  A generally covariant $U(1)^3$ gauge theory describing the $G_N \to 0$ limit
of Euclidean general relativity is an interesting test laboratory for general
relativity, specially because the algebra of the Hamiltonian and diffeomorphism
constraints of this limit is isomorphic to the algebra of the corresponding
constraints in general relativity. In the present work, we study boundary
conditions and asymptotic symmetries of the $U(1)^3$ model and show that while
asymptotic spacetime translations admit well-defined generators, boosts and
rotations do not. Comparing with Euclidean general relativity, one finds that
exactly the non-Abelian part of the $SU(2)$ Gauss constraint which is absent in
the $U(1)^3$ model plays a crucial role in obtaining boost and rotation
generators.
