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

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 $PdV$ 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 $P-V$ 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 $\rho_q$ grows. At some fixed parameters, we find that bigger volume difference between the smaller black holes($V_1$) and the bigger black holes($V_2$ ) will lead to a lower efficiency, while the bigger pressure difference $P_1-P_4$ 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 $Q$ and normalization factor $a$ can also promote heat engine efficiency which would infinitely approach the Carnot limit when $Q$ or $a$ goes to infinity.Comment: 28 pages, 16 figures, refernces added, discussion and computation improve

Note on the Radion Effective Potential in the Presence of Branes

In String Theory compactification, branes are often invoked to get the desired form of the radion effective potential. Current popular way of doing this assumes that the introduction of branes will not modify the background geometry in an important way. In this paper, we show by an explicit example that at least in the codimension 2 case, the gravitational backreaction of the brane cannot be neglected in deriving the radion effective potential. Actually, in this case, the presence of branes will have no effect on the dynamics of radion.Comment: 6 pages, no figures. Some discussion clarified, conclusion unchanged. To appear in Phys. Rev.

Gravitational potential in Palatini formulation of modified gravity

General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We conclude that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity is very small for a slowly moving source.Comment: 5 pages, no figure