Mass Curving Space-Time: Equations Explained

[Martin Sallberg]

It is often said that gravity is a curvature of space-time and not a force. But since gravity is caused by mass, there must be some way in which mass curves space-time. What are the equations for how mass affect space-time?

 

[Orodruin]

Gravity is not caused by mass, it is sourced by the stress-energy tensor. This is described by Einstein's field equations.

 

[Martin Sallberg]

Gravity is not caused by mass, it is sourced by the stress-energy tensor. This is described by Einstein's field equations.

What, then are the equations for energy affecting space-time?

 

[Orodruin]

I just told you, the Einstein field equations.

 

[pervect]

What, then are the equations for energy affecting space-time?

You could try Baez's "The Meaning of Einstein's equation", http://math.ucr.edu/home/baez/einstein/, which not only gives the equations (which might not make sense without the right background) but attempts to explain them.

If you don't need the explanation,it's just $G_{\mu\nu} = \frac{8 \pi G }{c^4} T_{\mu \nu}$, where $G_{\mu\nu}$ is the Einstein tensor, which is a measure derived from the curvature of space-time, and $T_{\mu\nu}$ is the stress-energy tensor, which describes the density of momentum and energy in the space-time.

But you probabby need more explanation for this to make any sense. Hence the reference to Baez's paper..

You will need some background to understand Baez's paper, though. I have no idea what your background is. You'll especially need some understanding of special relativity before attempting a serious understanding of GR, as Baez mentions himself. Some familiarity with vectors and vector spaces would be a good idea, as well.

 

[Ibix]

You can easily google the Einstein field equations. The source term is the stress-energy tensor, $T_{ij}$, which includes terms for various things like energy and momentum. The resulting curvature is described by the Einstein tensor $G_{ij}$, sometimes written out explicitly in terms of the Ricci tensor, $R_{ij}$ and Ricci scalar $R$.

Don't be deceived by the simple form. Both indices i and j run from 0-3, making it a compact notation for sixteen simultaneous non-linear second order differential equations. Relatively few analytical solutions are known. Generally they get solved numerically.

 

[PeterDonis]

The OP's question has been answered, and references giving the same answer are easily available. Thread closed.