Modern Physics Letters A

The Schwarzschild black hole in the Cold Dark Matter (CDM) halo is studied, and the radiation laws of the thin accretion disk near the black hole are discussed and summarized. The orbits of light around the black hole are also calculated. Additionally, using the Novikov–Thorne model’s light intensity function of the thin accretion disk, it is possible to solve for the shadow created by the thin accretion disk near the Schwarzschild black hole as well as the observed luminosity of the disk.

In this paper, we performed Lie symmetry analysis and applied $G^{\prime }/G$ expansion method on the nonlinear dissipative–dispersive equation. The purpose of this research is to find the vector fields and transform the nonlinear dissipative–dispersive equation into simpler forms. The Maple software was used to obtain the vector field and similarity reductions for nonlinear dissipative–dispersive equations. In addition, we obtained exact solutions based on the $G^{\prime }/G$ expansion method and power series method, including the hyperbolic functions, the trigonometric functions and the rational functions. The method we used is direct, concise, elementary and effective, and can be used for many other nonlinear evolution equations. Furthermore, the invariant subspaces of the nonlinear dissipative–dispersive equation were identified using the refined invariant subspaces method. The invariant subspaces of solutions to linear ordinary differential equations were used to prove that nonlinear dissipative–dispersive equation admits subspaces. The exact solutions were obtained by using generalized separated variables.

We present an exploration of helical or twisted hypersurfaces family denoted as $x$, which are dependent on three parameters and possess a space-like axis in the Minkowski 4-space ${𝕃}^4$. We provide an in-depth analysis of the fundamental forms, Gauss map, and shape operator associated with $x$. We establish a framework for defining the curvatures of any given family using the Cayley–Hamilton theorem. By applying this theorem, we derive the specific curvatures of the hypersurface under consideration. Furthermore, we investigate the conditions under which the curvatures of $x$ satisfy the umbilical conditions. Lastly, we examine the Laplacian of hypersurfaces family in ${𝕃}^4$, shedding light on its important properties.

In this paper, we consider two specific quantum systems governed by the one-dimensional Klein–Gordon equation within the Dunkl formalism. Our systems are characterized by a symmetrized Coulomb potential and an inverse quadratic interaction, respectively. For both systems, we construct closed-form solutions of bound state type.

The analytical expression of the density-dependent binding energy per nucleon for the relativistic mean field (RMF), the so-called relativistic energy density functional (Relativistic-EDF), is used to obtain the isospin-dependent symmetry energy and its components for the isotopic chain of Sc-, Ti-, V- and Cr-nuclei. The procedure of the coherent density fluctuation model is employed to formulate the Relativistic-EDF and Brüeckner energy density functional (Brüeckner-EDF) at local density. A few signatures of shell and/or sub-shell closure are observed in the symmetry energy and its components, i.e. surface and volume symmetry energy, far from the $\beta$-stable region for odd-$A$ Sc- and V-, and even–even Ti- and Cr- nuclei with nonlinear NL3 and G3 parameter sets. A comparison is made with the results obtained from Relativistic-EDF and Brüeckner-EDF with both NL3 and G3 for the considered isotopic chains. We find Relativistic-EDF outperforms the Brüeckner-EDF in predicting the shell and/or sub-shell closure of neutron-rich isotopes at $N=50$ for these atomic nuclei. Moreover, a relative comparison has been made for the results obtained with the nonlinear NL3 and G3 parameter sets.

A physical model that can quantitatively describe the spontaneous alpha-particle emission mechanism from atomic nuclei in the spherical nucleus approximation has been applied to the evaluation of the half-life of the ${}^{146}$Sm nuclide. The one-parameter, semi-empirical model used in this study has been developed in the frame of a quantum mechanical mechanism of alpha tunnelling through a potential barrier, taking into account centrifugal and overlapping effects. The calculation procedure yielded a value of $145.1\pm 0.3$Myr for the half-life of the extinct ${}^{146}$Sm isotope. This value, even if in disagreement with the few old measurements performed on the artificially obtained ${}^{146}$Sm, is thought to represent the most reliable indication of the $\alpha$-decay rate for such challenging nuclide.

The theta vacuum in QCD is obtained from the standard vacuum, after twisting by the exponential of the Chern–Simons term. However, a question remains–what is the quantum operator $U(g)$ for winding number 1? We construct this operator $U(g)$ in this note. The Poincaré rotation generators commute with it only if they are augmented by the spin $\frac{1}{2}$ representation of the Lorentz group, coming from large gauge transformations. This result is analogous to the well-known “spin-isopin” mixing result due to Jackiw and Rebbi [Phys. Rev. Lett. 36, 1116 (1976)], and Hasenfratz and ’t Hooft [Phys. Rev. Lett. 36, 1119 (1976)]. There is a similar result in fuzzy physics literature of Balachandran, Kurkcuoglu and Vaidya [Lectures on Fuzzy and Fuzzy Susy Physics (World Scientific Publishing Company, 2007)]. This shows that states can drastically affect representations of observables. This fact is further shown by charged states dressed by infrared clouds. Following Mund, Rehren and Schroer [arXiv:hep-th/2109.10342], we find that Lorentz invariance is spontaneously broken in these sectors. This result has been extended earlier to QCD (Balachandran, Nair, Pinzul, Reyes-Lega and Vaidya [arXiv:2112.08631 [hep-th]], reference given in the Final Remarks) where even the global QCD group is shown to be broken. It is argued that the escort fields of Mund, Rehren and Schroer [arXiv:hep-th/2109.10342] are the Higgs fields for Lorentz and color breaking. They are string-localized fields where the strings live in a union of de Sitter spaces. Their oscillations and those of the infrared cloud can generate the associated Goldstone modes.

In this paper, the different properties of generalized Vaidya spacetime are considered. We define the location of horizons. We show that the apparent horizon can contain the event horizon. The locations of all types of horizons are compared with the ones in the usual Vaidya spacetime. We investigate the time-like geodesics in this spacetime. New corrections to Schwarzschild and Vaidya cases appear and we give conditions when these corrections are not negligible. Also, we consider the conformal Killing vector and transform the metric to conformally static coordinates. We introduce a new constant of motion along null and time-like geodesics, which is generated by a homothetic Killing vector. The conformally static coordinates allow diagonalizing of the generalized Vaidya spacetime. The surface gravity has been calculated for the dust and stiff fluid cases.