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Energy-Momentum Tensor

  1. Mar 8, 2008 #1
    I was wondering if someone could clarify something that I read in a book (Nakahara's book on Geometry, Topology, Physics). In the section on the Einstein-Hilbert action, the author defines the energy-momentum tensor as
    [tex]\delta S_M = \frac{1}{2} \int T^{\mu \nu} \delta g_{\mu \nu} \sqrt{- g} d^4 x. [/tex]
    Shortly thereafter, he then writes that, "for example, [tex] T_{\mu \nu} [/tex] of a real scalar field is given by
    [tex] T_{\mu \nu} (x) = 2 \frac{1}{\sqrt{-g}} \frac{\delta}{\delta g^{\mu \nu} (x)} S_s = \cdots. [/tex]
    My question is, where did the integral over dx^4 go?
  2. jcsd
  3. Mar 8, 2008 #2


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