We construct a new class of higher-dimensional black hole solutions of f(R) theory coupled to a nonlinear Maxwell field. In deriving these solutions the traceless property of the energy-momentum tensor of the matter filed plays a crucial role. In n-dimensional spacetime the energy-momentum tensor of conformally invariant Maxwell field is traceless provided we take n=4p, where p is the power of conformally invariant Maxwell Lagrangian. These black hole solutions are similar to higher-dimensional Reissner-Nordstrom anti-de~Sitter black holes but only exist for dimensions which are multiples of four. We calculate the conserved and thermodynamic quantities of these black holes and check the validity of the first law of black hole thermodynamics by computing a Smarr-type formula for the total mass of the solutions. Finally, we study the local stability of the solutions and find that there is indeed a phase transition for higher-dimensional f(R) black holes with conformally invariant Maxwell source.

In this paper, we consider linearly charged dilatonic black holes and study their thermodynamical behavior in the context of phase transitions and thermodynamic geometry. We show that, depending on the values of the parameters, these black holes can undergo two types of phase transition. We also find that there are three critical behaviors near the critical points for these black holes: nonphysical unstable to physical stable, large to small, and small to large black-hole phase transitions. Next, we employ a thermodynamical metric to study the thermodynamical geometry of these black holes. We show that the characteristic behavior of the Ricci scalar of this metric enables one to recognize the type of phase transition and critical behavior of the black holes near phase-transition points. Finally, we will extend thermodynamical space by considering the dilaton parameter as an extensive parameter. With this consideration, we will show that the Weinhold, Ruppeiner, and Quevedo metrics provide extra divergencies that are not related to any phase-transition point, whereas our new method provides an effective mechanism to study phase transitions.

In this paper, we investigate the critical behavior of charged black holes of Einstein-Maxwell-dilaton gravity in the presence of two Liouville-type potentials which make the solution asymptotically neither flat nor AdS and has a parameter $\mathrm{$\Lambda${}}$ treated as a thermodynamic quantity that can vary. We obtain a Smarr-type relation for charged dilatonic black holes and find out that the volume is different from the geometrical volume. We study the analogy of the Van der Waals liquid-gas system with the charged dilatonic black hole system, while we treat the black hole charge as a fixed external parameter. Moreover, we show that the critical values for pressure, temperature, and volume are physical provided the coupling constant of dilaton gravity is less than one and the horizon is a sphere. Finally, we calculate the critical exponents and show that they are universal and are independent of the details of the system although the thermodynamic quantities depend on the dilaton parameter and the dimension of the spacetime.

Recently, Barrow argued that quantum-gravitational effects may introduce intricate, fractal features on the black hole horizon [J. D. Barrow, , The area of a rough black hole, Phys. Lett. B 808, 135643 (2020)]. In this viewpoint, black hole entropy no longer obeys the area law and instead it can be given by $S\sim A^{1+\delta /2}$, where the exponent $\delta$ ranges $0\le \delta \le 1$, and indicates the amount of the quantum-gravitational deformation effects. Based on this, and using the deep connection between gravity and thermodynamics, we disclose the effects of Barrow entropy on the cosmological equations. For this purpose, we start from the first law of thermodynamics, $dE=TdS+WdV$, on the apparent horizon of the Friedmann-Robertson-Walker universe, and derive the corresponding modified Friedmann equations by assuming that the entropy associated with the apparent horizon has the form of Barrow entropy. We also examine the validity of the generalized second law of thermodynamics for the Universe enclosed by the apparent horizon. Finally, we employ the emergence scenario of gravity and extract the modified Friedmann equation in the presence of Barrow entropy which coincides with one obtained from the first law of thermodynamics. When $\delta =0$, the results of standard cosmology are deduced.

We explore the effects of considering various infrared (IR) cutoffs, including the particle horizon, the Ricci horizon and the Granda–Oliveros (GO) cutoffs, on the properties of Tsallis holographic...

Many theoretical attempts toward reconstructing the potential and dynamics of the scalar fields have been done in the literature by establishing a connection between holographic/agegraphic energy density and a scalar-field model of dark energy. However, in most of these cases the analytical form of the potentials in terms of the scalar field have not been reconstructed due to the complexity of the equations involved. In this paper, by taking Hubble radius as system’s IR cutoff, we are able to reconstruct the analytical form of the potentials as a function of scalar field, namely, $V=V(\varphi )$ as well as the dynamics of the scalar fields as a function of time, namely, $\varphi =\varphi (t)$, by establishing the correspondence between holographic energy density and quintessence, tachyon, $K$-essence, and dilaton energy density in a flat Friedmann-Robertson-Walker universe.