Modern Physics Letters A

The study of thermodynamics in the view of the Hamiltonian approach is the newest tool to analyze the thermodynamic properties of the black holes (BHs). In this paper, we investigate the thermodynamics of d-dimensional $(d>3)$ asymptotically Anti-de Sitter (AdS) BHs. A thermodynamic representation based on symplectic geometry is introduced in this paper. We extend the thermodynamics of d-dimensional charged AdS BHs in the views of a Hamiltonian approach. Firstly, we study the thermodynamics in reduced phase space and correlate with the Schwarzschild solution. Then we enhance it in the extended phase space. In an extended phase space, the thermodynamic equations of state are stated as constraints. We apply the canonical transformation to analyze the thermodynamics of the said type of BHs. We plot $P$-$v$ diagrams for different dimensions d taking the temperatures $T<T_c$, $T=T_c$ and $T>T_c$ and analyze the natures of the graphs and the dependences on d. In these diagrams, we point out the regions of coexistence. We also examine the phase transition by applying “Maxwell’s equal area law” of the said BHs. Here, we find the regions of coexistence of two phases which are also depicted graphically. Finally, we derive the “Clapeyron equation” and investigate the latent heat of isothermal phase transition.

The Ricci dark energy is a model inspired by the holographic dark energy models with the dark energy density being proportional to Ricci scalar curvature. Here, this model is studied in the bumblebee gravity theory. It is a gravitational theory that exhibit spontaneous Lorentz symmetry breaking. Then, the modified Friedmann equation is solved for two cases. In the first case, the coupling constant $\xi$ is equal to zero and in the second case a solution in the vacuum, where the bumblebee field becomes a constant that minimizes the potential, is considered. The coupling constant controls the interaction gravity-bumblebee.

We know that in general relativity the Raychaudhuri equation gives the congruence and evolution of the geodesics. In this work, it is proposed that in brane cosmology the Raychaudhuri equation, apart from giving the collapse of the brane, it gives the evolution of the brane. Therefore, the Raychaudhuri equation gives the same information as the one of Friedmann’s, in the context of evolution.

In this short paper, we comment on the possibility of superluminal velocities and present–future correlations with reference to a paper recently published.

Black holes in $d<3$ spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose–Einstein condensates (BEC) of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower-dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as $N_d\sim {(L_d/{\ell }_p)}^{d-1}$, where $L_d$ is the relevant length for the system in the $(1+d)$-dimensional spacetime. In particular, this analysis shows that black holes cannot contain more than a few gravitons in $d=1$. Since dimensional reduction is a common feature of many models of quantum gravity, this result can shed light on the end of the Hawking evaporation. We also consider $(1+1)$-dimensional cosmology in the context of corpuscular gravity and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions.

In this paper, we study the thermal evolution of three types of quantum correlations under the homogeneous and inhomogeneous spin star Hamiltonian. It is shown that quantum discord (QD) is more stable than the other measures in the thermal regime, but concurrence is more efficient when the Hamiltonian parameters are employed. However, all quantum correlations can reach their maximum, if the inhomogeneous parameter raises. Quantum correlations can be enhanced by a weak external magnetic field and strong coupling parameter. But they vanish in the case of a strong magnetic field, weak coupling parameter, and high temperatures.

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory (CQFT) in higher orders. It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. Some features of U(1) axial vector gauge theory in Parisi Wu stochastic quantization are reported. These features are not absent if the theory is formulated in the conventional way. In particular we present arguments for renormalizability of the massive axial vector gauge theory coupled to a massless fermion.

This paper presents the effects of the Generalized Uncertainty Principle (GUP), i.e. its classical version expressed through the deformed Poisson brackets in the phase–space of a one-dimensional minisuperspace Friedmann cosmological model with a mixture of non-interacting dust and radiation. It is shown, in the case of this model, that starting from the specific representation of the deformed Poisson algebra, which corresponds to the change of the potential energy term of the oscillator, the size of the early universe can be related to its inflationary GUP expansion.

The Hirota equation, a modified nonlinear Schrödinger (NLS) equation, takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity. Its wave propagation is like in the ocean and optical fibers can be viewed as an approximation which is more accurate than the NLS equation. By considering the potential application of two mode nonlinear waves in nonlinear fibers under a certain case, we use the algebraic reductions from the Lie algebra $gl(2,ℂ)$ to its commutative subalgebra $Z_2=ℂ[\mathrm{\Gamma }]/({\mathrm{\Gamma }}^2)$ and $\mathrm{\Gamma }={({\delta }_{i,j+1})}_{ij}$ to define a weakly coupled Hirota equation (called Frobenius Hirota equation) including its Lax pair, in this paper. Afterwards, Darboux transformation of the Frobenius Hirota equation is constructed. The Darboux transformation implies the new solutions of ($q^{[1]}$, $r^{[1]}$) generated from the known solution ($q$, $r$). The new solutions ($q^{[1]}$, $r^{[1]}$) provide soliton solutions, breather solutions of the Frobenius Hirota equation. Further, rogue waves of the Frobenius Hirota equation are given explicitly by a Taylor series expansion of the breather solutions. In particular, by choosing different parameter values for the rogue waves, we can get different images.