We investigate the structure and radial oscillations of anisotropic compact stars composed of dark energy, using the vanishing complexity factor formalism within general relativity. This novel approach establishes a direct link between the energy density and anisotropic factor, providing a robust framework for studying these exotic stellar objects. Employing an Extended Chaplygin Gas equation of state, we numerically compute interior solutions for both isotropic and anisotropic stars, revealing distinct differences in their properties. Additionally, we examine the oscillation modes and frequencies of these stars, highlighting the impact of anisotropy on their pulsational behaviour. Our results reveal distinct differences in the stellar properties, such as the metric potentials, pressure, speed of sound, and relativistic adiabatic index, between the two cases. Furthermore, we calculate the large frequency separation for the fundamental and first excited modes, offering insights relevant for future asteroseismology studies. Our findings shed light on the complex interplay of gravity, matter, and anisotropy in compact stars, providing a new perspective on dark energy's role in their structure and dynamics.

中文翻译：

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复杂性因子消失形式中的各向异性暗能量星：静水平衡、径向振荡和观测意义


我们利用广义相对论中消失的复杂因子形式主义来研究由暗能量组成的各向异性致密星的结构和径向振荡。这种新颖的方法在能量密度和各向异性因子之间建立了直接联系，为研究这些奇异的恒星物体提供了一个强大的框架。采用扩展查普利金气体状态方程，我们对各向同性和各向异性恒星的内部解进行数值计算，揭示了它们性质的明显差异。此外，我们还检查了这些恒星的振荡模式和频率，强调了各向异性对其脉动行为的影响。我们的结果揭示了两种情况之间恒星特性的明显差异，例如度量势、压力、声速和相对论绝热指数。此外，我们计算了基本模式和第一激发模式的大频率间隔，为未来的星震学研究提供了相关见解。我们的发现揭示了致密恒星中引力、物质和各向异性的复杂相互作用，为暗能量在其结构和动力学中的作用提供了新的视角。