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

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