Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-02-08
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
28 pages, RevTeX, 3 PostScript figures
Scientific paper
10.1016/0393-0440(95)00031-3
We reformulate the standard local equations of general relativity for asymptotically flat spacetimes in terms of two non-local quantities, the holonomy $H$ around certain closed null loops on characteristic surfaces and the light cone cut function $Z$, which describes the intersection of the future null cones from arbitrary spacetime points, with future null infinity. We obtain a set of differential equations for $H$ and $Z$ equivalent to the vacuum Einstein equations. By finding an algebraic relation between $H$ and $Z$ this set of equations is reduced to just two coupled equations: an integro-differential equation for $Z$ which yields the conformal structure of the underlying spacetime and a linear differential equation for the ``vacuum'' conformal factor. These equations, which apply to all vacuum asymptotically flat spacetimes, are however lengthy and complicated and we do not yet know of any solution generating technique. They nevertheless are amenable to an attractive perturbative scheme which has Minkowski space as a zeroth order solution.
Iyer Savitri V.
Kozameh Carlos N.
Newman Ezra Ted
No associations
LandOfFree
The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Vacuum Einstein Equations via Holonomy around Closed Loops on Characteristic Surfaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-652845