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

General metric and flat metric

  1. Jun 25, 2015 #1
    What is the difference between General metric gαβ and flat metric ηβα in GR?
    Elaborate answers are appreciated.
     
  2. jcsd
  3. Jun 25, 2015 #2

    Nugatory

    User Avatar

    Staff: Mentor

    The metric tensor describes the geometry of spacetime in a coordinate-independent way. One very important special case is the metric tensor that describes a flat (no significant gravitational effects) spacetime; the ##\nu_{\alpha\beta}## that you're calling the "flat metric" are the components of that metric tensor written in Minkowski coordinates. You could use a different set of coordinates (Rindler or spherical or...) and the components would come out looking completely different, but it would still be the same flat spacetime.
     
  4. Jun 25, 2015 #3
    I do understand that the metric tensor used in provides independence from a particular coordinate system. But this still doesn't answer my question about the difference between general and flat metric clearly.Sorry sir.
     
  5. Jun 26, 2015 #4

    Nugatory

    User Avatar

    Staff: Mentor

    Your question is a bit like asking for the difference between an elephant and animal: all elephants are animals but not all animals are elephants.

    If there exists a coordinate system in which the metric for a given spacetime takes the form ##diag(-1,1,1,1)## then the spacetime is flat; if not, then it's not.
     
  6. Jun 26, 2015 #5

    Ibix

    User Avatar
    Science Advisor

    It's kind of like F=ma and F=mg. g is just an acceleration, but we give it a special symbol because it's a particular case of an acceleration that we use a lot.

    Similarly, [itex]\eta_{\mu\nu}[/itex] is just a metric tensor. It does everything any other metric tensor does. It's just that it describes a case of particular interest, the one where there is no gravity, or where gravity can be neglected.

    That analogy is a bit strained. but the best I can think of.
     
  7. Jun 26, 2015 #6

    Dale

    Staff: Mentor

    The flat metric has 0 curvature. The general metric may not have 0 curvature.

    Sorry that is not very elaborate, but the difference doesn't seem to require much elaboration.
     
    Last edited: Jun 26, 2015
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook