Kerr-AdS 黑洞的相結構

The phase structure of Kerr-AdS black holes

蔡育岱(Yu-Dai Tsai)

指導教授 ： 李湘楠

國立清華大學/理學院/物理學系/碩士(2013年)

https://doi.org/10.6843/NTHU.2013.00542

摘要

The phase structure of Kerr-AdS black holes is studied at three different temperatures, $T_{c1}$, $T_{c2}$ and $T_L$. At $T_{c1}$, a second order phase transition is identified to be in the same universality class as the van der Waals liquid-gas system. We derive the critical exponents ($alpha$, $eta$, $gamma$, $delta$)=(0, $frac{1}{2}$, 1, 3) associated to this phase transition, and discuss the free energy and the scaling symmetry near the critical point. $T_L$ is the lowest temperature under which a Kerr-AdS black hole could reduce to a Schwarzschild-AdS black hole, and this temperature correspond to the critical temperature determined in the Hawking-Page phase transition. $T_{c2}$ is the temperature which separates the stable and partially unstable isotherms. Along with $T_{c2}$, we found an asymptotic value of angular momentum $Omega_0$ = $1/l$ as $J$ goes to infinity. This asymptotic value reminisces us the minimal value of the molecule volume $V_0$ in the van der Waals liquid-gas system.

關鍵字

黑洞 ； 負宇宙常數空間 ； 相變 ； 凡得瓦 ； 临界指数 ； 黑洞熱力學

並列摘要

The phase structure of Kerr-AdS black holes is studied at three different temperatures, $T_{c1}$, $T_{c2}$ and $T_L$. At $T_{c1}$, a second order phase transition is identified to be in the same universality class as the van der Waals liquid-gas system. We derive the critical exponents ($alpha$, $eta$, $gamma$, $delta$)=(0, $frac{1}{2}$, 1, 3) associated to this phase transition, and discuss the free energy and the scaling symmetry near the critical point. $T_L$ is the lowest temperature under which a Kerr-AdS black hole could reduce to a Schwarzschild-AdS black hole, and this temperature correspond to the critical temperature determined in the Hawking-Page phase transition. $T_{c2}$ is the temperature which separates the stable and partially unstable isotherms. Along with $T_{c2}$, we found an asymptotic value of angular momentum $Omega_0$ = $1/l$ as $J$ goes to infinity. This asymptotic value reminisces us the minimal value of the molecule volume $V_0$ in the van der Waals liquid-gas system.

並列關鍵字

black hole ； Anti-de Sitter space ； phase transition ； van der Waals ； critical exponent ； thermodynamics

參考文獻

[1] Giovanni Arcioni and Ernesto Lozano-Tellechea. Stability and critical phenomena of black holes and black rings. Phys. Rev., D72:104021, 2005.

[2] Rabin Banerjee, Sujoy Kumar Modak, and Saurav Samanta. A New Phase Transition and Thermodynamic Geometry of Kerr- AdS Black Hole. 2010.

[3] Rabin Banerjee, Sujoy Kumar Modak, and Saurav Samanta. New approach to phase transitions in black holes. 2011.

[4] Rong-Gen Cai, Li-Ming Cao, and Ya-Wen Sun. Hawking-Page Phase Transition of black Dp-branes and R-charged black holes with an IR Cuto. JHEP, 0711:039, 2007.

[6] Rong-Gen Cai and Y.S. Myung. Critical behavior for the dilaton black holes. Nucl.Phys., B495:339-362, 1997.