论文标题
三维黑洞通过Noether对称性
Three-dimensional black holes via Noether symmetries
论文作者
论文摘要
我们研究了拉格朗日式的固定旋转btz型三维空间中的拉格朗日对称性。提出了对（2+1） - 维旋转BTZ型黑洞时空模型的Noethy对称性的详细分析。采用NOETHE对称方法，获得了每个Noether对称性的第一个积分（运动常数）以寻找确切的溶液。在求解第一个积分方程式之后，取决于函数$ f（r）$的形式，我们得出了一些新的（2+1）二维旋转BTZ型黑洞解决方案。我们讨论了派生的精确解决方案的物理含义。通过利用质量$ m $和Angular Momentum $ J $在$ r _ {\ pm} $方面，分析了获得的BTZ型黑洞溶液的热力学特性，其中$ r _+$是事件horizon和$ r _ { - } $是内部的。此外，显示热力学量遵守第一定律，并获得了我们发现的溶液的Smarr样公式。
We investigate the Noether symmetries of the Lagrangian for the stationary rotating BTZ-type three-dimensional spacetimes in $f(R)$ theory of gravity. A detailed analysis of Noether symmetries of (2+1)-dimensional rotating BTZ-type black hole spacetime model is presented. Applying the Noether symmetry approach, the first integrals (constants of motion) for each of Noether symmetries are obtained to look for the exact solutions. After solving the first integral equations depending on the form of the function $f(R)$, we derived some new (2+1)-dimensional rotating BTZ-type black hole solutions. We discussed the physical implications of the derived exact solutions. The thermodynamical properties of the obtained BTZ-type black hole solutions are analyzed by making use of the mass $M$ and the angular momentum $J$ in terms of $r_{\pm}$, where $r_+$ is the event horizon and $r_{-}$ is the inner horizon. Further, it is shown that thermodynamic quantities obey the first law, and the Smarr-like formulas of the solutions we found are obtained.
