论文标题
换班的黑洞
Hairy Black-holes in Shift-symmetric Theories
论文作者
论文摘要
假设具有球形对称性，标量场的时间独立性以及渐近平坦度的时间独立性，则具有移位对称性的黑洞标量头发受到Hui和Nicolis的无头发定理的约束。研究最多的反例是标量与高斯 - 骨网的线性耦合。但是，在这种情况下，换档对称电流$ j^2 $的规范在地平线上散发出对解决方案是否在物理上是合理的疑问。我们表明，这不是问题，因为$ j^2 $不是标量的数量，因为$ j^μ$在Gauss-Bonnet的存在下不是差异不变的电流。相同的理论可以用非分析函数$ g_5 \ sim \ log x $以Horndeski形式编写。在这种情况下，移位对称电流是差异不变的，但在分母中包含$ x $的功率，因此其在地平线上的差异再次是无关紧要的。我们确认，在存在非分析Horndeski功能的情况下，其他毛茸茸的解决方案是病理性的，一旦一个人与时间独立和球形对称性不同，就以物理量的分歧。我们将无毛定理推广到Horndeski和Dhost理论之外，这表明与高斯 - 骨网的耦合对于拥有头发是必要的。
Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current $J^2$ diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since $J^2$ is not a scalar quantity, since $J^μ$ is not a diff-invariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function $G_5 \sim \log X$. In this case the shift-symmetry current is diff-invariant, but contains powers of $X$ in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.
