2009/11/02 by Shao-Wen Wei, Yu-Xiao Liu, Chun-E Fu +2 · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Circular symmetry #Curvature #Legendre transformation #Noncommutative and Quantum Gravity Theories #Phase transition #Plane symmetry #Scalar curvature #Semiclassical physics #Symmetry (geometry) #hep-th
paper · pdf · doi:10.1155/2013/734138
published as Adv.High Energy Phys. 2013 (2013) 734138 · 16 pages, 6 figures
arxiv created 2009/11/02 · openalex publication_date 2013/01/01 · arxiv updated 2015/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the properties and thermodynamic stability of the plane symmetry black hole from the viewpoint of geometry. We find that the Weinhold curvature gives the first-order phase transition at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>is a parameter of the plane symmetry black hole while the Ruppeiner one shows first-order phase transition points for arbitrary<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>N</mml:mi><mml:mo>≠</mml:mo><mml:mn>1</mml:mn></mml:math>. Considering the Legendre invariant proposed by Quevedo et al., we obtain a unified geometry metric, which contains the information of the second-order phase transition. So, the first-order and second-order phase transitions can be both reproduced from the geometry curvatures. The geometry is also found to be curved, and the scalar curvature goes to negative infinity at the Davie phase transition points beyond semiclassical approximation.