(adsbygoogle = window.adsbygoogle || []).push({}); I've been wracking my brains trying to answer this but it's just really hard. If some one could help me out I would really appreciate it. Thank you so much in advanced!

Consider the family of hypersurfaces where each member is defined by the constancy of the function S(x^{c}) over that hypersurface and further require that each hypersurface be a null hypersurface in the sense that its normal vector field, n_{a}= S_{|a}be a null vector field.

Let ¡ be a member of the family of curves that pierces each such hypersurface orthogonally, meaning that the tangent vector to ¡, say k_{a}is everywhere collinear with the vector na at the point of piercing. Show that ¡ is a null geodesic and find the condition on the relation between n_{a}and k_{a}that allows the geodesic equation to be written in the simple form k_{a||b}k^{b}= 0.

Interpret your results in terms of waves and rays.

Where_{|a}denotes partial derivative with respect to a, and_{||a}denotes the covariant derivative with respect to a.

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# Tensor question about Hypersurfaces

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