An expression for mass of a spherically symmetric system is obtained by solving the Tolman–Oppenheimer–Volkoff equation, employing the homotopy perturbation method. With the help of this expression and the Einstein field equations, a set of interior solutions is arrived at. Thereafter, different aspects of the solution are explained as regards mass, density, pressure, energy, stability, mass–radius ratio, compactness factor and surface redshift. This analysis shows that all the physical properties, in connection to brown dwarf stars, are valid with the observed features.

中文翻译：

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同伦摄动法下理想流体的解析辐射模型

通过使用同伦扰动方法求解Tolman–Oppenheimer–Volkoff方程，可以获得球对称系统的质量表达式。借助该表达式和爱因斯坦场方程，得出了一组内部解。此后，从质量，密度，压力，能量，稳定性，质量半径比，致密性因子和表面红移方面解释了溶液的不同方面。该分析表明，与棕色矮星相关的所有物理性质对观察到的特征都是有效的。