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” 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: $\sigma$ with units of $(length)$, $\mu$ with units of $(length{)}^4$, and a dimensionless parameter $s$, thus defining a three-parameter model for which the line element of canonical acoustic black hole is a solution. The spacetime is equipped with spherical and static symmetry and has a single horizon determined in Schwarzschild coordinates by the region $r={\mu }^{1\mathrm{/}4}$. The solution admits a photon sphere at $r=(3\mu {)}^{1\mathrm{/}4}$, and it is shown that in the region $(3\mu {)}^{1\mathrm{/}4}\le r<\mathrm{\infty }$ 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 $r\ge {\mu }^{1\mathrm{/}4}$, while for $s\mathrm{\ne }1$ the scalar field blows up on the horizon.