Since the recent derivation of a well-defined D -> 4 limit for 4D
Gauss-Bonnet (4DGB) gravity, there has been considerable interest in testing it
as an alternative to Einstein’s general theory of relativity. In this paper, we
construct slowly rotating black hole solutions for 4DGB gravity in
asymptotically flat, de Sitter, and anti-de Sitter spacetimes. At leading order
in the rotation parameter, exact solutions of the metric functions are derived
and studied for all three of these cases. We compare how physical properties
(innermost stable circular orbits, photon rings, black hole shadow, etc.) of
the solutions are modified by varying coupling strengths of the 4DGB theory
relative to standard Einstein gravity results. We find that a vanishing or
negative cosmological constant in 4DGB gravity enforces a minimum mass on the
black hole solutions, whereas a positive cosmological constant enforces both a
minimum and maximum mass with a horizon root structure directly analogous to
the Reissner-Nordstrom de Sitter spacetime. Besides this, many of the physical
properties are similar to general relativity, with the greatest deviations
typically being found in the low (near-minimal) mass regime.
