Landau-Raychaudhuri Equation: History & Study

[victorneto]

Friends,

I am studying the Raychaudhuri Equation. But Landau also deduced this equation, in independent way. What necessary to know it is: in which Landau workmanship made the study that resulted in today known as Landau-Raychaudhuri Equation?

I thank since already any information the respect.
They forgive me the English. I am Brazilian and I do not write very in English.

Victorneto.

 

[George Jones]

From

http://www.ias.ac.in/pramana/v69/p49/fulltext.pdf

The Raychaudhuri equation is sometimes referred to as the Landau–Raychaudhuri equation. It may be worthwhile to point out precisely, the work of Landau, in relation to this equation. Landau’s contribution appears in his treatise The Classical Theory of Fields [10] and is also discussed in detail in [6,11]. ... where γ is the determinant of the 3-metric ... While deriving the inequality, Landau implicitly assumes the strong energy condition (though it is not mentioned with this name). Then, using it, he is able to show that γ must necessarily go to zero within a finite time. However, he mentions quite clearly that this does not imply the existence of a physical singularity in the sense of curvature. Though Landau’s work captures the essence of focusing, he does not explicitly mention geodesic focusing. Moreover, he does not introduce shear and rotation or write down the complete equation for the expansion.

 

[victorneto]

Dear George,

Thanks a lot for the useful return.

Yours truly,

Victor.