 
Summary: Nuclear Physics B296 (1988) 710716
NorthHolland, Amsterdam
INTEGRAL CONSTRAINTS IN GENERAL RELATIVITY
L.F. ABBOTT*
Departmentof Physics,Boston University,Boston,MA 02215t, USA
J. TRASCHEN*
DepartmentofAstronomyandAstrophysics, Universityof Chicago, Chicago,IL 60633, USA
RuiMing XU
Departmentof Physics, BrandeisUniversity, Waltham,MA 02254, USA
Received July 1987
Using a covariant formalism we derive the conditions for there to exist integral constraints on
energymomentum perturbations in an arbitrary background spacetime.
A conserved quantity corresponding to an asymptotic symmetry of an otherwise
arbitrary spacetime manifold can be constructed in general relativity provided that a
number of conditions are met. If we write the spacetime metric in the form
&,~ = g~. + h~,, where h~,~ vanishes (sufficiently rapidly) at infinity but is otherwise
arbitrary, then the background asymptotic metric g~,~ must satisfy the Einstein
equations with no energymomentum source term,
R~  ½~"R = 0, (1)
where R~" and R are the Ricci tensor and scalar curvature corresponding to ~,.. In
