Xu Mou, Lu Jianbo, Yang Shining, Jiang Hongnan
Department of Physics, Liaoning Normal University, Dalian 116029, China.
Entropy (Basel). 2023 May 18;25(5):814. doi: 10.3390/e25050814.
The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans-Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius r+ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values r+, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles' circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits.
广义相对论（GR）面临的诸多问题一直促使我们探索广义相对论的修正理论。考虑到研究黑洞（BH）熵及其在引力物理学中的修正的重要性，我们在修正引力的广义布兰斯 - 迪克（GBD）理论下研究了一种球对称黑洞的热力学熵修正。我们推导并计算了熵和热容量。结果发现，当事件视界半径(r_+)的值较小时，熵修正项对熵的影响非常明显，而对于较大的(r_+)值，修正项对熵的贡献几乎可以忽略不计。此外，我们可以观察到，随着事件视界半径的增加，GBD理论中黑洞的热容量将从负值变为正值，这表明黑洞存在相变。鉴于研究测地线结构对于探索强引力场的物理特性很重要，我们还在GBD理论框架内研究了静态球对称黑洞中粒子圆轨道的稳定性。具体而言，我们分析了最内稳定圆轨道对模型参数的依赖性。此外，测地线偏差方程也被用于研究GBD理论中粒子的稳定圆轨道。给出了黑洞解的稳定性条件以及实现稳定圆轨道运动所需的径向坐标的有限范围。最后，我们展示了稳定圆轨道的位置，并得到了在圆轨道上运动的粒子的角速度、比能和角动量。
