论文标题
jt重力和近超级热力学，用于$ ads_ {4,5} $的kerr黑洞的旋转扰动
JT gravity and near-extremal thermodynamics for Kerr black holes in $AdS_{4,5}$ for rotating perturbations
论文作者
论文摘要
我们研究了近地平线2D重力理论，该理论捕获了Kerr黑洞的接近极端热力学，其中固定了多余的角动量$ΔJ$和多余的质量$ΔM$的线性组合。这些对应于极端kerr黑洞的质量和角动量的过程，使它们在极端。对于kerr $ ads_4 $，我们持有$Δj-\ mathcal {l} \，Δm= 0 $，而迈尔斯 - 佩里（MP）type kerr black black hole in $ ads_5 $我们持有$Δj_{φ_{1,2}} \ hspace {-0.2cm} - \ Mathcal {l} _ {φ_{1,2}}} \，Δm= 0 $。我们表明，在近地平线上，2D Jackiw-Teitelboim理论能够捕获高尺寸黑洞的热力学在近乎极端温度下的较小的黑洞$ T_H $。我们通过概括文献中通过参数$ \ mathcal {l} $和$ \ Mathcal {l} _ {φ_{φ_{1,2}} $的近地平线限制来证明这一点。由此产生的JT理论捕获了此类几何形状的几乎极端热力学，只要我们确定了近地平线的温度$ t^{（2）} _ h $，近地平线$ ads_2 $ geometry为$ t^{（2）} _ h = t_h = t_h/（t_h/（1-μ\，\，\，\，\ Mathcal {l}） $ t^{（2）} _ h = t_h/（1-μ\，（（\ Mathcal {l} _ {φ_1}+\ Mathcal {l} _ {l} _ {φ_2} _ {φ_2}）$ 5D Kerr的$ $ $ $ $ $ $ $，$μ $μ\，（\ Mathcal {l} _ {φ_1}+\ Mathcal {l} _ {φ_2}）<1 $。我们还争辩说，这种理论将自己嵌入到Kerr几何形状的较高维理论中。
We study the near horizon 2d gravity theory which captures the near extremal thermodynamics of Kerr black holes where a linear combination of excess angular momentum $δJ $ and excess mass $δM$ is held fixed. These correspond to processes where both the mass and the angular momenta of extremal Kerr black holes are perturbed leaving them near extremal. For the Kerr $AdS_4$ we hold $δJ-\mathcal{L}\,δM=0 $ while for Myers-Perry(MP) type Kerr black hole in $AdS_5$ we hold $δJ_{φ_{1,2}}\hspace{-0.2cm}-\mathcal{L}_{φ_{1,2}}\,δM=0$. We show that in near horizon, the 2d Jackiw-Teitelboim theory is able to capture the thermodynamics of the higher dimensional black holes at small near extremal temperatures $T_H$. We show this by generalizing the near horizon limits found in literature by parameters $\mathcal{L}$ and $\mathcal{L}_{φ_{1,2}}$ for the two geometries. The resulting JT theory captures the near extremal thermodynamics of such geometries provided we identify the temperature $T^{(2)}_H$ of the near horizon $AdS_2$ geometry to be $T^{(2)}_H=T_H/(1-μ\,\mathcal{L})$ for 4d Kerr and $T^{(2)}_H=T_H/(1-μ\,(\mathcal{L}_{φ_1}+\mathcal{L}_{φ_2}))$ for 5d Kerr where $μ$ is their chemical potential, with $μ\,\mathcal{L}<1$ and $μ\,(\mathcal{L}_{φ_1}+\mathcal{L}_{φ_2})<1$ respectively. We also argue that such a theory embeds itself non-trivially in the higher dimensional theory dual to the Kerr geometries.
