to understand Foucalt's pendulum, coriolis force, as well as the mathematics of gyroscopes, including the parallel axis theorem. While trying to learn about those things, i discovered that Hamilton was the one who coined the term 'tensor,' and he had nothing to do with Ricci, or the invention of the Ricci calculus, which is now apparently called "tensor analysis" due to Einstein. So there is some confusing stuff going on. Nevertheless, apparently Hamilton broke up quaternions into two parts, one part called a tensor, and the other part was either a vector, or a versor or a scalar. Not sure yet. But my linear algebra is good enough to use it. Anything I don't happen to recall, only takes a moment to look up. Regards PS: I am perfectly content to continue the discussion in the other thread, where revprez was involved, but whenever you're ready. Link to comment Share on other sites More sharing options...
□h=-16πT Posted May 31, 2005 Share Posted May 31, 2005 I don't mind when we continue. Just post in that thread when you want to start again and if there's anything you've been wondering about etc. I've only read about quaternions up to the ol' "Brougham Bridge" equations really, not bothered really going into them, I have too much other stuff on the go. I don't know much about mathematics history, bit more interested in the mathematics itself. The 1/2 is important because it means that the einstein tensor obeys the Bianchi identities and hence conserves local energy and momentum. Link to comment Share on other sites More sharing options...
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