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Register a new userBlack holes in massive gravity as heat engines
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The paper at hand studies the heat engine provided by black holes in the presence of massive gravity. The main motivation is to investigate the effects of massive gravity on different properties of the heat engine. It will be shown that massive gravity parameters and gravitons mass modify the efficiency of engine on a significant level. Furthermore, it will be shown that it is possible to have the heat engine for non-spherical black holes in massive gravity and we study the effects of topological factor on properties of the heat engine. Surprisingly, it will be shown that the highest efficiency for the heat engine belongs to black holes with hyperbolic horizon, while the lowest one belongs to spherical black holes.
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We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -mu^2/4 +c_2 m^2$ in the four dimensional case, where $mu$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.
We extend to non-static black holes our benchmarking scheme that allows for cross-comparison of the efficiencies of asymptotically AdS black holes used as working substances in heat engines. We use a circular cycle in the p-V plane as the benchmark cycle. We study Kerr black holes in four spacetime dimensions as an example. As in the static case, we find an exact formula for the benchmark efficiency in an ideal-gas-like limit, which may serve as an upper bound for rotating black hole heat engines in a thermodynamic ensemble with fixed angular velocity. We use the benchmarking scheme to compare Kerr to static black holes charged under Maxwell and Born-Infeld sectors.
We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1) gauge field with gauge coupling g, there is a new ultraviolet scale Lambda=g M_{Pl}, invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Lambda. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light elementary electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.
The anomaly cancelation method proposed by Wilczek et al. is applied to the black holes of topologically massive gravity (TMG) and topologically massive gravito-electrodynamics (TMGE). Thus the Hawking temperature and fluxes of the ACL and ACGL black holes are found. The Hawking temperatures obtained agree with the surface gravity formula. Both black holes are rotating and this gives rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. It is found that the terms in this U(1) gauge field correspond exactly to the correct angular velocities on the horizon of both black holes as well as the correct electrostatic potential of the ACGL black hole. So the results for the Hawking fluxes derived here from the anomaly cancelation method, are in complete agreement with the ones obtained from integrating the Planck distribution.
In this paper, we formulate two new classes of black hole solutions in higher curvature quartic quasitopological gravity with nonabelian Yang-Mills theory. At first step, we consider the $SO(n)$ and $SO(n-1,1)$ semisimple gauge groups. We obtain the analytic quartic quasitopological Yang-Mills black hole solutions. Real solutions are only accessible for the positive value of the redefined quartic quasitopological gravity coefficient, $mu_{4}$. These solutions have a finite value and an essential singularity at the origin, $r=0$ for space dimension higher than $8$. We also probe the thermodynamic and critical behavior of the quasitopological Yang-Mills black hole. The obtained solutions may be thermally stable only in the canonical ensemble. They may also show a first order phase transition from a small to a large black hole. In the second step, we obtain the pure quasitopological Yang-Mills black hole solutions. For the positive cosmological constant and the space dimensions greater than eight, the pure quasitopological Yang-Mills solutions have the ability to produce both the asymptotically AdS and dS black holes for respectively the negative and positive constant curvatures, $k=-1$ and $k=+1$. This is unlike the quasitopological Yang-Mills theory which can lead to just the asymptotically dS solutions for $Lambda>0$. The pure quasitopological Yang-Mills black hole is not thermally stable.
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