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arXiv · hep-th/0312029

Penrose Limits and Spacetime Singularities

Matthias Blau·Monica Borunda·Martin O'Loughlin·George Papadopoulos
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Abstract

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.

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Matthias Blau, Monica Borunda, Martin O'Loughlin, George Papadopoulos. 2003-12-14. Penrose Limits and Spacetime Singularities. https://doi.org/10.1088/0264-9381%2F21%2F7%2Fl02

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