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General Relativity

  1. Jan 24, 2007 #1
    Is it accurate to claim that space-time curvature in general relativity means a curvature of a space-time with a Minkowski pseudo-metric?
  2. jcsd
  3. Jan 25, 2007 #2
    Locally, and with the right coodinates.
  4. Jan 25, 2007 #3


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    That doesn't sound right.

    I'd suggest saying that SR is done with a Minkowskian metric, while GR has a more general space-time with a Lorentzian metric.

    The flat Minkowskian metric is a special case of the more general Lorentzian metric (whcih is not necessarily flat).

    A manifold with either a Lorentzian or Minkowskian metric is a pseudo-Riemannian manifold because the metric tensor is not positive definte (those pesky minus signs).
  5. Jan 25, 2007 #4
    Ok, that definition makes sense.

    Right, and so can we take a collection of local Lorentzian patches and form a curved space-time, which is thus as agreed upon also Lorentzian, and with maintaining a causal connection?

    In other words, is "bending" a space with a Lorentzian metric unproblematic in terms of extending the causal structures?
  6. Jan 25, 2007 #5
    A principal assumption of general relativity is that spacetime can be modeled as a Lorentzian manifold of signature (3,1).
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