Nashed Gamal G L, Bamba Kazuharu
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, El Sherouk City, Cairo 11837, Egypt.
Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan.
Entropy (Basel). 2021 Mar 17;23(3):358. doi: 10.3390/e23030358.
We explore the quadratic form of the f(R)=R+bR2 gravitational theory to derive rotating -dimensions black hole solutions with ai,i≥1 rotation parameters. Here, is the Ricci scalar and is the dimensional parameter. We assumed that the -dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter , whereas, in the case of N>4, it depends on parameter , owing to the contribution of the correction R2 term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter to be b<116Λ to obtain a positive entropy.
我们探索f(R)=R + bR²引力理论的二次形式，以推导具有i≥1个旋转参数ai的旋转维度黑洞解。这里，R是里奇标量， 是维度参数。我们假设 - 维时空是静态的，并且它具有零曲率边界的平坦视界。我们通过计算诸如视界半径和质量等物理量之间的关系来研究黑洞的物理性质。我们还证明，在四维情况下，高阶曲率对黑洞没有贡献，即黑洞不依赖于维度参数 ，而在N>4的情况下，由于修正R²项的贡献，它依赖于参数 。我们通过应用重新定位方法分析黑洞解的守恒量、能量和角动量。此外，我们计算诸如温度和熵等热力学量，并局部检验黑洞解的稳定性，结果表明它们具有热力学稳定性。而且，熵的计算对参数b施加了限制，即b<116Λ才能获得正熵。
