The action for a class of three-dimensional dilaton-gravity theories with a cosmological constant can be recast in a Brans-Dicke type action, with its free $ω$ parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ($ω\to\infty$), a dimensionally reduced cylindrical four-dimensional general relativity theory ($ω=0$), and a theory representing a class of theories ($ω=-3$). The Hamiltonian formalism is setup in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates $\{M,P_M\}$, $M$ being the mass parameter and $P_M$ its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrödinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.
Taking a thermodynamic perspective, we study the weak gravity conjecture in the context of 4D Einstein-Maxwell-dilaton theory. We find closed-form expressions for the corrected thermodynamic quantities in the presence of four-derivative terms in the action, and in particular the charge-to-mass ratio and entropy, for several families of solutions of special magnetic-to-electric charge ratio or dilaton coupling constant. Assuming that dyonic black holes themselves are the conjectured charged states, this places constraints on the Wilson coefficients of the theory which we show are satisfied unde…
It is known that scalar-tensor gravity models can be studied in Einstein and Jordan frames. In this paper, we consider a model of scalar-tensor gravity in Einstein's frame to calculate the Lifshitz-like black hole solutions with different horizon topologies. We study thermodynamic properties and first order van der Waals like phase transition, and find that the Lifshitz parameter affects the phase structure. In addition, we investigate thermal stability by using the behavior of heat capacity and various methods of geometrical thermodynamics.
AdS black holes show richer transition behaviors in extended phase space by assuming the cosmological constant and its conjugate quantity to behave like thermodynamic pressure and thermodynamic volume. We study the extended thermodynamics of charged dilatonic AdS black holes in a class of Einstein-Maxwell-dilaton theories that can be embedded in gauged supergravities in various dimensions. We find that the transition behaviors of higher dimensional dilatonic AdS black holes are different from the four dimensional counterparts, and new transition behaviors emerges in higher dimensions. First, t…
We consider Einstein-Maxwell-Dilaton theory in $(2+1)$-dimensions where the coupling between the scalar field and the Maxwell invariant is the dilatonic coupling $f(ϕ) = \exp (-2αϕ)$ and obtain novel exact rotating black hole solutions. The dilatonic parameter $α$ impacts the metric function, affecting the rotating properties of the black hole, its mass and also its thermodynamics. Calculating the entropy we find that it is always positive and the dilatonic black holes may have higher entropy than the BTZ black hole. Depending on the parameters, the dilatonic BTZ-like black hole may be thermod…
Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational $4d$ model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors $\vecλ_i$ obeying $\vecλ_i (\vecλ_1 + \vecλ_2) > 0$, $i =1,2$. The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. Th…
Extended phase space thermodynamics and $P-V$ criticality: Brans-Dicke-Born-Infeld vs Einstein-Born-Infeld-dilaton black holes
受黑洞和Van der Waals液/气系统的热力学类比的启发，本文研究了两个双重子Born-Infeld黑洞及其共形解Brans-Dicke-Born-Infeld解的$P-V$临界性.由于共形约束的存在，我们必须忽略旧的玻色子Born-Infeld理论的拉格朗日量及其黑洞解，而引入一个新的拉格朗日量。我们在Einstein和Jordan标架下得到了球对称非线性荷电黑洞解，并计算了相关的守恒量和热力学量。在此基础上，我们考虑了宇宙学常数与压强的比例关系，对相空间进行了扩展。通过数值计算得到了热力学坐标的临界值，并绘制了相应的$P-V$图和$G-T$图。对这些相图的研究有助于我们研究晶体的相变。我们还分析了不同参数对黑洞相变的影响。
Static spherically symmetric black hole solution is obtained in the framework of Einstein-dilaton theory with nonlinear Maxwell and Yang-Mills fields of power-law type. It is observed that black hole might have two horizons similarly as it takes place for linear gauge fields case. Thermodynamics of the black hole is studied, namely the behaviour of temperature is examined and the first law is written. The concept of extended phase space is also utilized, namely we have written and analyzed the equation of state for the black hole and examined the Gibbs free energy. The Gibbs free energy shows …
According to the gauge/gravity duality, the Van der Waals transition of charged AdS black holes in extended phase space is conjectured to be dual to a renormalization group flow on the space of field theories. So exploring the Van der Waals transition is potentially valuable for studying holographic properties of charged black hole thermodynamics. There are different transition behaviors for charged dilatonic AdS black holes in Einstein-Maxwell-dilaton (EMD) theory with string-inspired potential with different dilaton coupling constants in diverse dimensions. In this work, we find a special cl…
A Hamiltonian approach for the Thermodynamics of AdS black holes
本文研究了D维Schwarzschild-anti de Sitter（SAdS）黑洞的热力学性质。简要讨论了SAdS时空的最小热力学，突出了它的一些优点和缺点。最小SAdS热力学扩展内的哈密顿方法，通过引入一个额外的自由度。我们证明，宇宙学常数可以引入的热力学描述的SADS黑洞的史瓦西问题的正则变换，密切相关的反德西特热力学体积的引入。所提出的处理是一致的，在这个意义上，它是兼容的引入新的热力学势，并尊重黑洞热力学定律。通过要求热力学变量的均匀性，我们能够构建一个新的状态方程，完全表征SAdS黑洞的热力学。处理自然产生的现象学常数，可以与不同的边界条件下的微观理论。从SAdS热力学的推广中可以预期一系列全新的现象。
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for higher-order theory of gravity, although two Hamiltonians emerging from the same action differing by total derivative terms are related through canonical transformation, the difference transpires while attempting canonical quantization, which is predominant in non-minimally coupled higher-order theory of gravity. We follow Dirac's constraint analysis to formulate ph…
In lower dimensions, charged AdS black holes in an extended phase space, where the cosmological constant is interpreted as the thermodynamic pressure, are typically absent of liquid/gas phase transitions. We investigate the criticality of lower dimensional charged, dilatonic, asymptotically AdS (CDAdS$_d$) black holes generated from consistent truncations of RNAdS$_{d+2}$ black objects. We demonstrate that CDAdS$_{d}$ black holes in $d<4$ can exhibit rich van der Waals behavior and confirm that the associated critical exponents match those expected from mean field theory.
