International Journal of Modern Physics A

In this paper, in the context of the Magueijo–Smolin (MS) model and using the Foldy–Wouthuysen transformation for relativistic spin-1/2 particles, we study the nonrelativistic limit (NRL) of the Dirac equation within the doubly special relativity. This leads to obtaining a deformed Schrödinger–Pauli equation; there, we test the influence of the MS model on the NRL of the Dirac equation. However, we also examine the efficacy and behavior of the Foldy–Wouthuysen transformation in deriving the NRL in the presence of MS model. Besides, we compute that the energies shift in the context of MS model and check if the deformed Schrödinger–Pauli equation form still shows explicitly the g-factor 2.

In this work, we generalize the theory of perturbations in a ($D+1$)-dimensional space–time with cosmological constant, studying scalar, vector and tensor perturbations, as well as its structure in Newtonian and Synchronous gauge. We also show the theory of perturbations in the context of brane cosmology, where branes are embedded in a set of D-spatial dimensions, a temporal dimension, and an additional spatial dimension. In both standard and brane cosmology, an unperturbed space–time is provided with a Friedmann–Lemaitre–Robertson–Walker metric and arbitrary sectional curvature, the matter content has the shape of a perfect fluid. In addition, we consider the arbitrary sectional curvature, obtaining the respective equations in the Newtonian and Synchronous gauge. We highlight that the results presented in this paper can be used to treat brane cosmology with two concentric branes or tackle the ${\sigma }_8$ tension with a braneworld approach. Finally, as an example of the utility of all the technology presented in this paper, we show an application to the energy flux and the repercussions in the framework of the braneworlds.

In classical electrodynamics, the well-known Lorentz force law falls short of providing a satisfactory result for the trajectory of point-like charged particles when considering that particle’s own self-force. While there have been many historical attempts, Gralla, Harte and Wald developed a new model for classical charged particles that is free from pathologies while being consistent with Maxwell’s equations and conserves stress-energy. Expanding upon this approach, we derive a relativistically correct, modified Lorentz force law in vector form, which includes radiation reaction, and spin- and magnetic moment-dependent correction terms, suitable to be included in classical electrodynamics lectures and beam dynamics simulation tools. As by-products we obtain evolution equations for mass, spin angular momentum and the radiated power. We compare the new equations to the classical ones and use the new equations to conduct numerical simulations, showing that the results are free of any nonphysical artifacts, and which might be possible to test in future experiments at particle accelerators. The new equations foster improved insight into beam dynamics.

The decay widths of ${\rho }^{\prime }\to \pi \pi ,\omega \pi ,\rho \eta$, ${\omega }^{\prime }\to \rho \pi ,\omega \eta$ and ${\pi }^{\prime }\to \rho \pi$ are recalculated within the extended Nambu–Jona-Lasinio (NJL) quark model. It is shown that the mass of ${\rho }^{\prime }(1450)$ meson derived in the NJL model agrees with the one given in Particle Data Group tables but significantly deviates from the recent result of CMD-3 collaboration. Comparisons with earlier theoretical results are presented.

This work explores the dark energy nature of logarithmic $f(R,L_m)$-gravity models with observational constraints, where $L_m$ represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian $L_m=\rho$, a flat FLRW space–time metric and an arbitrary function $f(R,L_m)=\frac{R}{2}+L_m-\mu ln{L}_m$, where $\mu$ is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{q0}$ and ${\mathrm{\Omega }}_{\mu 0}$. Using the most recent two observational datasets as 32 $H(z)$ and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with $1-\sigma ,2-\sigma ,3-\sigma$ errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term $\mathrm{\Lambda }$. We found that the effective equation of state parameter is in the range $-1\le \omega \le 0$ over $-1\le z<\infty$ with present value $\omega \approx -0.6971,-0.7120$.

In this paper, we derive the entropy product rule for Taub–Newman–Unti–Tamburino (Taub–NUT)–de Sitter black hole (BH) and Taub–NUT–anti-de Sitter BH. We show that the entropy products in terms of both the physical horizons are mass-independent. Both perturbative approximation and direct method have been considered. By introducing the cosmological horizon, we show that for Taub–NUT–de Sitter BH, there exists a mass-independent entropy functional relation in terms of three horizons namely event horizon (EH), Cauchy horizon (CH) and cosmological horizon (CHH) which depends on cosmological parameter ($\mathrm{\Lambda }$) and the NUT parameter (N). For Taub–NUT–anti-de Sitter BHs, we determine the mass-independent entropy functional relations in terms of two physical horizons (namely EH and CH) which depends on only NUT parameter. Sometimes some complicated functions of EH entropy and CH entropy are also strictly mass-independent. This is plausible only due to the new formalism developed in [S. Wu and D. Wu, Phys. Rev. D 100, 101501(R) (2019)] for NUT class of BHs. The formalism states that a generic four dimensional Taub–NUT spacetime should be described completely in terms of three or four different types of thermodynamic hairs. They could be defined as the Komar mass ($M=m$), the angular momentum ($J_n=mn$), the gravitomagnetic charge ($N=n$), the dual (magnetic) mass $(\tilde{M}=n)$. Finally, we could say that this universality is mainly due to the presence of new conserved charges $J_N=MN$ which is closely analogue to the Kerr-like angular momentum $J=aM$.

In this paper, the effects of the Ohmic and magnetic density currents are investigated in the linearized Euler–Heisenberg (EH) electrodynamics (ED). The linearization is introduced through an external magnetic field, in which the vector potential of the EH ED is expanded around a magnetic background field that we consider uniform and constant in this paper. From the EH linearized equations, we obtain the solutions for the refractive index associated with the electromagnetic wave superposition, when the current density is ruled by the Ohm law, and in the second case, when the current density is set by an isotropic magnetic conductivity. These solutions are functions of the magnetic background $(B)$ of the wave propagation direction $(k)$. It also depends on the conductivity and on the wave frequency. As a consequence, the dispersion and the absorption of plane waves change when $B$ is parallel to $k$ in relation to the case of $B$ perpendicular to $k$ in the medium. The characteristics of the refraction index are related to direction of $B$ and of the wave polarization, where there is an open discussion for the birefringence in this medium.

In this paper, we investigate relations or differences among various conserved quantities which involve the matter Energy Momentum Tensor (EMT) in general relativity. These quantities include the energy with Einstein’s pseudo EMT, the generalized Komar integral, or the ADM energy, all of which can be derived from Noether’s second theorem, as well as an extra conserved charge recently proposed in general relativity. For detailed analyses, we apply definitions of these charges to a system of free massive particles. We employ the post-Newtonian (PN) expansion to make physical interpretations. We find that the generalized Komar integral is not conserved at the first non-trivial order in the PN expansion due to non-zero contributions at spatial boundaries, while the energy with Einstein’s pseudo EMT at this order agrees with a total energy of massive particles with gravitational interactions through the Newtonian potential, and thus is conserved. In addition, this total energy is shown to be identical to the ADM energy not only at this order but also all orders in the PN expansion. We next calculate an extra conserved charge for the system of massive particles, at all orders in the PN expansion, which turns out to be a total number of particles. We call it a gravitational charge, since it is clearly different from the total energy. We finally discuss an implication from a fact that there exist two conserved quantities, energy and gravitational charge, in general relativity.