International Journal of Theoretical Physics最新文献

Black hole (BH) thermodynamics is a research field integrating gravitational theory, thermodynamics and quantum theory, which has been the focus of attention. The phase transition (PT) of BHs is an important part of BH thermodynamics. Through the study of BH PT, we will have a deeper understanding of the nature of BHs, and the gravity theory related to BHs will be developed. In the study of the influence of massive gravity parameters on PT dynamics, we study the thermodynamic PT process of AdS BHs in massive gravity in detail. We compare the cases with different massive gravity parameters. Based on the Gibbs free energy landscape, we study the kinetic properties of PT. We find that the two wells have the mallme depth at a certain temperature on the free energy landscape. Due to thermal fluctuations, the large black hole (LBH) state and small black hole (SBH) state can be transitioned to each other. By solving the Fokker-Planck equation, we study the probabilistic evolution of the PT of AdS BHs in massive gravity. The results show that the initial state of the BH evolves faster with the increase of the parameter (varvec{lambda }). In addition, for SBH state and LBH state, the mean first passage time increases with the increase of the parameter (varvec{lambda }). Considering that the mean first passage time of the PT of AdS BHs in massive gravity can be obtained, this work can play an important role in limiting the massive gravity parameter according to observations in the future.

We show that the free energy (mathcal {F}) and temperature T of black holes, considered as a thermodynamic system, can be viewed as an A-discriminant of an appropriately-defined polynomial. As such, mathematical results about A-discriminants may lead to implications about black hole thermodynamics. In particular, for static spacetimes with spherical, planar, or hyperbolic symmetry, the number of distinct thermodynamic phases depend on the number of distinct terms in the metric component (g_{tt}). We prove that if (g_{tt}) consists of (N_{f}) distinct terms, then the (mathcal {F})-T curve consists of (N_f-2) cusps, which in turn leads to (N_f-1) distinct thermodynamic phases. This result is applied to explicit examples of the Schwarzschild-AdS, Reissner–Nordström, power-law Maxwell, and Euler–Heisenberg black holes.

We introduce a property weaker than congruence-permutability and show that every d(_{text {0}})-algebra has this property. We also show that in general d(_{text {0}})-algebras are not congruence-permutable, and that a sufficient condition for a d(_{text {0}})-algebra to be congruence-permutable is being directed. However this condition is not necessary.

This paper aims to investigate the two-dimensional Klein-Gordon oscillator system in a dynamical noncommutative (DNC) space. We address the deformed system using the time-independent perturbation theory, where the energy eigenvalues and eigenvectors are obtained in relativistic and nonrelativistic regimes, also the effects of the dynamical and non-dynamical noncommutative settings are successfully examined. Then some numerical results are given and used to extensively study the conduct of the system under the various considerations. Note that in the DNC space, the space-space commutation relations and noncommutative parameter are position-dependent. The first-order corrections to the eigensystem are found, then, it is shown that the energy shift depends on the DNC parameter (tau ). Moreover, using the accuracy of energy measurement, we put an upper bound on the parameter (tau ). Knowing that, with a set of two-dimensional Bopp-shift transformation, we link the noncommutative problem to the standard commutative one.

In this work, the radial Schrödinger equation with pseudoharmonic oscillator is first expressed in both de Sitter and Anti de Sitter spaces time using the Extended Uncertainty Principle (EUP) formalism. The eigensolutions of the Schrödinger equation is obtained in exact form using the Nikiforov-Uvarov functional analysis (NUFA) method. The effects of quantum numbers and spatial deformation parameter on the eigensolutions obtained are studied in both spaces. In addition, the graphical variations of both thermodynamic properties and expectation values with temperature parameter and quantum numbers, respectively, have been discussed for varying deformation parameters. The energy eigenvalues increase with increase in the spatial deformation parameter in Anti de Sitter (AdS) spacetime and there is an energy decrease in de Sitter (dS) spacetime, as deformation parameter increases. The variations observed for thermodynamic properties and expectation values with temperature and quantum number, respectively in dS spacetime are inversely related to that observed in AdS spacetime.

We make an analysis of r.m.s. and charge radii of heavy flavored mesons introducing the three-loop correction to the static potential (V(r)=-frac{4alpha _s}{3r}+br). Considering linear as parent and Coulomb as perturbation, the first order wave function is used to study the corresponding correction in coordinate space. The wave function is then used to study the r.m.s. and charge radii of heavy flavored mesons. The computed results are then compared with the data available in literature. The results show significant improvements compared to our earlier works.

Acoustic waves on a crystal lattice, long internal waves in a density-stratified ocean, ion acoustic waves in a plasma, and shallow-water waves with weakly non-linear restoring forces are all represented mathematically by the KdV equation. Its importance and wide range of applications have led to the development and analysis of multiple solutions in the scientific community. Beside those in this article we prove the existence of superposed solutions of KdV equation. Some theorems and corollary on the existence of superposed and superposed-type solutions for KdV equations with variable coefficients are presented in this article. The six sets of superposed solutions to the variable coefficient KdV equation are obtained by using the corollary and theorem on the existence of superposed solutions. It was demonstrated that superposed solutions of the KdV problem with variable coefficients can be constructed by combining two elementary solutions that contain reciprocal Jacobi elliptic functions. Additionally, we present a few theorems and corollaries about the existence of superposed-type solutions for this equation in the literature. The most significant and fascinating of them all is the splitting technique theorem. We obtained many superposed-type solutions of KdV equations with variable coefficients in terms of the Jacobi elliptic function by using the splitting technique. It is additionally confirmed that the generalised Miura transformation is a sub-case of the splitting procedure. This represents an additional modification to the generalised Miura transformation. These theorems explain why a number of seemingly bizarre superposition-type solutions to a number of newly published nonlinear equations have appeared. It is further demonstrated that the solutions produced by the generalised Miura transformation are specific examples of solutions obtained through the application of the splitting technique. Plots in two dimensions, three dimensions, contour, and density have all been used to illustrate the features of the derived solutions.

We study the confinement of a quantum particle to the squared cotangent potential in the background of global monopole spacetime. By dealing with s-states, we obtain the energy levels from the exact solutions to the Schrödinger equation. Then, we show that the topology of the global monopole spacetime influences the energy levels. Further, we show that there is a non-null revival time with regard to the squared cotangent potential and how it is influenced by the global monopole topology.

This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in Dey and Fring (Phys. Rev. D 90, 084005, 2014). Specifically, we examine the system when expressed in terms of commutative variables, utilizing a generalized form of the standard Bopp-shift relations recently introduced in Biswas et al. (Phys. Rev. A 102, 022231, 2020). We solved the time dependent system and obtained the analytical form of the eigenfunction using the method of Lewis invariants, which is associated with the Ermakov-Pinney equation, a non-linear differential equation. We then obtain exact analytical solution set for the Ermakov-Pinney equation. With these solutions in place, we move on to compute the dynamics of the energy expectation value analytically and explore their graphical representations for various solution sets of the Ermakov-Pinney equation, associated with a particular choice of quantum number. Finally, we determined the generalized form of the uncertainty equality relations among the operators for both commutative and noncommutative cases. Expectedly, our study is consistent with the findings in Dey and Fring (Phys. Rev. D 90, 084005, 2014), specifically in a particular limit where the coordinate mapping relations reduce to the standard Bopp-shift relations.

We conduct a detailed analysis of Natário’s “zero-expansion” warp drive spacetime, focusing on scalar curvature invariants within the 3(+)1 formalism. This paper has four primary objectives: First, we establish the Petrov type classification of Natário’s spacetime, which has not been previously determined in the literature. We prove that Natário’s spacetime is Petrov type I, not fitting the Class B warped product spacetime definition. Second, we assess the relative magnitude of the Weyl scalar curvature invariant and compare it with the amplitudes of Einstein’s scalar and the Ricci quadratic and cubic invariants within the warp-bubble zone. Previous studies have focused on Ricci curvature and the energy-momentum tensor, neglecting the Weyl curvature, which we demonstrate plays a significant role due to the sharp localization of the form function near the warp-bubble radius. Third, we visualize several curvature invariants for Natário’s warp drive, as well as momentum density, which we show as the critical physical quantity governing the orientation of the warp drive trajectory, overshadowing space volume changes. Fourth, we critically examine claims that Natário’s warp drive is more realistic than Alcubierre’s. We demonstrate that Natário’s spacetime exhibits curvature invariant amplitudes 35 times greater than Alcubierre’s, given identical warp-bubble parameters, making Natário’s concept even less viable. Additionally, we address Mattingly et al.’s analysis, highlighting their underestimation of curvature invariant amplitudes by 21 orders of magnitude.