Abstract
An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry has typically been assumed. However, the existence of electric and gravitational line operators, arising from gaugeinvariant dressed observables, for example associated to axial or Fefferman-Graham like gauges, indicates the existence of non-antipodally symmetric initial data. This note studies aspects of the solutions corresponding to such non-symmetric initial data. The explicit evolution can be found, via a Green function, and bounds can be given on the asymptotic behavior of such solutions, evading arguments for singular behavior. Likewise, objections to such solutions based on infinite symplectic form are also avoided, although these solutions may be superselected. Soft charge conservation laws, and their modification, are briefly examined for such solutions. This discussion strengthens (though is not necessary for) arguments that soft charges characterize gauge field degrees of freedom, but not necessarily the degrees of freedom associated to the matter sourcing the field.
Highlights
An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity
This has played a role in discussions of soft charges, where antipodal symmetry has typically been assumed
The explicit evolution can be found, via a Green function, and bounds can be given on the asymptotic behavior of such solutions, evading arguments for singular behavior
Summary
Most of the discussion of the present paper will be given for EM, based on previous work [17, 18] much of this analysis is expected to have a straightforward gravitational extension. This field configuration is somewhat singular, and in particular has infinite energy. The field configuration (2.5) has the same behavior as Coulomb, and in particular the same energy density, near the origin. With finite energy initial data, corresponding to an EM field that disperses to infinity, we might expect regular evolution. This seems at odds with claims [5,6,7,8, 16] of singular behavior at I+. A Green’s theorem argument gives the electric field for t > 0, Ei(x) = −∂t d3x′ These expressions are consistent with a gauge potential in radiation gauge, given by. Given such explicit formulas for the solution of the EM field equations, the asymptotics are readily explored
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
