Gravitational analog of the canonical acoustic black hole in Einstein-scalar-Gauss-Bonnet theory
In this work, in the context of modified gravity, a curved spacetime analogous to the 'canonical acoustic black hole (CABH)' is constructed. The source is a self-interacting scalar field which is non-minimally coupled to gravity through the Gauss–Bonnet invariant. The scalar-Gauss–Bonnet coupling function is characterized by three positive parameters: σ with units of (length), μ with units of (length)4, and a dimensionless parameter s, thus defining a three-parameter model for which the line element of CABH is a solution. The spacetime is equipped with spherical and static symmetry and has a single horizon determined in Schwarzschild coordinates by the region r = μ^(1/4). The solution admits a photon sphere at r = (3μ)^(1/4), and it is shown that in the region (3μ)^(1/4) ⩽ r < ∞ the scalar field satisfies the null, weak, and strong energy conditions. Nonetheless, the model with s = 1 has major physical relevance since for this case the scalar field is well defined in the entire region r ⩾ μ^(1/4), while for s ≠ 1 the scalar field blows up on the horizon.