75 research outputs found

    Phase Transition of Black Holes in Brans–Dicke Born–Infeld Gravity through Geometrical Thermodynamics

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    Using the geometrical thermodynamic approach, we study phase transition of Brans–Dicke Born–Infeld black holes. We apply introduced methods and describe their shortcomings. We also use the recently proposed new method and compare its results with those of canonical ensemble. By considering the new method, we find that its Ricci scalar diverges in the places of phase transition and bound points. We also show that the bound point can be distinguished from the phase transition points through the sign of thermodynamical Ricci scalar around its divergencies

    Effects of dark energy on the efficiency of charged AdS black holes as heat engine

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    In this paper, we study the heat engine where charged AdS black holes surrounded by dark energy is the working substance and the mechanical work is done via PdVPdV term in the first law of black hole thermodynamics in the extended phase space. We first investigate the effects of a kind of dark energy (quintessence field in this paper) on the efficiency of the RN-AdS black holes as heat engine defined as a rectangle closed path in the PVP-V plane. We get the exact efficiency formula and find that quintessence field can improve the heat engine efficiency which will increase as the field density ρq\rho_q grows. At some fixed parameters, we find that bigger volume difference between the smaller black holes(V1V_1) and the bigger black holes(V2V_2 ) will lead to a lower efficiency, while the bigger pressure difference P1P4P_1-P_4 will make the efficiency higher but it is always smaller than 1 and will never be beyond Carnot efficiency which is the maximum value of the efficiency constrained by thermodynamics laws, this is consistent to the heat engine in traditional thermodynamics. After making some special choices for thermodynamical quantities, we find that the increase of electric charge QQ and normalization factor aa can also promote heat engine efficiency which would infinitely approach the Carnot limit when QQ or aa goes to infinity.Comment: 28 pages, 16 figures, refernces added, discussion and computation improve