Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I What are the equations of mass distorting space-time?

  1. May 2, 2017 #1
    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?
     
  2. jcsd
  3. May 2, 2017 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Gravity is not caused by mass, it is sourced by the stress-energy tensor. This is described by Einstein's field equations.
     
  4. May 2, 2017 #3
    What, then are the equations for energy affecting space-time?
     
  5. May 2, 2017 #4

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I just told you, the Einstein field equations.
     
  6. May 2, 2017 #5

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
  7. May 2, 2017 #6

    Ibix

    User Avatar
    Science Advisor

    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.
     
  8. May 3, 2017 #7

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    The OP's question has been answered, and references giving the same answer are easily available. Thread closed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What are the equations of mass distorting space-time?
Loading...