Mass Curving Space-Time: Equations Explained

In summary, "Mass Curving Space-Time" is a concept in Einstein's theory of General Relativity where massive objects can cause the fabric of space-time to curve, affecting the motion of other objects around them. It is related to gravity as it is the result of the curvature of space-time caused by massive objects. The equations that explain this concept are the Einstein Field Equations, and it affects the motion of objects by causing them to follow curved paths. "Mass Curving Space-Time" can be observed and measured through experiments and observations, providing evidence for Einstein's theory of General Relativity.
  • #1
Martin Sallberg
20
0
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?
 
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  • #2
Gravity is not caused by mass, it is sourced by the stress-energy tensor. This is described by Einstein's field equations.
 
  • #3
Orodruin said:
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?
 
  • #4
I just told you, the Einstein field equations.
 
  • #5
Martin Sallberg said:
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.
 
  • #6
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.
 
  • #7
The OP's question has been answered, and references giving the same answer are easily available. Thread closed.
 

1. What is "Mass Curving Space-Time"?

"Mass Curving Space-Time" refers to the concept in Einstein's theory of General Relativity, where massive objects such as planets and stars can cause the fabric of space-time to curve, affecting the motion of other objects around them.

2. How is "Mass Curving Space-Time" related to gravity?

In Einstein's theory of General Relativity, gravity is not a force between objects, but rather the result of the curvature of space-time caused by massive objects. This means that the more massive an object is, the more it curves space-time and the stronger its gravitational pull.

3. What are the equations that explain "Mass Curving Space-Time"?

The equations that explain "Mass Curving Space-Time" are the Einstein Field Equations, which relate the curvature of space-time to the distribution of matter and energy in the universe. They are a set of ten equations that form the basis of Einstein's theory of General Relativity.

4. How does "Mass Curving Space-Time" affect the motion of objects?

"Mass Curving Space-Time" affects the motion of objects by causing them to follow curved paths around massive objects, rather than traveling in straight lines. This is because the objects are following the natural curvature of space-time caused by the massive object's presence.

5. Can "Mass Curving Space-Time" be observed or measured?

Yes, "Mass Curving Space-Time" has been observed and measured through various experiments and observations, such as the bending of starlight around massive objects and the detection of gravitational waves. These observations have provided evidence for the existence of "Mass Curving Space-Time" and Einstein's theory of General Relativity.

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