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Nuclear Physics B296 (1988) 710-716 North-Holland, Amsterdam
 

Summary: Nuclear Physics B296 (1988) 710-716
North-Holland, 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
Rui-Ming 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
energy-momentum 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 energy-momentum source term,
R~ - ~"R = 0, (1)
where R~" and R are the Ricci tensor and scalar curvature corresponding to ~,.. In

  

Source: Abbott, Laurence - Center for Neurobiology and Behavior & Department of Physiology and Cellular Biophysics, Columbia University

 

Collections: Biology and Medicine