Recently, Alzain proposed a modified inertial formalism of modified Newtonian dynamics (MOND), wherein Galiliean invariance is violated and new Lorentz transformation properties from an inertial to an accelerated frames are posited. Milgrom’s acceleration constant is then found to be invariant under the aegis of these new space-time coordinate transformations. In this model, a modified equation of hydrostatic equilibrium is proposed, which can be applied to relaxed galaxy clusters. However, when we apply this equation to a Chandra sample of 12 clusters, we find that the total dynamical mass obtained using Alzain’s model is much smaller than the baryonic mass for almost all the clusters, thereby implying that this original model is not viable. A variant of this model with a value of \(a_0\) about two times smaller than that which fits galaxy data, is necessary in order to reconcile the missing mass problem in clusters, without the need for dark matter.

最近，Alzain提出了修改牛顿动力学（MOND）的修改惯性形式，其中违反了伽利略不变性，并且提出了从惯性到加速框架的新的洛伦兹变换性质。然后，在这些新的时空坐标转换的支持下，发现米尔格罗姆的加速度常数是不变的。在该模型中，提出了一个修正的静水力平衡方程，该方程可用于松弛星系团。但是，当我们将此方程应用于12个星团的Chandra样本时，我们发现使用Alzain模型获得的总动力学质量比几乎所有星团的重子质量小得多，从而暗示该原始模型不可行。此模型的变体，其值为\（a_0 \） 为了调和星团中丢失的质量问题而不需要暗物质，大约需要比适合星系数据的小约两倍的数据。