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Raychaudhuri equation in Jacobson's paper (gr-qc/9504004) ?

  1. May 18, 2010 #1
    In Jacobson's famous paper "Thermodynamics of Spacetime: The Einstein Equation of State" (gr-qc/9504004) Phys. Rev. Lett. 75, 1260–1263 (1995) , he wrote the Raychaudhuri equation as (Eq.(4) in his paper):


    However, in General Relativity textbooks, Raychaudhuri equation is written as: (for example, Eq.(9.2.32) in Wald's GR book)


    Why is the term [tex]\hat{\omega}_{ab}\hat{\omega}^{ab}[/tex] missing in Jacobson's paper, or is it equal to Zero?
  2. jcsd
  3. May 18, 2010 #2


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    How are \sigma and \hat{\sigma} defined?
  4. May 18, 2010 #3

    George Jones

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    The link to the paper is


    Because a lightlike vector is orthogonal to itself, the null generators of the horizon are orthogonal to the horizon (hypersurface orhtogonal), and thus, by Frobenius' theorem, the vorticity tensor vanishes.
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