I am trying to use the Israel junction conditions for a null surface, but I am running into complications with defining a normal vector for a null surface.(adsbygoogle = window.adsbygoogle || []).push({});

As I understand it the normal vector is defined to be perpendicular to the surfaces tangent vectors [itex]n\cdot e_i=0[/itex], as well as satisfying [itex]n\cdot n=0[/itex].

However, this does not fix [itex]n[/itex] completely, it can still be rescaled by an overall factor (as opposed to the case for a time like surface where this is fixed by the normalization [itex]n\cdot n=1[/itex]). Is this correct? Or is there another convenient constraint one should impose as well to fix it completely?

The issue is then that when I try to use it in the junction formalism my result seems to depend on this overall arbitrary normalization. (see eg http://iopscience.iop.org/0264-9381/14/5/029/pdf/q70520.pdf , equation (5) )

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# Normal to a null surface

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