Expansion of a trapped surface - clarification needed

[TomCurious]

Homework Statement

I was just reading this article on the arXiv: http://arxiv.org/abs/0711.0313 , which discusses trapped surfaces and black holes.
There is a simple qualm I have, though, but it is persistent, and I cannot seem to come to terms with it.

Looking at equation's (1) and (2) of the document, we find (forgive me, I do not know latex:

Expansion along n = metric dually contracted with covariant derivative of one null vector +n*l*covariant derivative of n + l*n*covariant derivative of n,

where n and l are the two null vectors which are normal to the trapped surface.

Homework Equations

On the surface, we can reconstruct the metric as Qab = Gab + NaLa
(taken from Eric Poisson's book)

Expansion can easily be defined as the derivative of the cross-sectional area of the geodesic congruence, divided by the area. Going infinitesimal, and using some Differential Geometry, this is equivalent to the surface metric (Qab) fully contracted with the covariant derivative of one of null vectors.

The Attempt at a Solution

Perhaps the error lies in the definition, that is to say, Qab = Gab + NaLa + LaNa ? It is a fine point, but one that I cannot seem to find the answer to.

 

[George Jones]

On the surface, we can reconstruct the metric as Qab = Gab + NaLa
(taken from Eric Poisson's book)

Where is this in Poisson's book?

Perhaps the error lies in the definition, that is to say, Qab = Gab + NaLa + LaNa ?

See equation (2.28) from (the hard-copy version of) Poisson's book.

 

[TomCurious]

Oh, I see. Thank you very much! I was looking at equation (2.14) - my bad!