Modern Physics Letters A

This paper focuses on the issues of motion of various kinds of charged, magnetized, and neutral test particles in the vicinity of static and spherically symmetric electrically charged black holes in the Einstein-Æther gravitational theory. Our purpose here is to analyze the effects of the free parameters occurring in the Einstein-Æther theory for particle motion in curved spacetime. Specifically, we have studied the stability of circular and radially varying orbits of different kinds of particles by varying the free parameters $c_{13}$ and $c_{14}$, and also varying the particle’s specific energy, specific angular momentum, and electric charge of the black hole. As a special case, we investigate the charged particle motion around the black holes with a uniform magnetic field by checking the characteristics of the particle’s innermost stable circular orbit. Finally, we propose few values of the parameters $c_{13}$ and $c_{14}$ which mimic the behavior of spin of a Kerr black hole to model an astrophysical black hole.

It is known that entropy of black hole gets correction at quantum level. Universally, these corrections are logarithmic and exponential in nature. We analyze the impacts of these quantum corrections on thermodynamics of Born–Infeld BTZ black hole in massive gravity by considering both such kinds of correction. We do comparative analysis of corrected thermodynamics with their equilibrium values. Here, we find that the exponential correction yields to the second point of the first-order phase transition. Also, quantum correction affects significantly the Helmholtz free energy of larger black holes. We study the equation of state for the exponential corrected black hole to obtain a leading order virial expansion.

The role played by the congruence in the prediction of the gravitational energy in the teleparallel equivalent of general relativity is discussed. It is shown that some congruences yield unphysical predictions. It is also shown that the energy–momentum tensor density predicted by the proper reference frame of an arbitrary accelerated observer vanishes along the observer’s worldline, regardless of its acceleration. The latter result is discussed and arguments both against and in favor of the use of this type of frame to describe the gravitational energy are presented; arguments against the belief that the principle of equivalence is incompatible with the localization of the gravitational energy are also presented. A gauge condition is applied to the teleparallel frame and its consistence is discussed: using three different tetrads for the pp-wave spacetimes, it is shown that the most consistent prediction comes from the tetrad that satisfies this gauge. The possibility of having a well-defined concept of absolute vacuum is also discussed.

In this paper, we study a homogeneous and isotropic flat Friedmann–Robertson–Walker (FRW) universe in Rastall gravity, in which there exist the components of radiation and dust. That is to say, the density of fluid ${\rho }_{\gamma }$ satisfies the barotropic equation of state $p_{\gamma }=(\gamma -1){\rho }_{\gamma }$, where $\gamma =4/3$ and $1$, and the equation of state $w=\gamma -1$. We derive the modified Friedmann equations, and the effective equation of state $\tilde{w}$ in this universe model. For the dust-dominated case, the effective equation of state $\tilde{w}$ is described by $\frac{\lambda -1}{3\lambda -1}$, where $\lambda$ is the Rastall parameter. As $\frac{1}{3}<\lambda <\frac{2}{3}$, we have $\tilde{w}<-\frac{1}{3}$ which means an accelerated expansion of the universe occurs. Along with the conditions for the convergent modified Friedmann equations and the positive density of dust, the Rastall parameter $\lambda$ should be in the range of $(\frac{1}{2},\frac{2}{3})$. In other words, the various $\tilde{w}$ for $\frac{1}{2}<\lambda <\frac{2}{3}$ correspond to those of quintessence with the general barotropic equation of state $(\gamma =1)$. For the general case, the Rastall universe full of radiation and dust, the expression of $\tilde{w}$ is complicated involving the Rastall parameter, the density of radiation and the density of dust. As the ratio of the densities of dust and radiation is smaller than $\frac{2-3\lambda }{2(2\lambda -1)}$, $\tilde{w}$ is less than $-\frac{1}{3}$. Moreover, to keep the density of dust positive, the Rastall parameter should be restricted in $(\frac{1}{2},\frac{2}{3})$ too. By the numerical calculation, we find that $\tilde{w}$ from $\frac{1}{3}$ decreases as $N(N\equiv lna(t))$ increases. And $\tilde{w}$ for different $\lambda \in (\frac{1}{2},\frac{2}{3})$ ultimately tend to $\frac{\lambda -1}{3\lambda -1}$, the value of which are in the range of $(-1,-\frac{1}{3})$. Obviously, the expansion of the cosmology filled with radiation and dust or only dust in Rastall gravity $(\frac{1}{2}<\lambda <\frac{2}{3})$ accelerates without any “exotic” energy whose equation of state $w<-\frac{1}{3}$.

In modified gravity, we investigate the universe’s accelerating expansion in a vacuum. We obtain a highly nonlinear differential equation from the variation of Einstein–Hilbert action with the consideration of a Robertson–Walker metric. Because the differential equations have non-analytic solutions, the expansion phase of the Friedmann–Robertson–Walker universe is studied using numerical approaches. We analyzed the acceleration phases of the cosmos for different periods, cosmic jerk and snap parameters, and their dependencies on the initial values and coupling parameters involved in various $f(R)$ gravity models. Using a parametric technique, we also give the values of the jerk and snap parameters in different accelerating stages of the universe. Finally, the behavior of the dark energy component is addressed for $f(R)$ models.

In this work, we reexamine the holographic dark energy concept proposed already for cosmological applications. By considering, more precisely, the bounds on the entropy arising from lattice field theory on one side and Bekenstein–Hawking entropy of black holes on another side, it is shown that the so-called holographic dark energy cannot be mimicked as easily as claimed in the literature. In addition, the limits on the electron $(g-2)$ experiments are taken into account again. It is shown that the corrections to the electron magnetic momentum are of the order of ${𝒪}(10^{-23})$.

This work introduces a procedure to obtain vortex configurations described by first-order equations in generalized Maxwell–Chern–Simons models without the inclusion of a neutral field. The results show that the novel methodology is capable of inducing important modification in the vortex core, leading to vortex configurations with unconventional features.

In this paper, we introduce a generalization of the Dunkl derivative with two parameters to study the Schrödinger equation in Cartesian and polar coordinates in two dimensions. The eigenfunctions and the energy spectrum for the harmonic oscillator and the Coulomb problem are derived in an analytical way and it is shown that our results are properly reduced to those previously reported for the Dunkl derivative with a single parameter.

The current theoretical analysis model for high-dimensional quantum key distribution (QKD) was developed without carefully considering the dead time and after-pulse of the single-photon detectors. Here, we propose a new model that accounts for these two effects. With this model, we analyze the effects of various properties of the single-photon detector on the performance of the high-dimensional quantum key distribution and show numerically that the high-dimensional quantum key distribution can be achieved up to 180 km with InGaAs/InP-type single-photon detectors. This work can improve our understanding of the factors that determine the performance of high-dimensional quantum key distribution and will help to promote the application of single-photon detectors based on avalanche photodiodes in high-dimensional quantum key distribution.