This work is to introduce a new kind of modified gravitational theory, named as f(ℛ,𝒢,𝒯 ) (also f(ℛ,𝒯 ,𝒢)) gravity, where ℛ is the Ricci scalar, 𝒢 is Gauss–Bonnet invariant and 𝒯 is the trace of the energy–momentum tensor. With the help of different models in this gravity, we investigate some physical features of different relativistic compact stars. For this purpose, we develop the effectively modified field equations, conservation equation, and the equation of motion for test particle. Then, we check the impact of additional force (massive test particle followed by a nongeodesic line of geometry) on compact objects. Furthermore, we took three notable stars named as HerX − 1, SAXJ1808.4 − 3658 and 4U1820 − 30. The physical behavior of the energy density, anisotropic pressures, different energy conditions, stability, anisotropy, and the equilibrium scenario of these strange compact stars are analyzed through various plots. Finally, we conclude that the energy conditions hold, and the core of these stars is so dense.

中文翻译：

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f(ℛ,𝒢,𝒯 ) 引力中的致密星

这项工作是介绍一种新的修正引力理论，命名为F(ℛ,𝒢,𝒯 )（还F(ℛ,𝒯 ,𝒢)) 重力，其中ℛ是 Ricci 标量，𝒢是 Gauss-Bonnet 不变量和𝒯是能量-动量张量的迹。在这种引力的不同模型的帮助下，我们研究了不同相对论致密星的一些物理特征。为此，我们开发了有效修正的场方程、守恒方程和测试粒子的运动方程。然后，我们检查附加力（大量测试粒子后跟非测地线几何线）对紧凑物体的影响。此外，我们选取​​了三颗著名的明星，分别命名为她X - 1,萨克斯杰1808.4 - 3658和4ü1820 - 30. 通过各种图表分析了这些奇怪致密恒星的能量密度、各向异性压力、不同能量条件、稳定性、各向异性和平衡情景的物理行为。最后，我们得出结论，能量条件成立，这些恒星的核心是如此密集。