Abstract
In the context of dilaton coupled Einstein gravity with a negative cosmological constant and a Born–Infeld field, we study heat engines where a charged black hole is the working substance. Using the existence of a notion of thermodynamic mass and volume (which depend on the dilaton coupling), the mechanical work takes place via the pdV terms present in the first law of extended gravitational thermodynamics. The efficiency is analyzed as a function of dilaton and Born–Infeld couplings, and the results are compared with analogous computations in the related conformal solutions in the Brans–Dicke–Born–Infeld theory and black holes in anti-de Sitter space-time.
Highlights
Recent interest in treating the cosmological constant as a dynamical parameter [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] has led to important extensions of the classical thermodynamic properties of a black hole [16,17,18,19], which relates the mass M, surface gravity κ, and outer horizon area A of a black hole solution to the energy, temperature, and entropy (U, T, and S, resp.) according to
The cosmological constant treated as pressure p = − /8π, has a conjugate variable, the thermodynamic volume V associated with the black hole
An extended thermodynamical phase space treatment leads to an exact identification of small to large black hole phase transition in charged AdS and related black holes to a van der Waals liquid–gas phase transition [27,28], including an exact map of critical exponents
Summary
Recent interest in treating the cosmological constant as a dynamical parameter [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] has led to important extensions of the classical thermodynamic properties of a black hole [16,17,18,19], which relates the mass M, surface gravity κ, and outer horizon area A of a black hole solution to the energy, temperature, and entropy (U , T , and S, resp.) according to (in geometrical units where G, c, h , kB are set to unity). Pressure for asymptotically non-flat/ads black holes with Liouville type potentials has been introduced and the corresponding PV criticality studied in good detail in [68] and extended to conformally coupled scalars, i.e., the Brans– Dicke–Born–Infeld solutions [45] Following these works, and the existence of an extended first law with pressure and volume, including the presence of PV criticality allows us to naturally define a heat engine, exactly as in the examples considered for AdS, leading to extension of the results of [30,44,45,68]. We first study the dilatonic Born–Infeld model and later study the corrections to efficiency of heat engines in Brans–Dicke–Born–Infeld model
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