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arXiv · 0910.4756

The Volume of the Past Light-Cone and the Paneitz Operator

Sohyun Park·R. P. Woodard
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Abstract

We study a conjecture involving the invariant volume of the past light-cone from an arbitrary observation point back to a fixed initial value surface. The conjecture is that a 4th order differential operator which occurs in the theory of conformal anomalies gives $8\pi$ when acted upon the invariant volume of the past light-cone. We show that an extended version of the conjecture is valid for an arbitrary homogeneous and isotropic geometry. First order perturbation theory about flat spacetime reveals a violation of the conjecture which, however, vanishes for any vacuum solution of the Einstein equation. These results may be significant for constructing quantum gravitational observables, for quantifying the back-reaction on spacetime expansion and for alternate gravity models which feature a timelike vector field.

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Sohyun Park, R. P. Woodard. 2009-10-25. The Volume of the Past Light-Cone and the Paneitz Operator. https://doi.org/10.1007/s10714-010-1014-4

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