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.

在这项工作中，在修正引力的背景下，构建了一个类似于“经典声学黑洞（CABH）”的弯曲时空。源是一个自相互作用标量场，它通过 Gauss-Bonnet 不变量与重力非最小耦合。标量-高斯-博内耦合函数的特征在于三个正参数：σ的单位为（长度），μ的单位为（长度）⁴，以及一个无量纲的参数s，从而定义了一个三参数模型，其中线元素CABH 是一个解决方案。时空具有球对称性和静态对称性，并且具有由区域r = μ ^1/4在 Schwarzschild 坐标中确定的单一视界. 该解在r = (3 μ ) ^1/4处允许光子球，并且表明在区域 (3 μ ) ^1/4 ⩽ r < ∞ 中，标量场满足零、弱和强能量条件。尽管如此，s = 1的模型具有重要的物理相关性，因为在这种情况下，标量场在整个区域r ⩾ μ ^{1/4 中}被很好地定义，而对于s ≠ 1，标量场在地平线上爆炸。