International Journal of Geometric Methods in Modern Physics

In this paper, we discuss how in certain theories of spacetime admitting a maximal proper acceleration Hawking radiation does not completely evaporate the black hole. The black hole remnant’s mass depends on the inverse of the maximal acceleration. Furthermore, as a consequence of a duality between the minimum mass that a Schwarzschild black hole can have in such spacetimes and the maximal acceleration, we show that in certain theories with a maximal acceleration, there must be an upper uniform bound on the value of the force that can be exerted on test particles.

Motivated by the work of Astashenok et al. [Causal limit of neutron star maximum mass in f(R) gravity in view of GW190814, Phys. Lett. B 816 (2021) 136222], the present work aims at studying the behavior of f in f(R) gravity and attempts to study the causal mass–radius relation of a massive neutron star. To initiate the study, the background evolution is taken as of modified Chaplygin gas. We observed the positive behavior of f. The Tolman–Oppenheimer–Volkoff equation has been taken into consideration which states the spherical stellar structure of non-rotating neutron stars. We also observed that the mass–radius relationship is close to the Tolman–Oppenheimer–Volkoff limit. The change of density of neutron stars with respect to the radius clearly manifests the actual variation of density from the core to the surface of a neutron star in the background evolution of modified Chaplygin gas, which can unify the early inflation with the late time acceleration of the universe.

In the present work, we consider the recently proposed non-interacting Barrow holographic dark energy (Int. J. Geom. Methods Mod. Phys. 18(01) (2021) 2150014, doi:10.1142/S0219887821500146) with Hubble horizon as IR cutoff in a flat FLRW universe. We examine the evolutionary behavior of deceleration parameter and equation of state parameter for the different Barrow exponent $\mathrm{\Delta }$, and observe suitable behavior in the model. We choose $\mathrm{\Delta }>2$ in the non-interacting Barrow holographic dark energy which is explained by a phantom scalar field, then we exhibit the phantomic narration of the Barrow holographic dark energy with $\mathrm{\Delta }>2$ and reconstruct the potential of the phantom scalar field.

In this paper, we formulate exact anisotropic interior solutions of the Einstein field equations preserving spherically symmetric geometry in the context of $f(T,{𝒯})$ gravity. To make the system close, we consider a linear function in torsion scalar $(T)$ and trace of energy–momentum tensor $({𝒯})$, and employ the well-known Karmarkar condition with metric potential of the form $e^{\lambda (r)}=1+c{r}^2{(\mathrm{\text{erf}}(1+a{r}^2))}^2$. We consider standard data of some well-known compact star models (Vela X-1, PSR J1614-2230, Cen X-3 and EXO 1785-248) to estimate the unknown model parameters. We perform physical analysis of the developed model in detail, which includes density profile, pressure profile, anisotropy factor, mass function, gravitational/surface redshift, compactness factor, energy bounds, stability criteria, and the equilibrium condition. The analysis leads us to conclude that solutions are well-behaved and physically viable.

In this paper, we study the effect of the Generalized Uncertainty Principle (GUP) on the shadow of GUP-modified Kerr black hole and the correspondence between the shadow radius and the real part of the quasinormal modes (QNMs). We find that the shadow curvature radius of the GUP-modified Kerr black hole is bigger compared to the Kerr vacuum solution and increases linearly monotonically with the increase of the GUP parameter. We then investigate the characteristic points of intrinsic curvature of the shadow from a topological point of view to calculate the angular size for these curvature radii of the shadow. To this end, we have used the EHT data for the M87* black hole to constrain the upper limits of the GUP parameter and our result is $\beta <10^{95}$. Finally, we have explored the connection between the shadow radius and the scalar/electromagnetic/gravitational QNMs. Using the orbit of S2 star we have obtained a bound for the GUP parameter $\beta <10^{87}$. The GUP-modified Kerr black hole is also used to provide perfect curve fitting of the particle oscillation upper and lower frequencies to the observed frequencies for three microquasars and to restrict the values of the correction parameter in the metric of the modified black hole to very reasonable bound $\beta <10^{77}$.

Recently, Barrow et al. showed that chaotic dynamical systems may be obtained from small fluctuations of torsion in cosmological plasmas. Following this idea our goal in this paper is to show analytically that torsion fluctuations in primordial plasmas induce chiral fluctuations, magnetic field fluctuations, dynamo plasma instabilities, as well as rapid oscillations in the chiral plasma. These phenomena are important in plasma relaxation to allow for a plasma dynamo instability to induce a lower electric voltage in plasmas. This phenomenon is induced in Minkowskian plasma physics, but to our knowledge it is proved for the first time in Einstein–Cartan sort of cosmology. In cosmological models where torsion gravity and electromagnetic fields are non-minimally coupled, dynamo instability is obtained when conductivity fluctuations are driven by torsion. Moreover, symmetry breaking of plasmas is shown here to be obtained from conductivity torsion fluctuations, which serves to bypass Zeldovich anti-dynamo theorem, inducing a dynamo onset, as shown recently in domain planar walls [L. Garcia de Andrade, Einstein–Cartan spin-polarised nucleons in domain wall dynamos, Ann Phys. (N.Y.) 432 (2021) 168558.]. Moreover, chiral charge fluctuations are shown to be induced by torsion fluctuations. It is shown that chiral charges may vanish, whereas the effective chiral charges may be driven by torsional fluctuations. It is also shown that dynamo electric field induces a magnetic helicity which oscillates and dynamo action is shown to dominate oscillations. This agrees with the results obtained from loop voltage. Chiral effective charges’ fluctuations are derived to be proportional to the product of anisotropic conductivity and magnetic field fluctuations.

The purpose of this paper is to investigate the non-singular solutions of gravitationally vacuumed condensate star in the realm of the f(R, T, Q) theory, where Q = R_σηT^ση. The three-layered gravastar structure has been constructed in the cylindrical spacetime under the effects of electromagnetism in the modified theory. Furthermore, we have studied the effects of electromagnetism on the effective matter, which involves the perfect fluid and isotropic pressure in it. To gain this objective, we consider the cylindrical spacetime and evaluate the three regions mathematically. The metric coefficients are calculated independently for each region. To match the region I and II at a hypersurface, the junction conditions have been calculated. To figure out the dependency of the thickness of shell on different physical features of gravastar, we interpret it graphically as well as mathematically. Subsequently, the noticeable facts are accomplished.

In this paper, we investigate Barrow holographic dark energy (BHDE) using Hubble horizon as infrared cut-off in the framework of Bianchi-I, anisotropic model by considering hybrid expansion law (HEL). We have examined different cosmological parameters like energy density parameters, EoS parameter of BHDE model, which support the present accelerated expansion of the Universe. We have also reconciled BHDE by reconstructing the evolution of scalar field potential. The K-essence has been taken for the study of this reconstruction, which also exhibits the accelerated expansion at present.

In this paper, we developed, in detail, the geometric structure of a certain type of geometry usually used in physical applications. This paper contains building blocks (BB), tensors of different orders, curves admitted by the geometry and a comparison between this geometry and others used in the literature. Second-order symmetric and skew-symmetric tensors, usually used for physical applications in the context of the geometrization philosophy, are given. Also, in the framework of the same philosophy, the admitted curves can be used as equations of motion of test particles for any field theory constructed in this geometry.

This study explores the anisotropic stellar structures in the background of f(R) modified gravity, where R is a Ricci scalar. To complete this analysis, we use the spherically symmetric space-time. Further, an anisotropic source of matter is used to investigate the stability of stellar structures. The embedded class-I approach is used to demonstrate the behavior of stellar structures. Schwarzschild space-time is taken as exterior space-time to calculate the values of involved parameters. The observational data of three different stars, like LMC X-4, Cen X-3, and EXO 1785-248, are taken for the current analysis. For this study, we used Starobinsky-like model f(R) = R + βR² for f(R) modified gravity. The stability analysis is discussed via the equation of state (EoS) parameters, Tolman–Oppenheimer–Volkoff (TOV) equation, anisotropy, etc. Graphical and analytical results are provided as viable results in f(R) gravity.

In this paper, we discuss wormhole models in the Einsteinian-cubic-gravity for some specific shape functions of the form $b(r)=r^{-n}{r}_0^{n+1}$, $b(r)=r^n{r}_0^{1-n}$, and $b(r)=A{tan}^{-1}(Cr)$. For this purpose, we consider the spherically symmetric static geometry with anisotropic source of matter for which different energy conditions are analyzed. We present the wormhole conditions and the energy conditions graphically. In particular, we notice that the null energy condition is strongly violated, which confirms the presence of exotic matter for the specific shape functions chosen here. Therefore, traversable wormholes exist in the Einsteinian-cubic-gravity for the hybrid-specific shape functions $b(r)=r^{-n}{r}_0^{n+1}$, $b(r)=r^n{r}_0^{1-n}$, and $b(r)=A{tan}^{-1}(Cr)$.

In this paper, we examine the optical soliton solutions of nonlinear partial differential equations belonging to the nonlinear Schrödinger (NLS) class which includes cubic focusing NLS equation and paraxial NLS equation in a Kerr media. We construct the optical soliton of these models using a new extended direct algebraic method (NEDAM). The resulting solutions carry a variety of new families including singular solutions of Types 1 and 2, dark, darkly bright and dark singular soliton solutions. Sufficient conditions are provided for these structures to exist. NEDAM is successfully applied to supposed nonlinear model and provides us some new and interesting solitary wave solutions. These solutions contain the trigonometric-, hyperbolic- and exponential-type functions. Moreover, to present the physical importance of the considered model, some 3D and 2D diagrams of obtained solutions are plotted by using Mathematica under the suitable choice of involving parameters values.

This paper presents theoretical arguments that certain virtual bound states carry the trace component of affine torsion. The motivation for this work is that Einstein–Cartan theory, which extends general relativity by including torsion to model intrinsic angular momentum, is becoming more credible. We are not aware of any situation for which there is evidence or substantial argument for the presence of torsion trace, except in the continuum theory of edge dislocations in crystals. The main evidence for the hypothesis consists of analogies between the structure of virtual bound states and (a) geometry of dislocations in crystal lattices, which are modeled with torsion; and (b) modeling of intrinsic angular momentum by torsion in Einstein–Cartan theory and the theory of micro-elasticity. The work focuses on conjectured presence of torsion in para-positronium, which intermediates annihilation of an electron and a positron with opposite z-spins. If the virtual bound state carries torsion, then the local law of conservation of angular momentum can hold over the spacelike separation during annihilation.

In this paper, the Lie symmetry analysis method is applied to the space-time fractional cubic Schrödinger equation. The group generators are obtained for the system of space-time fractional differential equations. They are utilized to reduce the system of fractional partial differential equations with Riemann–Liouville fractional derivative to the system of fractional ordinary differential equations with Erdélyi–Kober fractional derivative. Then, the power series method is applied to derive explicit solutions for the reduced systems. Furthermore, the traveling wave solutions of the integer-order cubic Schrödinger equation is obtained.

$\kappa$-Poincaré invariant gauge theories on $\kappa$-Minkowski space-time, which are noncommutative analogs of the usual U(1) gauge theory, exist only in five dimensions. These are built from noncommutative twisted connections on a hermitian right module over the algebra coding the $\kappa$-Minkowski space-time. We show that twisting the action of this algebra on the hermitian module, assumed to be a copy of it, affects neither the value of the above dimension nor the noncommutative gauge group defined as the unitary automorphisms of the module leaving the hermitian structure unchanged. Only the hermiticity condition obeyed by the gauge potential becomes twisted. Similarities between the present framework and algebraic features of twisted spectral triples are exhibited.

Let M be an almost cosymplectic manifold such that the Reeb vector field is Killing. In this paper, it is proved that if the metric of M satisfying the $\eta$-Einstein condition is an $\eta$-Ricci soliton, then either M is Ricci flat or the potential vector field is an infinitesimal contact transformation. Also, a concrete example of cosymplectic $3$-manifold admitting non-trivial Ricci and $\eta$-Ricci solitons is constructed.