  In this manuscript, we show that the external Schwarzschild metric can be a
good approximation of exact black hole solutions of entangled relativity. Since
entangled relativity cannot be defined from vacuum, the demonstrations need to
rely on the definition of matter fields. The electromagnetic field being the
easiest (and perhaps the only) existing matter field with infinite range to
consider, we study the case of a charged black hole -- for which the solution
of entangled relativity and a dilaton theory agree -- as well as the case of a
pure radiation -- for which the solution of entangled relativity and general
relativity seem to agree, despite an apparent ambiguity in the field equations.
Based on these results, we argue that the external Schwarzschild metric is an
appropriate mathematical idealization of a spherical black hole in entangled
relativity. The extension to rotating cases is briefly discussed.
