We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The volume of the past light-cone and the Paneitz operator.
- Authors
Park, Sohyun; Woodard, R.
- 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 fourth order differential operator which occurs in the theory of conformal anomalies gives 8 π 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.
- Subjects
DIFFERENTIAL operators; INVARIANTS (Mathematics); LOGICAL prediction; ASTRONOMICAL observations; ASTRONOMICAL perturbation; GENERAL relativity (Physics); RIEMANNIAN geometry
- Publication
General Relativity & Gravitation, 2010, Vol 42, Issue 12, p2765
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-010-1014-4