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We study the P-V criticality and phase transition in the extended phase space of charged anti-de Sitter black holes in canonical ensemble of ghost-free massive gravity, where the cosmological constant is viewed as a dynamical pressure of the black hole system. We give the generalized thermodynamic first law and the Smarr relation with massive gravity correction. We find that not only when the horizon topology is spherical but also in the Ricci flat or hyperbolic case, there appear the P-V criticality and phase transition up to the combination k + C0²c2m² in the four-dimensional case, where k characterizes the horizon curvature and c2m² is the coefficient of the second term of massive potential associated with the graviton mass. The positivity of such combination indicate the van der Waals-like phase transition. When the spacetime dimension is larger then four, the Maxwell charge there seems unnecessary for the appearance of critical behavior, but a infinite repulsion effect needed, which can also be realized through negative valued C3m² or c4m², which is third or fourth term of massive potential. When c3m² is positive, a Hawking-Pagelike black hole to vacuum phase transition is shown in the five-dimensional chargeless case. For the van der Waals-like phase transition in four and five spacetime dimensions, we calculate the critical exponents near the critical point and find they are the same as those in the van der Waals liquid-gas system. [ABSTRACT FROM AUTHOR]

We consider a static self-gravitating perfect fluid system in Lovelock gravity theory. For a spacial region on the hypersurface orthogonal to static Killing vector, by the Tolman's law of temperature, the assumption of a fixed total particle number inside the spacial region, and all of the variations (of relevant fields) in which the induced metric and its first derivatives are fixed on the boundary of the spacial region, then with the help of the gravitational and fluid equations of the theory, we can prove a theorem says that the total entropy of the fluid in this region takes an extremum value. A converse theorem can also be obtained following the reverse process of our proof. We also propose the definition of isolation quasilocally for the system and explain the physical meaning of the boundary conditions in the proof of the theorems. [ABSTRACT FROM AUTHOR]

We consider a self-gravitating system containing a globally timelike Killing vector and a nonlinear Born-Infeld electromagnetic field and scalar fields. We prove that under certain boundary conditions (asymptotically flat/anti-de Sitter) there cannot be any nontrivial field configurations in the spacetime. To explore nontrivial solutions, one should break any of the conditions we imposed. The case with another type of nonlinear electromagnetic field is also analyzed, and similar conclusions have been obtained under certain conditions. [ABSTRACT FROM AUTHOR]

We consider a static self-gravitating system consisting of perfect fluid with isometries of a (D -- 2)-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations of motion suggests a generalized mass function. A Tolman-Oppenheimer-Volkoff-like equation is obtained by using this mass function and gravitational equations. We investigate the maximum entropy principle in Lovelock gravity, and find that this Tolman-Oppenheimer-Volkoff equation can also be deduced from the so-called "maximum entropy principle" which was originally customized for Einstein gravity theory. This investigation manifests a deep connection between gravity and thermodynamics in this generalized gravity theory. [ABSTRACT FROM AUTHOR]

When the phase structure of the black brane in a grand canonical ensemble is discussed, the bubble phase with the same boundary data should be included in this structure. As such, the phase transitions among bubbles, black branes, and "hot flat space" are possible, therefore giving a much enriched phase structure. We also argue that under some conditions, either the grand canonical ensemble it sol t is unstable or there are some unknown new phases. [ABSTRACT FROM AUTHOR]