QPOs are seen as peak features in the X-ray power spectral density of stellar mass black holes and neutron stars, of which frequencies can be measured with high precision. These QPO frequencies are believed to be related to fundamental frequencies of test particles, which are mainly determined by the background metric. We consider the metric introduced in Ghasemi-Nodehi and Bambi (Eur Phys J C 76:290, 2016). The fundamental frequencies in this metric are sensitive to some of the metric parameters but insensitive to other parameters, which means, the differences in fundamental frequencies in this metric and those in the Kerr ones can be significant for small changes of some but not all parameters around the Kerr value. By comparing with the QPO observations of GRO J1655-40, we find that only one parameter of the Ghasemi-Nodehi–Bambi metric can be strongly constrained, but other parameters cannot. We also use nested algorithm to investigate whether better constraints on the Ghasemi-Nodehi–Bambi metric parameters can be obtained from QPO observations of multiple objects by simulations. We find that four parameters can be strongly constrained while other parameters cannot . Our results suggest that QPOs may be important tools for testing the Kerr metric.

QPO被视为恒星质量黑洞和中子星在X射线功率谱密度中的峰值特征，其频率可以高精度测量。这些QPO频率被认为与测试粒子的基频有关，基频主要由背景度量确定。我们考虑在Ghasemi-Nodehi和Bambi中引入的指标（Eur Phys JC 76：290，2016）。此度量标准中的基本频率对某些度量标准参数敏感，但对其他参数不敏感，这意味着，此度量标准中的基本频率与Kerr频率中的基本频率之差对于某些但并非所有参数周围的微小变化可能很重要。 Kerr值。通过与GPO J1655-40的QPO观察结果进行比较，我们发现，只有Ghasemi-Nodehi-Bambi指标的一个参数可以受到严格约束，而其他参数则不能。我们还使用嵌套算法来研究是否可以通过模拟从多个对象的QPO观测中获得对Ghasemi-Nodehi-Bambi度量参数的更好约束。我们发现，四个参数可以受到严格约束，而其他参数则不能。我们的结果表明，QPO可能是测试Kerr指标的重要工具。