标题： 四维爱因斯坦-高斯-博内引力标量-张量形式中的黑洞：解的唯一性及暗物质的新候选者 显示英文标题

标题： Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter

摘要： 在这项工作中，我们研究了正则化的四维爱因斯坦-高斯-博内引力理论中的静态黑洞；这是一种属于霍恩德斯基因类的偏移对称标量张量理论。该理论具有一种简单的黑洞解，可以以封闭形式写出，并且我们证明它是该理论唯一的静态、球对称和渐近平坦的黑洞真空解。我们进一步表明，不允许这种几何结构存在渐近平坦、时间相关的、球对称的扰动，这表明它可能是该理论唯一允许的球对称真空解（一个类似于比尔科夫定理的结果）。最后，我们考虑了这些黑洞的热力学性质，并发现它们蒸发后的最终状态是一个由理论耦合常数决定大小的残余物。我们推测，这类来自原始黑洞的残余物可能充当暗物质，并且我们限制了它们形成质量以及理论耦合常数的参数空间。 显示英文摘要

摘要： In this work we study static black holes in the regularized 4D Einstein-Gauss-Bonnet theory of gravity; a shift-symmetric scalar-tensor theory that belongs to the Horndeski class. This theory features a simple black hole solution that can be written in closed form, and which we show is the unique static, spherically-symmetric and asymptotically-flat black hole vacuum solution of the theory. We further show that no asymptotically-flat, time-dependent, spherically-symmetric perturbations to this geometry are allowed, which suggests that it may be the only spherically-symmetric vacuum solution that this theory admits (a result analogous to Birkhoff's theorem). Finally, we consider the thermodynamic properties of these black holes, and find that their final state after evaporation is a remnant with a size determined by the coupling constant of the theory. We speculate that remnants of this kind from primordial black holes could act as dark matter, and we constrain the parameter space for their formation mass, as well as the coupling constant of the theory.