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We present a theory of modified gravity, inspired by the gauge theories,where the commutator algebra of covariant derivative gives us an added termwith respect to the General Relativity, which represents the interaction ofgravity with a substratum. New spherically symmetric solutions of this theoryare obtained and can be view as solutions that reproduce, the mass, the charge,the cosmological constant and the Rindler acceleration, without coupling withthe matter content, i.e., in the vacuum.

New Black Holes Solutions in a Modified Gravity