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algebraic analysis answering appears associated background barrier that forbids basis behavior BRASILEIRO DE PESQUISAS CENTRO BRASILEIRO change classical colour compact region conditions connected consider constant constitutes containing coordinate corresponding critical radius defined definite deformation density dependence derivative described direct consequence discontinuity disturbances dynamics effective geometry eikonal Elbaz electrodynamics energy equation of motion equivalently examined example exhibit fact field theory FÍSICAS follows null form function gauge field given Gluon Confinement group Hadamard's horizon instance interaction Lagrangian massless spin-one particles Maxwell metric Minkowski null cone model modification namics necessary non-Abelian gauge theory non-linear Novello null geodesies obtain occur particular potential precisely principle proceed propagation proper property pure quantity radial related required restrict result Rio de Janeiro shows simple solution space spacetime spherically symmetric standard Yang-Mills static structure summarize surface terms travel uniquely V.A. De Lorenci vector VeJJ version Yang-Mills theory yields