International Journal of Geometric Methods in Modern Physics

We generalize the original Nash theory of gravity by adding the matter fields by specifying a proper form of the field equations on more general footings for space with matter contents. We first derive the equations of motion in the flat Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime and examine the behaviors of the solutions by invoking specific forms of the Hubble parameter. We also classify the physical behaviors of the solutions by employing the stability analysis. We check the consistency of the model by considering particular cosmological parameters. We use observational data from Supernovae Ia (SNeIa) and baryonic acoustic oscillations (BAO) to constrain the parameters of the model. Interestingly, we discover the best fit of our model with ${\mathrm{\Omega }}_{m0}=0.25$ and $H_0=0.4$ for ${\tau }_0=0.3$ and ${\rho }_0=0.5$ assuming the Hubble parameter $H\propto {\rho }^{-2}$.

This work investigates the nature of singularity formed from string-oriented charged perfect fluid collapse in theory of f (R) gravity. The spherically symmetric spacetime is assumed to be filled with a string-oriented charged perfect fluid. The gravitational collapse of the fluid is analyzed to understand the effects of electric field on the time and radii of apparent horizons and singularity formation. The presence of an electric field was discovered to increase the mass of the collapsing system, the radii of apparent horizon development, and the time gap between the event horizon and singularity. The term $f(R_0)$ acts as an anti-gravity term. However, the presence of electric field accelerates the gravitational collapse.

The second post-Newtonian hydrodynamic equations are analyzed within the framework of a plane wave solution. The hydrodynamic equations for the mass and momentum density are coupled with six Poisson equations for the Newtonian and post-Newtonian gravitational potentials. Perturbations of the basic fields and gravitational potentials from a background state by assuming plane wave representations lead to a dispersion relation where the Jeans instability condition emerges. The influence of the first and second post-Newtonian approximations on the Jeans mass is determined. It was shown that the relative difference of the first post-Newtonian and the Newtonian Jeans masses is negative while the one of the second post-Newtonian approximation is positive. The two contributions imply a smaller mass needed for an overdensity to initiate the gravitational collapse than the one given by the Newtonian theory.

In this paper, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss–Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss–Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of non-linear electrodynamics (NLED), plasma and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

In this paper, we study conformal Ricci soliton and almost conformal Ricci soliton within the framework of paracontact manifolds. Here, we have shown the characteristics of the soliton vector field and the nature of the manifold if para-Sasakian metric satisfies conformal Ricci soliton. We also demonstrate the feature of the soliton vector field V and scalar curvature when the para-Sasakian manifold admitting conformal Ricci soliton and vector field is pointwise collinear with the characteristic vector field $\xi$. Next, we prove that if a K-paracontact manifold confesses a gradient conformal Ricci soliton, then it is Einstein. Next, we show that a para-Sasakian metric reveals with an almost conformal Ricci soliton that is either Einstein or $\eta$-Einstein metric if the soliton vector field V is an infinitesimal contact transformation. Lastly, we decorate an example of conformal Ricci soliton on para-Sasakian manifold.

We explore an autonomous system analysis of dark energy models with interactions between dark energy and cold dark matter in a general systematic approach to cosmological fluids. We investigate two types of models such as local and non-local ones. In particular, a local form of interaction is directly proportional to only the energy density, while a non-local interaction is directly proportional to the energy density as well as the Hubble parameter. As a consequence, it is explicitly demonstrated that in both cases there exist the stability points in terms of cosmological parameters. This work aims at obtaining acceleration and stability using interaction models without modifying the matter or geometric component of the Universe.

In this paper, we investigate the recently proposed New Barrow Agegraphic Dark Energy (NBADE) model by taking the distinct values of Barrow parameter $\mathrm{\Delta }$ in the context of Friedmann–Robertson–Walker (FRW) Universe. We have used different diagnostic tools to discriminate NBADE model from $\mathrm{\Lambda }$CDM model, namely statefinder pair $(r,s)$, $(r,q)$, ${\omega }_B-{\omega }_B^{\prime }$ pair, jerk parameter and $O_m(z)$ diagnostic planes. The trajectories for the evolution of statefinder parameters $r-s$, $r-q$, ${\omega }_B-{\omega }_B^{\prime }$ pair, jerk parameter and $O_m$ diagnostic are plotted of NBADE model using distinct values of the Barrow parameter $\mathrm{\Delta }$ at initially ${\mathrm{\Omega }}_{B0}=0.70$ and $H_0=67$.

In this paper, the Morris–Thorne wormholes are studied in the background of $f(R,T)=R+\alpha R^2+\beta lnT$ gravity, where $\alpha$ and $\beta$ are constants. The wormhole solutions are derived in two cases with different assumptions for the matter forms. In each case, the null energy condition (NEC) is analyzed and the range of parameters satisfying the NEC are determined. Further, the stability of solutions is examined with the help of the generalized Tolman–Oppenheimer–Volkoff (TOV) equation.

In this paper, we introduce a new kind of super warped product spaces ${\bar{M}}_{(I)}=I^{1|0}{\times }_f{M}^{m|n}$, ${\bar{M}}_{(II)}=I^{0|1}{\times }_f{M}^{m|n}$, and ${\bar{M}}_{(III)}=I^{1|1}{\times }_f{M}^{m|n}$, where $M^{m|n}$ is a supermanifold of dimension $m|n$, $I^{\delta |{\delta }^{\prime }}$ is a superdomain with $I=(0,1)$ and $\delta ,{\delta }^{\prime }\in \{0,1\}$, subject to the warp functions $f(t)$, $f(\bar{t})$, and $f(t,\bar{t})$, respectively. In each super warped product space, ${\bar{M}}_{(I)}$, ${\bar{M}}_{(II)}$, and ${\bar{M}}_{(III)}$, it is shown that Einstein equations ${Ḡ}_{AB}=-\bar{\mathrm{\Lambda }}{ḡ}_{AB}$, with cosmological term $\bar{\mathrm{\Lambda }}$ are reducible to the Einstein equations $G_{\alpha \beta }=-\mathrm{\Lambda }{g}_{\alpha \beta }$ on the super space $M^{m|n}$ with cosmological term $\mathrm{\Lambda }$, where $\bar{\mathrm{\Lambda }}$ and $\mathrm{\Lambda }$ are functions of f(t), $f(\bar{t})$, and $f(t,\bar{t})$, as well as (m, n). This dependence points to the origin of cosmological terms which turn out to be within the warped structure of the super spacetime. By using the generalized Robertson–Walker spacetime, as a super spacetime, and demanding for constancy of $\bar{\mathrm{\Lambda }}$, we can determine the warp functions and $\mathrm{\Lambda }$ which result in finding the solutions for Einstein equations ${Ḡ}_{AB}=-\bar{\mathrm{\Lambda }}{ḡ}_{AB}$ and $G_{\alpha \beta }=-\mathrm{\Lambda }{g}_{\alpha \beta }$. We have discussed the cosmological solutions, for each kind of super warped product space, in the special case of $M^{3|0}$.

The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras, called Hom-pre-Malcev algebras. We also introduce the notion of Kupershmidt operators of Hom–Malcev and Hom-pre-Malcev algebras and show the connections between Hom–Malcev and Hom-pre-Malcev algebras using Kupershmidt operators. Hom-pre-Malcev algebras generalize Hom-pre-Lie algebras to the Hom-alternative setting and fit into a bigger framework with a close relationship with Hom-pre-alternative algebras. Finally, we establish a deformation theory of Kupershmidt operators on a Hom–Malcev algebra in consistence with the general principles of deformation theories and introduce the notion of Nijenhuis elements.

In this study, we present the evolution of cosmological perturbations in a universe consisting of standard matter and interacting vacuum. We use the 1 + 3 covariant formalism in perturbation framework and consider two different models for the interacting vacuum; namely, a linear interacting model and interaction with creation pressure model. For both models, we derive the evolution equations governing the growth of linear perturbations for both radiation- and dust-dominated universe. We find numerical solutions in appropriate limits, namely long and short wavelengths. For both models, the perturbations grow with time (decay with redshift), showing that structure formation is possible in an accelerated cosmic background. The perturbation amplitudes — and their relative scalings with those of $\mathrm{\Lambda }$CDM — depend on the values of the interaction parameters considered, and in a way that can be used to constrain the models using existing and future large-scale structure data. In the vanishing limits of the coupling parameters of the interaction, we show that standard $\mathrm{\Lambda }$CDM cosmology, both background and perturbed, is recovered.

The aim of this paper is to explore the conceptual and mathematical physics foundations of the work of Sir Roger Penrose. This is a transcript of an interview that took place on 15 November 2021.

In this study, a homogeneous and anisotropic Bianchi type-I universe model is considered taking the cosmological constant as a variable in the context of f (R, T) gravity. The presented model relies on a unique condition of constant jerk parameter as j = 1, which corresponds to a flat $\mathrm{\Lambda }$CDM model that leads to a variable deceleration parameter. The exact solution of the field equations is obtained under that condition, and the physical and geometrical features of the model are discussed through the paper. The model has been shown to be successful in explaining recent cosmological observations such as the universe’s expansion decelerates in the early universe and accelerates in the late universe, in agreement with their current data.

In this paper, the tunneling of scalar particles near the event horizons of Riemann space time, BTZ black hole and Schwarzschild–de Sitter black hole are investigated by applying Hamilton–Jacobi equation with Lorentz violation theory in curved space time. The modified Hamilton–Jacobi equation is derived from Klein–Gordon equation of scalar particles induced by Lorentz violation theory in curved space time. The Hawking temperatures of Riemann space time and the BTZ black hole are modified due to the effect of Lorentz violation theory. Moreover, the Bekenstein–Hawking entropy near the event horizon of Schwarzschild–de Sitter black hole is also modified due to Lorentz violation theory. It is observed that the modified values of Hawking temperatures and change in Bekenstein–Hawking entropy depend upon the ether-like vectors $u^{\alpha }$.

We introduce the complete pseudo-Riemannian manifold ${𝔼}_3^1$ with a conformally flat pseudo-metric satisfying Einstein’s equation. First, we get a theorem that associates the curvatures of a non-degenerate surface belonging to conformally equivalent spaces, say ${𝔼}_3^1$ and ${ℝ}_1^3$. Next, we evaluate the existence of non-degenerate helicoidal surfaces in some conformally flat pseudo-spaces with pseudo-metrics corresponding to particular conformal factors (for example, a certain rotational symmetry with translational symmetry). We determine these conformal factors according to the causal characters of the axis of rotation. Right after, we get a two-parameter family of non-degenerate helicoidal surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions, corresponding to both spacelike and timelike axes of rotation. As for the lightlike axis, we discuss some particular cases.

In this paper, Dirac’s equation in anisotropic Bianchi-type-I background spacetimes is treated with respect to orthonormal frames. By specializing to the massless spinor case and metrics with power-law scale factors and planar symmetry, an analytical expression of the approximate time evolution operator (TEO) is derived. By use of this operator, all approximate spinor solutions can be generated. By construction, these solutions agree asymptotically and at early times with the exact solutions.

The operator approach is also well adapted for studying the case of small deviations from conformally flat backgrounds. In particular, it can be shown that the limiting case of vanishing anisotropy renders the correct result.

We explore some cosmological features of the newly suggested 4D Gauss–Bonnet gravity through two different models assuming a varying cosmological constant $\mathrm{\Lambda }(t)$. Observational constraints, such as the cosmic transit and the flat curvature, have been considered in constructing the models. The cosmology in this work has been probed using a given scale factor derived from the desired cosmic behavior which is the inverse of the usual viewpoint. Several models for $\mathrm{\Lambda }(t)$ have been proposed in the literature; we use two different ansatze of varying $\mathrm{\Lambda }$ and compare the obtained result. We have found that the second ansatz for the varying $\mathrm{\Lambda }$, expressed in terms of the Hubble parameter H, gives better results than the first one. The sound speed causality condition along with all nonlinear energy conditions are satisfied for the case of $\mathrm{\Lambda }(H)$. The cosmographic parameters have been investigated.

Traversable wormholes are always supported by negative energy and therefore an exotic matter source is required for their principle existence. In this work, we consider Casimir energy density as an exotic matter source in the framework of f (T) gravity. In this way, we examine the behavior of shape function, equation of state parameters, energy conditions and stability conditions for wormhole geometry in teleparallel and f (T) gravity. We also assume three different generalized uncertainty principle corrected Casimir wormhole models. We analyze the effect of the generalized uncertainty principle minimal parameter on the constructed wormhole properties in f (T) gravity.