Paper · Jan 20, 2017
Parametric Solution of a Small-Large Black Hole Coexistence Curve
As on arXiv
Abstract
We consider the first-order phase transition of a charged anti-de Sitter black hole, and find that the equation of state with the conditions of the two coexisting phases, leads to the two coupled equations about the thermodynamic volumes of small black hole and large black hole. By solving the equations, it is found that each reduced volume is only a function of the parameter . All properties of the coexistence curve can be studied from the two volume functions. In particular, each thermodynamic quantity is described by a piecewise analytic function. The demarcation point is located at . The thermodynamic function but not its derivative, is continuous at the point. This property is completely different from that of the ven der Waals fluid. Moreover, the thermodynamic behaviors as are discussed. From which one can easily obtain some critical exponents and amplitudes for small-large black hole phase transitions.
- Submitted
- Jan 20, 2017
- Subjects
- gr-qc
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 12A.5Reduced Distance and Reduced Volume
A space-time Bishop–Gromov theorem.
- 12A.6𝓛-Geodesics and the Variational Formulas
Perelman's §7.1 derived line by line: the first and second variation of 𝓛-length, 𝓛-Jacobi fields, adapted fields, Hamilton's Harnack expressions, and the differential inequalities for the reduced distance.
- 12A.7Monotonicity of the Reduced Volume
The 𝓛-exponential map and its Jacobian, the injectivity domain, the limit at τ = 0, barrier inequalities on complete flows, and min ℓ ≤ n/2, following Morgan and Tian's chapters 6 and 7.