International Journal of Geometric Methods in Modern Physics

We consider a $(4+2k)$-dimensional Einstein–Gauss–Bonnet model with the cosmological $\mathrm{\Lambda }$-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional cosmological model deals with three factor spaces: the external 3-dimensional “our” world and internal subspaces with dimensions $k_1=k$ and $k_2=k$.

We present a unified approach for the study of idealized gravitational compact objects like wormholes (WHs) and horizonless stars, here simulated by the presence of boundary conditions at a deeply inner wall. At the classical level, namely neglecting quantum effects, the presence of the wall leads to characteristic echoes following the usual ringdown phase, such that it can discriminate black holes from other horizonless, and probably exotic, compact objects. With regard to this issue, an analytical though approximated expression for the complex frequencies of the quasinormal echoes is found and discussed. At the quantum level, we show that static WHs do not radiate.

In this paper, we present a complete classification of static plane symmetric spacetimes via their homothetic symmetries of the energy–momentum tensor, known as homothetic matter collineations (HMCs). The HMC equations for these spacetimes are derived and then solved by considering the degeneracy and non-degeneracy of the energy–momentum tensor. In the former case, we have obtained 6, 11 and infinite number of HMCs, while in the latter case, the solution of HMC equations yields 6-, 7-, 8-, 10- and 11-dimensional algebra of HMCs. The obtained HMCs generate some differential constraints involving the components of the energy–momentum tensor. Some examples of static plane symmetric spacetime metrics satisfying these constraints are provided and the physical interpretations of these metrics are discussed.

We study the Horizon Wave Function (HWF) description of a generalized uncertainty principle (GUP) black hole in the presence of two natural cutoffs as a minimal length and a maximal momentum. This is motivated by a metric which allows the existence of sub-Planckian black holes, where the black hole mass $m$ is replaced by $M=m(1+\frac{{\beta }^2}{2}\frac{m_{\mathrm{\text{pl}}}^2}{m^2}-\beta \frac{m_{\mathrm{\text{pl}}}}{m})$. Considering a wave-packet with a Gaussian profile, we evaluate the HWF and the probability that the source might be a (quantum) black hole. By decreasing the free parameter, the general form of probability distribution, ${{𝒫}}_{\mathrm{\text{BH}}}$, is preserved, but this resulted in reducing the probability for the particle to be a black hole accordingly. The probability for the particle to be a black hole grows when the mass is increasing slowly for larger positive $\beta$, and for a minimum mass value it reaches to $0$. In effect, for larger $\beta$ the magnitude of $M$ and $r_H$ increases, matching with our intuition that either the particle ought to be more localized or more massive to be a black hole. The scenario undergoes a change for some values of $\beta$ significantly, where there is a minimum in ${{𝒫}}_{\mathrm{\text{BH}}}$, so this expresses that every particle can have some probability of decaying to a black hole. In addition, for sufficiently large $\beta$, we find that every particle could be fundamentally a quantum black hole.

Toward a unified algebraic theory for mean-field Hamiltonian describing paired- and unpaired-mode effects, in this paper, we propose a generalized Hartree–Bogoliubov mean-field Hamiltonian in terms of fermion pair and creation-annihilation operators of the $\mathrm{\text{SO}}(2N+1)$ Lie algebra. We diagonalize the generalized Hartree–Bogoliubov mean-field Hamiltonian and throughout its diagonalization we can first obtain the unpaired mode amplitudes which are given by the self-consistent field parameters appeared in the Hartree–Bogoliubov theory together with the additional self-consistent field parameter in the generalized Hartree–Bogoliubov mean-field Hamiltonian and by the parameter specifying the property of the $\mathrm{\text{SO}}(2N+1)$ group. Consequently, it turns out that the magnitudes of these amplitudes are governed by such parameters. Thus, it becomes possible to make clear a new aspect of such results. We construct the Killing potential in the coset space $\frac{\mathrm{\text{SO}}(2N)}{U(N)}$ on the Kähler symmetric space which is equivalent to the generalized density matrix. We show another approach to the fermion mean-field Hamiltonian based on such a generalized density matrix. We derive an $\mathrm{\text{SO}}(2N+1)$ generalized Hartree–Bogoliubov mean-field Hamiltonian operator and a modified Hartree–Bogoliubov eigenvalue equation. We discuss on the mean-field theory related to the algebraic mean-field theory based on the generalized density matrix and the coadjoint orbit leading to the nondegenerate symplectic form.

In this paper, in the framework of the Brans–Dicke [Phys. Rev. 124 (1961) 925] Gravitation theory, we propose to study the spatially homogeneous, anisotropic and axially symmetric model filled with dark matter and dark energy. Here, we consider the modified holographic Ricci dark energy proposed by Chen and Jing [Phys. Rev. B 679 (2009) 144] as a feasible state of darkness. To achieve a solution, we consider the time-dependent deceleration parameter, which contributes to the average scale factor of $a(t)=\mathrm{\text{exp}}\left(\right.\frac{1}{\beta }\sqrt{2\beta t+\alpha }\left)\right.$, where $\alpha >0$ and $\beta >0$ are arbitrary constants. We have derived field equations of Brans–Dicke theory of gravitation with the help of an axially symmetric anisotropic Bianchi-type space-time. We have determined the cosmological parameters, namely, deceleration parameter, matter energy density, anisotropic dark energy density, BD scalar field, skewness parameter, EoS parameter and jerk parameter. Here, the various phenomena like the Big Bang, expanding the universe, and shift from anisotropy to isotropy are observed in the model. A comprehensive physical debate of these dynamic parameters is provided through a graphical representation. We observe that we have a quintessence model that exhibits a smooth transition from decelerated stage to an accelerated phase of the universe. This situation is in complete agreement with the modern cosmology scenario. Some physical and geometric behaviors are also discussed and discovered to be in excellent agreement with SNe Ia Supernova’s latest observations.

In this study, we handle the spherical product surface in Galilean $3$-space ${𝔾}_3$. We calculate the Laplacian operator of the Gauss map of this surface. Then we give the necessary and sufficient conditions for spherical product surface to have harmonic Gauss map and we give a visualization of this type surface in ${𝔾}_3$. Furthermore, we make a classification of spherical product surface having pointwise 1-type Gauss map in ${𝔾}_3$. Lastly, we visualized this type spherical product surface of the first kind in ${𝔾}_3$.

This paper is devoted to exploring exact charged solutions in a cloud of strings through minimal geometric deformation technique in three-dimensional gravity. For this purpose, we first evaluate the exact charged isotropic solution for static circular symmetry using Takabayashi equation of state and extend it to obtain three concrete anisotropic charged models. We investigate energy conditions as well as speed of sound constraint to check the viability of the respective solutions. It is concluded that the second model is a realistic one as it fulfills all the physical characteristics as well as stability criterion while the rest of two solutions do not satisfy the physical constraints.

In the current study, we discuss Gödel-type universe in $f(R,G)$ gravity. Analysis has been done by considering anisotropic and perfect fluid distributions. Energy conditions for two proposed $f(R,G)$ gravity models have been studied for suitable values of model parameters. Furthermore, Tolman–Oppenheimer–Volkoff equation has been developed with cylindrical coordinates in $f(R,G)$ gravity. The graphical analysis for both these models suggests that Tolman–Oppenheimer–Volkoff equation is obeyed in a specific interval for the radial coordinate $r$. A polytropic equation of state has been discussed for two $f(R,G)$ gravity models. By analyzing the energy conditions, it is concluded that Gödel-type universe with both $f(R,G)$ gravity models supports the expansion of the universe for certain range of radial coordinates.

We obtain a positive upper bound of total mass from a relative volume comparison by a weighted integral norm of Ricci curvature.

In this work, we develop some interesting models of cosmos exhibiting anisotropic properties in the extended scalar-tensor theory. In the first place, we consider the LRS Bianchi type I (BI) geometry filled with matter contents as magnetized bulk viscous cloud of strings. We developed analytic solutions and explore the cosmological significance of some interesting physical measures like cosmic volume, directional Hubble parameter, deceleration parameter, viscosity factor, particle energy density, shear and expansion scalars, and string tension density. Moreover, modified holographic Ricci dark energy is introduced in anisotropic scenario to discuss the dynamics of anisotropic comic models. In order to construct the exact cosmic solutions, we take hybrid law of scale factor as well as some viable ansatz for scalar field and its scalar potential. The physical viability of model parameters is discussed through graphical analysis. Physical analysis of both models show that our results are in agreement with the current observations and hence are cosmologically viable and promising.

In this paper, we have obtained a new class of solutions of modified field equations (FEqs) in $f(R,T)$ gravity with barotropic equation of state (EoS) i.e. $p_r=\alpha \rho +\beta$. For this purpose, we assume spherically symmetric metric with anisotropic matter distribution and formulated the FEqs. We apply Durgapal transformation and choose suitable gravitational potential to solve the dynamical equations numerically. By varying parametric values $a$ and $b$ (appearing in gravitational potential), we generate special cases of solutions. We plot physical quantities like energy density, anisotropy parameter, radial and tangential pressures in all particular cases. It is concluded that all the plots hold physical acceptability criteria and show consistency which admits modified $f(R,T)$ gravity for compact star models.

The paper builds the original foundations of a new operator theoretic setting for the study of quantum dynamics of non-perturbative aspects originated from Green’s functions in Quantum Field Theory with strong couplings.

This paper reviews the persistent rigid-body motions and examines the geometric conditions of the persistence of some special frame motions on a slant helix. Unlike the Frenet–Serret motion on general helices, the Frenet–Serret motion on slant helices can be persistent. Moreover, even the adapted frame motion on slant helices can be persistent. This paper begins by explaining one-dimensional rigid-body motions and persistent motions. Then, it continues to present persistent frame motions in terms of their instantaneous twists and axode surfaces. Accordingly, the persistence of any frame motions attached to a curve can be characterized by the pitch of an instantaneous twist. This work investigates different frame motions that are persistent, namely frame motions whose instantaneous twist has a constant pitch. In particular, by expressing the connection between the pitch of Frenet–Serret motion and the pitch of adapted frame motion, it demonstrates that both the Frenet–Serret motion and the adapted frame motion are persistent on slant helices.

This paper deals with spherically symmetric gravitational collapse of inhomogeneous perfect fluid in Einstein Gauss–Bonnet gravity. The physical quantities have been plotted in the EGB gravity. The Ricci Scalar and Kretschmann scalar have been determined to study the curvature singularity. The shell focusing curvature singularities are generated at last stage of gravitational collapse of object. The formation of singularity and apparent horizon depends on the initial data. Also, the energy conditions have been discussed for the reasonable energy momentum tensor. The presence of GB coupling constant $\alpha$ modifies the structure of singularity and formation of apparent horizon.

We have investigated the cosmic transit behavior of LRS Bianchi-I universe in modified $f(R,T)$ gravity theory whose functional form is taken as $f(R,T)=R+2f(t)$, where $R$ is Ricci scalar and $T$ is the energy–momentum tensor. Subjecting the deceleration parameter $q$ to periodic variations as $q=kcos(\beta t)-1$, where $k,\beta >0$, the oscillatory behavior of EoS parameter and violation of energy–momentum conservation in the wide range of parameters have been observed. Hubble parameter oscillates but remains positive which signify the alternate decelerating and accelerating expansion of universe with no singularity.

In this paper, we study Riemannian submersions whose total manifolds admit a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we study the harmonicity of Riemannian submersion from Ricci soliton and give a characterization for such a submersion to be harmonic.

In this paper, differential properties of the one-parameter Lorentzian spatial motions are developed with explicit expressions independent of coordinates systems. In term of this, we calculate the Disteli formulae of a spacelike line trajectory and derive the connections with kinematic geometry of the axodes. Lastly, a theoretical expression of a spacelike inflection line congruence are investigated in detail.