International Journal of Geometric Methods in Modern Physics

In this paper, we study the collapse of a thin dust shell from the point of view of the horizon dynamics. We identify the critical surfaces at which time and space coordinates interchange their roles and investigate their properties by using the formalism of trapped surfaces. We show the existence of marginally outer trapped surfaces that are associated with the presence of quasi-local horizons. A particular shell configuration that avoids the formation of horizons is interpreted as naked shell.

We present a rigidity result in Lorentzian geometry, related to Bartnik’s conjecture, under the hypothesis of the existence of a concircular vector field with certain properties. We also study the relationship between two different notions of concircular vector fields found in the literature, and give conditions for a generalized Robertson–Walker spacetime to have a timelike concircular vector field.

In the framework of $f(P)$ gravity, we examine the nature of cosmological parameters by choosing different models of $f(P)$ gravity at past, present as well as future epoch for Hubble parameter from parameterized deceleration parameters. It is found that equation of state parameter leads to quintessence behavior and its ranges lie within Planck data for different constraints. We also study the squared sound speed and the thermodynamics for specific choice of constants. The squared sound speed corresponds to the viable results. Similarly, the validity of GSLT is also investigated for both linear and nonlinear models of $f(P)$ theory. However, the thermal equilibrium condition holds for both $f(P)$ models for specific choice of constants.

In this paper, Radiative Correction (RC) to the Casimir energy was computed for the self-interacting massive/massless Lifshitz-like scalar field, confined between a pair of plates with Dirichlet and Mixed boundary conditions in $3+1$ dimensions. Moreover, using the results obtained for the Dirichlet Casimir energy, the RC to the Casimir energy for Periodic and Neumann boundary conditions were also draw outed. To renormalize the bare parameters of the Lagrangian, a systematic perturbation expansion was used in which the counterterms were automatically obtained in a position-dependent manner. In our view, the position dependency of the counterterm was allowed, since it reflected the effects of the boundary condition imposed or the background space in the problem. All the answers obtained for the Casimir energy were consistent with well-known physical expects. In a language of graphs, the Casimir energy for the massive Lifshitz-like scalar field confined with four boundary conditions (Dirichlet, Neumann, Mixed, and Periodic) was also compared to each other, and as a concluding remark, the sign and magnitude of their values were discussed.

The Vaidya–Bonner metric is a non-static generalization of Reissner–Nordström metric and this paper deals with the investigation of the curvature restricted geometric properties of such a metric. The scalar curvature vanishes and several pseudosymmetric-type curvature conditions are fulfilled by this metric. Also, it is a $2$-quasi-Einstein, $\mathrm{\text{Ein}}(3)$ and generalized Roter type manifold. As a special case, the curvature properties of Reissner–Nordström metric are obtained. It is noted that Vaidya–Bonner metric admits several generalized geometric structures in comparison to Reissner–Nordström metric and Vaidya metric.

We study the $f(R,T)$ cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case $f(R,T)=f_1(R)+f_2(T)$ and the case $f(R,T)=f_1(R)+f_2(R)f_3(T)$. In each case, we state general theorems which determine completely the form of the unknown functions $f_i$ such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric$.$ In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

In this work, we focus on the phase space singularities of interactive quintessence model in the presence of matter fluid. This model is related to swampland studies, that the outcomes affect all these swampland-related models with the same dynamical system. We shall form the dynamical system corresponding to the cosmological system, which is eventually autonomous, and by using the dominant balances technique we shall investigate the occurrence or not of finite-time singularities. Our results indicate that the dynamical system of the model may develop finite-time singularities, but these are not general singularities, like in the case that the matter fluids were absent, in which case singularities occurred for general initial conditions. Hence, the presence of matter fluids affects the dynamical system of the cosmological system, making the singularities to depend on the initial conditions, instead of occurring for general initial conditions.

In this paper, we have investigated the physical behavior of cosmological models in modified Teleparallel gravity with a general function $f(T)=\alpha T+\beta {(-T)}^n$ where $\alpha ,\beta$ and $n$ are model parameters and $T$ is the torsion scalar. We have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. We have derived the deceleration parameter $q(\omega ,H(z))$ in terms of equation of state (EoS) parameter $\omega$ and Hubble parameter $H(z)$. We have investigated the variation of $q$ over the observed values of Hubble constant in various observations within the range of redshift $0.07\le z\le 2.30$. Also, we have studied effective energy density ${\rho }^{\mathrm{\text{eff}}}$, effective pressure $p^{\mathrm{\text{eff}}}$ and effective EoS parameter ${\omega }^{\mathrm{\text{eff}}}$. We have observed that the second term of $f(T)$ function behaves just like variable cosmological term $\mathrm{\Lambda }$ (${\omega }^{\mathrm{\text{eff}}}\approx -1$) at late-time universe and causes the acceleration in expansion and works just like dark energy candidates. Also, we have evaluated the age of the present universe for various stages of matter $p=\omega \rho$ and various $f(T)$ functions.

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An $n$-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)_n GRW spacetime is Einstein. The properties of (GR)_n GRW spacetimes equipped with almost Ricci soliton are studied.

This analysis explores the solutions for wormhole in $f(R,\phi ,\chi )$ gravity, where $\chi ,\phi$, and $R$ represent the kinetic term, scalar potential, and Ricci scalar, respectively. For this study, we use the spherically symmetric spacetime with the anisotropic source of matter. Further, we use the linear equation of state to complete this current investigation in the background of conformal symmetry motion. By plugging non-zero conformal Killing vectors, we discuss the feasible phantom wormhole configurations. Under the linear equation of state, the stability of wormhole solutions with specific values of parameters is also checked by using the Tolman–Oppenheimer–Volkoff equation. Further, the energy conditions are also discussed with conformal motions. Moreover, it is concluded that our inquired solutions are physically viable in $f(R,\phi ,\chi )$ gravity.

This work is aimed at the study of traversable wormholes, proposed by Morris and Thorne [Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395], in the framework of $f(R,T)=R+\alpha R^n+\lambda T$ gravity, where $\alpha$, $\lambda$ and $n$ are constants. The wormhole solutions are obtained and analyzed by using a simplest form of shape function. Further, the existence of photon spheres outside the throat of wormhole due to the gravitational lensing effect is detected.

In this study, we addressed the influence of quantum singularity on the topological state. The quantum singularity creates the defect in the momentum space ubiquitously and leads to the phase transition for the topological material. The kinetic equation reveals that the defect generates an anomaly without the characteristic energy scale. In the holographic model, the three-dimensional dislocations map into the gravitational bulk as domain walls extending along the AdS radial direction from the boundary. The creation/annihilation of the domain wall causes the quantum phase transition by ’t Hooft anomaly generation and is controlled by the gauge field. In other words, the phase transition is realized by the anomaly inflow. This ’t Hooft anomaly is caused by a phase ambiguity of the ground state resulting from the singularity in parameter space. This singularity gives the basis for the boundary’s topological state with the Berry connection. ’t Hooft anomaly’s renormalization group invariance shows that the total Berry flux is conserved in the UV layer to the IR layer. Phase transition entails domain wall constitution, which generates the entropy from the non-universal form or quantum entropy correction.

In this paper, we start the investigation of a new natural approach to “unifying” noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional ($AF$) $C^{\ast }$-algebras. The defining inductive sequence of an $AF$ $C^{\ast }$-algebra is lifted to enable the construction of a sequence of NCGFT of Yang–Mills–Higgs types. This paper focuses on derivation-based noncommutative field theories. A mathematical study of the ingredients involved in the construction of a NCGFT is given in the framework of $AF$ $C^{\ast }$-algebras: derivation-based differential calculus, modules, connections, metrics and Hodge *-operators, and Lagrangians. Some physical applications concerning mass spectra generated by Spontaneous Symmetry Breaking Mechanisms (SSBM) are proposed using numerical computations for specific situations.

In this study, the analytical solutions of the Klein–Gordon equation for any $l$ states of the modified effective mass potential under the modified unequal scalar and vector Coulomb–Hulthén potential (MUSVCH-P) are derived by using an approximation method to the centrifugal potential term in the symmetries of relativistic noncommutative three-dimensional real space (RNC: 3D-RS). The new analytical expressions for eigenvalues of the energy spectrum and the new mass of mesons, such as charmonium and bottomonium that have the quark and antiquark flavor, have been estimated by using Bopp’s shift method, and perturbation theory. The energy state equation depends on the global parameters characterizing the noncommutativity space and the potential parameter $(v_0,s_0,v_1,s_1,m_0,m_1,\delta )$ in addition to the Gamma function and the discreet atomic quantum numbers $(j,l,s,m)$. The expression for the new energy spectra is applied to obtain the new mass spectra of heavy quarkonium systems (charmonium and bottomonium) in the symmetries of (RNC: 3D-RS). The comparisons show that our theoretical results are in very good agreement with the reported works.

In this paper, we examine the embedded wormhole solutions in the modified $f(\mathcal{ℛ},T)$ theory of gravity, where $T$ denotes the trace of the energy–momentum tensor and $\mathcal{ℛ}$ is the Ricci scalar. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. We explore the feasible solutions for the specific model of $f(\mathcal{ℛ},T)$ theory of gravity. Energy conditions have been explored using the approach mentioned above. Conclusively, we find that obtained wormhole solutions are acceptable, as the null energy condition is violated in the specific region.

In this work, we develop a novel method to obtain numerical solution of well-known Korteweg–de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie group methods. This paper is a first attempt to combine DBFs and high order geometric numerical integrator for solving such a nonlinear partial differential equation (PDE) which preserves conservation laws. To demonstrate the performance of the proposed method we consider five test problems. We reckon $L_{\infty }$, $L_2$ and root mean square (RMS) errors and compare them with other results available in the literature. Besides the errors, we also monitor conservation laws of the KDV equation and we show that the method in this paper produces accurate results and preserves the conservation laws quite good. Numerical outcomes show that the present novel method is efficient and reliable for PDEs.

The aim of this paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson–Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein’s field equations without cosmological constant is vacuum. Finally, we construct a nontrivial example of pseudosymmetric spacetime.

Motivated by Palle’s investigation on the handness of chirality of vorticity in Einstein–Cartan cosmology [Entropy 5 (2014)], several aspects of chiral torsional handness in magnetogenesis and cosmology are presented. In the first one, we obtain torsion bounds from massive photons and axial anomalies. In the second, we deal with magnetogenesis from photon mass and in the third, we discuss chiral torsion degrees of freedom to obtain a torsion cosmological constant dependent solution. The torsion solution decays fast and implies a strong suppression of torsion at present universe. Our result contains the Poplawski [Phys. Lett. B (2010)] results in the case axial torsion vector associated to Einstein–Cartan fermionic sector matter and conformal anomalies of quarks. In the third example, a magnetic field bound from chiral torsionic dynamos is obtained as $10^{-11}\mathrm{\text{G}}$. In the non-minimal cosmological models, chiral dynamos are sourced by massive photons, London currents and chiral magnetic effect (CME). Chiral chemical potential is found to be mimic by torsion. Cosmological constant bound $\mathrm{\Lambda }\sim 10^{-34}{\mathrm{\text{cm}}}^{-2}$ is found. At the early universe, the cosmological constant $\mathrm{\Lambda }\sim 10^{22}{\mathrm{\text{cm}}}^{-2}$ is obtained. Torsion used in the present universe is $10^{-19}\mathrm{\text{GeV}}$. In the last and fourth example, chiral anisotropic currents are obtained and magnetic helicity is shown to depend upon torsion when the chiral chemical potential is non-constant.