In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers–Perry spacetime with equal momenta and the scalar field is identified with the Hamilton–Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers–Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers–Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity\(-1\) character of the Myers–Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity\(-1\) metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr+-de Sitter case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory.

在五个维度中，我们考虑了一个一般的平移对称和奇偶保留标量张量动作，它包含标量场的二阶协变导数。构建了一个旋转隐形黑洞解决方案，其中度量由具有相等动量的 Myers-Perry 时空给出，标量场由 Hamilton-Jacobi 势确定。这个非平凡的标量场具有与测试粒子的静止质量相关的额外头发，并且该解决方案不需要对理论的耦合函数进行任何微调。有趣的是，我们展示了由这个标量场产生的非形式变换，并且具有恒定程度的非形式性，使 Myers-Perry 度量保持不变（直到微分同胚）具有相等的动量。这意味着标量场的头发，与恒定变形参数一起，可以一致地吸收到质量和变形度量的单个角度参数的进一步重新定义中。这些结果使用 Myers-Perry 度量扩展到更高的奇数维度，其中所有动量都相等。度量非形式变换下不变性的关键主要是同质性\(-1\)具有相等动量的 Myers-Perry 度量的特征。从这个观察开始，我们考虑任意维度中的一般类同质性\(-1\)度量，我们列出了确保此类度量在具有恒定程度的非形式变换下保持不变（直至微分同胚）的条件变形和具有恒定动力学项的标量场。还考虑了对 Kerr+-de Sitter 情况的扩展，其中表明可能存在旋转隐身解决方案，前提是对标量张量理论的耦合函数进行一些微调。