This paper investigates the dynamics of spherical collapse in the framework of energy–momentum squared gravity. This theory overcomes the big-bang singularity and provides viable cosmological consequences in the early time universe. We proceed our work by considering the nonstatic spherically symmetric space–time in the interior and static spherically symmetric metric in the exterior regions of the star. The Darmois junction conditions between interior and exterior geometries are derived. We construct dynamical equations through the Misner–Sharp technique to analyze the impact of matter variables and dark source terms on the collapsing phenomenon. A correlation among dark source terms, Weyl scalar and matter variables is also established. Due to the presence of multivariate function and its derivatives, space–time is no longer considered to be conformally flat. To obtain conformally flat space–time, we have considered a particular model of this gravity which yields conformally flat space–time and homogeneity of the energy density through the entire system. We conclude that positive dark source terms as well as negative pressure gradient provide the anti-gravitational behavior leading to the stability of self-gravitating objects and hence prevent the collapsing process.

中文翻译：

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能量动量平方重力中球面坍塌的动力学

本文研究了能量-动量平方重力框架下球形坍塌的动力学。该理论克服了大爆炸奇点，并在早期宇宙中提供了可行的宇宙学后果。我们通过考虑恒星内部的非静态球对称时空和恒星外部区域的静态球对称度量来继续我们的工作。导出了内部和外部几何形状之间的 Darmois 连接条件。我们通过 Misner-Sharp 技术构建动力学方程，分析物质变量和暗源项对坍缩现象的影响。还建立了暗源项、外尔标量和物质变量之间的相关性。由于多元函数及其导数的存在，时空不再被认为是共形平坦的。为了获得共形平坦的时空，我们考虑了这种重力的特定模型，它产生了共形平坦的时空和整个系统的能量密度的均匀性。我们得出结论，正暗源项和负压梯度提供了反引力行为，导致自引力物体的稳定性，从而防止坍缩过程。