Equation for how much an object curves space-time

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The discussion centers on the equation for how much an object curves space-time, with the initial reference to Newton's law of gravitation, F=Gm1m2/r^2, being deemed insufficient for this purpose. The correct framework is provided by the Einstein Field Equations, which relate the stress-energy tensor to the Einstein Tensor, indicating how energy affects space-time curvature. For those seeking to understand this topic better, several recommended resources include introductory textbooks and popular science books by experts in the field. Caution is advised against relying solely on Wikipedia for scientific learning. Overall, a solid grasp of general relativity and its mathematical foundations is essential for understanding space-time curvature.
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hey guys, I asked my( well she's not mine since i don't take physics yet)physics tacher if there is an equation to find out how much a body can curve space-time, but she gave me f=Gm1m2/r^2. But I'm pretty sure that's not it. I know that the equation is not linear. Could one of you guys who knows about this help clarify this?
 
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That is the equation for Newtonian gravity, which is correct for many situations. Only when things are very dense of moving very quickly does that not work.

The full set of equations (at least as far as we know) are called the Einstein Field Equations.

Without going into the full mathematical detail, this set of equations equates the 'stress-energy tensor' which describes the energy present in the situation you're dealing with, and the Einstein Tensor. The Einstein Tensor is actually a function of something called the metric, and it is the metric that tells you how much space-time is curved. So for a given distribution of energy, the field equations are solved to find the metric for which the Einstein Tensor equals the Stress Energy Tensor (I hope that made sense!).

Some folk around here caution against using Wikipedia to learn science, for good reason, however the Wiki entry for the Einstein Field Equation isn't terrible, so you could have a read of that.

A better option would be to try a textbook. I reccomend 'Gravity' by James Hartle but there are plenty of other introductory Relativity textbooks that may also be useful.
 
thank you very much
 
Recommend some good popular books

I agree with Wallace, except that if you, rubecuber, haven't taken a lot of college physics, I'd recommend instead a popular book by an expert, such as Geroch, General Relativity from A to B, Wald, Space, Time, and Gravity, or Thorne, Black Holes and Time Warps, all of which are excellent. For advanced undergraduate physics majors, the textbooks by Hartle, Carroll, Schutz, D'Inverno, Stephani, OHanian and Ruffini, would all be excellent choices (there are still more which would not be bad, but these would all be particularly good first textbooks, I think).
 
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