Scalar field probes of power-law space-time singularities

We analyse the effective potential of the scalar wave equation near genericspace-time singularities of power-law type (Szekeres-Iyer metrics) and showthat the effective potential exhibits a universal and scale invariant leadingx^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided thatthe metrics satisfy the strict Dominant Energy Condition (DEC). This resultparallels that obtained in hep-th/0403252 for probes consisting of families ofmassless particles (null geodesic deviation, a.k.a. the Penrose Limit). Thedetailed properties of the scalar wave operator depend sensitively on thenumerical coefficient of the x^{-2}-term, and as one application we show thattimelike singularities satisfying the DEC are quantum mechanically singular inthe sense of the Horowitz-Marolf (essential self-adjointness) criterion. Wealso comment on some related issues like the near-singularity behaviour of thescalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde