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):(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d\theta}{d\lambda}=-\frac{1}{2}\theta^{2}-\sigma^{2}-R_{ab}k^{a}k^{b}[/tex]

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

[tex]\frac{d\theta}{d\lambda}=-\frac{1}{2}\theta^{2}-\hat{\sigma}_{ab}\hat{\sigma}^{ab}+\hat{\omega}_{ab}\hat{\omega}^{ab}-R_{cd}k^{c}k^{d}[/tex]

Why is the term [tex]\hat{\omega}_{ab}\hat{\omega}^{ab}[/tex] missing in Jacobson's paper, or is it equal toZero?

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

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