International Journal of Geometric Methods in Modern Physics

The idea that general relativity could be an effective model, of a yet unknown theory of gravity, has gained momentum among theoretical physicists. The polynomial affine model of gravity is an alternative model of affine gravity that possesses many desirable features to pursue a quantum theory of gravitation. In this paper, we argue that such features are a consequence of the lack of a metric structure in the building of the model, even though a emergent metric could be defined. The model introduces additional degrees of freedom associated to the geometric properties of the space, which might shed light to understand the nature of the dark sector of the Universe. When the model is coupled to a scalar field, it is possible to define inflationary scenarios.

In this paper, we explore some emerging properties of the stellar objects in the frame of the $f(R,\varphi )$ gravity by employing the well-known Karmarkar condition, where $R$ and $\varphi$ represent the Ricci scalar and scalar potential, respectively. We demonstrate the embedded class-I technique by using the static spherically symmetric line element along with anisotropic fluid matter distribution. Furthermore, to achieve our goal, we take a specific expression of metric potential $g_{rr}$, already presented in the literature, and proceed by using the Karmarkar condition to obtain the second metric potential. To get the value of unknown parameters of the compact structures, we compare the Krori–Barua spacetime with spherically symmetric spacetime. Moreover, we examine the physical attributes of compact objects by presuming three viable $f(R,\varphi )$ models. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkoff equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars.

In this paper, we investigate the deflection angle and the trajectories of the light rays near black holes in M-theory scenarios. Using the Gauss–Bonnet theorem, we first discuss the deflection angle of the light rays near four- and seven-dimensional AdS black holes derived from the M-theory compactifications on the real spheres on $S^7$ and $S^4$, respectively. Then, we examine brane number effect and the rotating parameter on such light behaviors. We finish this work by providing a study of the light ray trajectories via the equations of motion associated with $M2$ and $M5$-branes.

In this paper, we have investigated Bianchi type-III bulk-viscous string cosmological models in the frame-work of scalar–tensor theory of gravitation. To solve the field equations for the bulk-viscous fluid and perfect fluid under the following physically relevant conditions: (i) Expansion scalar ($𝜃$) in the model is directly proportional to the shear scalar ($\sigma$). (ii) $p=\omega \rho$, where $\omega (0\le \omega \le 1)$ is a constant (iii) $\xi ={\xi }_0{\rho }^{\gamma }$, where ${\xi }_0$ and $\gamma (>0)$ are real constants. The observed phase transition of the presented universe from the early decelerating phase to the present epoch is in good accordance with the astronomical measurements. A detailed discussion on energy conditions and stability of the all models is analyzed through graphical representation.

Immediate local impacts of cosmic acceleration upon a rapidly rotating black hole are very interesting in recent studies. In this paper, the stability of a rapidly rotating black hole and the minimum value of the ratio between the black hole’s angular momentum to it’s mass which ensures the stability, are investigated simultaneously. Also, two modern forms of uncertainty relations are proposed by enhancing the usual Heisenberg algebra with superior terms, in order to supervise on thermodynamic properties of the rotating black hole. An asymptotically flat Kiselev black hole solution, cultivated by quintessence field is chosen for this purpose. The local shifts in spacetime geometry next to the rotating black hole can be resolved from a modified metric, occupying the surrounding spacetime of the black hole. The angular momentum of a rotating black hole depends on the rate of change in acquiring mass by it. On the other hand, at the same time, due to the effect of the quintessence field, there exists repulsive gravitational force inside the black hole. So, there is an uncertainty in the position of innermost stable circular orbit as well as radius of the rotating black hole. This uncertainty is also investigated in our work. Relying on two new forms of uncertainty principle, the modified thermodynamic variables like black hole’s Hawking temperature, heat-capacity, entropy at the black hole’s event horizon, etc. are computed under rotation. Quantum corrections of black hole’s Hawking temperature, entropy, free-energy, etc. are also explored. Further, quantum corrected heat capacity of the rotating black hole is studied and also thermal stability is inquired. The existence of transitions of phase in case of a rapidly rotating black hole are also found out. Again, quantum corrected entropy of black hole contains logarithmic terms and their effects on thermal stability of the rotating black hole are also discussed. Modifications in the mass-temperature, specific heat, etc. of a rotating black hole are also presented according to the modified extension parameters.

In this paper, we study the PNDP-manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the Weyl tensor are the dimensions of the PNDP-manifold and the interaction that emerges as “virtual” point-like manifolds and as a manifold with positive/ negative dimensions results in the generation of the purely electric or purely magnetic parts of the Weyl tensor. The PNDP metric for the electric or magnetic parts of the Weyl tensor is also derived. The generalized Lorentz transformations on the PNDP manifold are introduced. These can give rise to novel forms of gauge theories if we consider local Lorentz transformations. Also we briefly show that principal fiber bundles with PNDP manifolds as base manifolds can be constructed.

This paper aims to provide an explicit computation of the equivariant noncommutative residue density of which yield the metric and Einstein tensors on even-dimensional Riemannian manifolds. A considerable contribution of this paper is the development of the spectral Einstein functionals by two vector fields and the equivariant Bismut Laplacian over spinor bundles. We prove the equivariant Dabrowski–Sitarz–Zalecki-type theorems for lower dimensional spin manifolds with (or without) boundary.

The presence of matter in general relativity can cause spacetime to curve. This paper investigates the spacetime properties of the Einstein–Maxwell–Yang–Mills (EMYM) black hole by discussing the geodesic motion of neutral and charged particles. By studying the Lagrangian of these particles, equations of motion and effective potential are obtained in the asymptotic flat and (A)dS spacetimes. Moreover, for the motion of a neutral particle, it is found that there exist stable elliptic/hyperbolic orbits and unstable orbits with different energies by discussing the effective potential and the phase-plane analysis. However, for the motion of a charged particle, there exists an equilibrium point that separates these orbits. In addition, the effects of the system parameters on the potential are analyzed, including the masses of the black hole and charged particles, charges, the cosmological constant, and the strength of the external magnetic field.

In this paper, we present a complete solution for the problem of a relativistic particle without spin, of mass M and charge e, subject to linear combination of the Yukawa and Deformed Hulthén Potentials. In particular, we assess the radial Green’s function for the l states by introducing appropriate approximations of the terms (1/r) and (1/(r)). By choosing an appropriate spacetime transformation, the energy spectrum and the normalized wave functions of the bound states are obtained from the poles of Green’s function and its residues.

Magnetic flux surfaces allow us to examine surfaces in a laboratory environment. In this paper, we obtain differential equations to find the magnetic flux surfaces. Differential equations are needed for defining, modeling and solving engineering problems. They are particularly widely used in systems and control theory. First, we thought of linear combinations of Killing vector fields in three-dimensional Euclidean space $E^3$. We obtain partial differential equations by using these vectors. We find magnetic flux surface families with the solutions of these equations. Examples of the magnetic flux surface families members found by solving each equation are given.

In this paper, we reconstruct an $f(T)$ function from $\mathrm{\Lambda }$CDM model and obtained field equations for this function $f(T)=\frac{T}{2}+c_1{(-T)}^{\frac{1}{2}}-2\mathrm{\Lambda }$ in a flat FLRW viscous-fluid dusty universe, where $T$ is the torsion scalar, $c_1$ is an arbitrary constant and $\mathrm{\Lambda }$ is the cosmological constant. We have solved the field equations and obtained an scale factor $a(t)=c_2\left[\right.\mathrm{\text{sinh}}\left(\right.\frac{2\mathrm{\Lambda }}{9{(1-{\xi }_0)}^2}t+\frac{c_1\mathrm{\Lambda }}{3(1-{\xi }_0)}\left)\right.{\left]\right.}^{\frac{3(1-{\xi }_0)}{2}},{\xi }_0\ne 1$ with $c_2$ as an integrating constant and ${\xi }_0$ is an arbitrary constant generated from viscous fluid, and this type of scale factor gives a time-dependent deceleration parameter. We have made observational constraints on Hubble parameter $H(z)$ and apparent magnitude $m(z)$ with observational datasets $H(z)$ data and SNe Ia data by applying ${\chi }^2$-test, to obtain the best-fit values of model parameters. Using these values of cosmological parameters, we have discussed our model results. We have obtained a transit phase accelerating quintessence dark energy model in viscous-fluid universe with effective equation of state ($-1.65\le {\omega }^{\mathrm{\text{eff}}}\le -0.79$).

In this paper, the gravitational field is revisited as a manifestation of defects in continuum media. The Schwarzschild solution is then interpreted as a permanent plastic deformation of space-time and we conjecture that a discrete dislocation leads to a discrete mass spectrum. The dislocation of this black hole is considered as a quasi-local defect, once it vanishes at the spatial infinity. The C-metric is also considered under this viewpoint. The dislocations in such a space-time reveal how the quasi-local defect interacts with a global defect due to the semi-infinite cosmic string. The disclinations are obtained in agreement at certain limits with the literature.

This study focuses on the dynamics of magnetized strange quark matter collapsing near a star in rainbow gravity. The study computes various dynamical variables, including mass density, pressure, and magnetic field strength, to ensure the physical existence of the fluid, and graphically verifies the energy conditions. These variables combine to form a black hole, and the study estimates the time and distance of apparent horizon formation, which are both reduced by the magnetic field. Additionally, the study observes that the energy of probing particles impacts mass density, pressure, magnetic field intensity, distance, and time of horizon creation, which helps to resolve the information paradox. It is also noticed that the magnetic field accelerates the collapse.

In this paper, we introduce the notion of radical transversal screen slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds with examples. We obtain an existence theorem and study the geometry of distributions involved in the definition. Moreover, we define the notion of radical transversal screen semi-slant lightlike submersions with examples and prove a characterization theorem. We also study the integrability and totally geodesic foliations of distributions on a fiber of these lightlike submersions.

The $(G^{\prime }/G)$-expansion scheme is used to execute many wave results for the partial differential equation, namely, the nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation which plays a significant role in mathematical physics, and this equation is accomplished in quantum electron–positron–ion magneto plasmas. The Lie approach is used to find the infinitesimal generators, and group invariant solutions, and help us to reduce the considered PDEs into ODEs. Then a planer dynamical system approach is used to see the existence of closed-form solutions. All possible phase portraits are obtained and the existence of electrostatic wave potentials is reported. Meantime, periodic and super-nonlinear electrostatic wave potentials are found for different initial value conditions with the help of the Runge–Kutta method. Moreover, new traveling wave patterns of the considered models are constructed and presented graphically. Then, the conserved vectors of the given physical model with the use of the multiplier scheme are presented.

The major goal of this study is to examine the viability and stability of anisotropic compact stellar objects using the Karmarkar condition in $f({𝒬})$ gravity, where ${𝒬}$ is a scalar of nonmetricity that explains gravitational effects. We consider a static spherical metric in inner and Schwarzschild spacetime in outer regions of the star to analyze the physical attribute of Vela $\mathrm{\text{X}}-1$, SAX J 1808.4−3658, 4U 1608−52, PSR J0348+0432 and 4U 1820−30 compact stars. The unknown parameters are determined through observational values of the radius and mass of the considered compact stars. We take a specific model of this theory to evaluate the energy density, pressure elements, anisotropy, equation of state parameters and energy bounds in inner region of suggested stellar objects. The equilibrium position of these stars is examined through Tolman–Oppenheimer–Volkoff equation and their stability checked by Herrera cracking method and adiabatic index. We find more viable as well as stable compact stars in this modified theory.

A curvature identity is studied through homogenous pseudo-Riemannian four-manifolds with nontrivial isotropy. Then, special classes of the considered spaces i.e. weakly-Einstein examples are completely classified.