Momentum Tensor Research Articles

Dynamical system approach of interacting dark energy models in $f(R,T^{\phi})$ gravity

Abstract We have examined an isotropic and homogeneous cosmological model in $f(R,T^{\phi})$ gravity, where $R$ represents the Ricci scalar and $T^{\phi}$ exhibits the energy momentum tensor's trace. We examine the stability criteria by performing the dynamical system analysis for our model $f(R,T^{\phi})=R+2(aT^{\phi}+b)$, where $a$ $\&$ $b$ are the constants. We derive a set of autonomous equations and find their solutions by assuming a flat potential $V_{0}$. We assess the equilibrium points from these equations and find the eigenvalues. We analyze the physical interpretation of the phase space for this system. We obtain three stable equilibrium points. We also examine the interaction between scalar field and dark energy, represented by $Q=\psi H\rho_{de}$ and determine the equilibrium points for this interaction. We identify four stable equilibrium points for this interaction. We calculate the values of the physical parameters for both scenarios at each equilibrium point, indicating the Universe's accelerated expansion.

Thin-shell wormholes with non-collapsing dark energy throats connecting flat Minkowski spacetimes

This research revisits the thin-shell wormhole connecting two Minkowski spacetimes — originally introduced by Matt Visser. Upon setting a particular timelike hypersurface with a de-sitter-induced line element, the corresponding thin-shell wormhole (TSW) possesses a minimum radius and a uniform surface energy–momentum tensor in the form of dark energy. The bounded from below radius for the throat implies that it does not collapse. The r−τ profile curve of the hypersurface is a Catenary in r−τ plane where r and τ are the radial coordinate and the proper time on the throat, respectively. It is also shown that while the throat is dynamic, the surface energy–momentum tensor of the dark energy is in the form of an effective cosmological constant in the spherically symmetric TSW. The 4-dimensional cylindrically symmetric TSW with a similar throat profile shares the same features as its spherical counterpart, however, its uniform surface energy–momentum tensor does not mimic an effective cosmological constant. The higher-dimensional generalization of the spherically symmetric TSW admits the same properties as in the 4-dimensional one.

Mimetic Weyl geometric gravity

We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space–time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained by starting from a conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and an effective matter term, respectively. After linearizing the action in the Weyl scalar by introducing an auxiliary scalar field, we include the mimetic field, constructed from the same auxiliary scalar field used to linearize the action, via a Lagrange multiplier. The conformal invariance of the action is maintained by imposing the trace condition on the effective matter energy–momentum tensor, built up from the ordinary matter Lagrangian, and some specific functions of the Weyl vector, and the scalar field, respectively, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the Mimetic Weyl geometric gravity by considering the dynamics of an isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker FLRW Universe. The generalized Friedmann equations of the model are derived, and their solutions are obtained numerically for a dust filled Universe. Moreover, we perform a detailed comparison of the predictions of the considered model with a set of observational data for the Hubble function, and with the results of the ΛCDM standard paradigm. Our results indicate that the present model give a good description of the observational data, and they reproduce almost exactly the predictions of the ΛCDM scenario. Hence, Mimetic Weyl geometric gravity can be considered a viable alternative to the standard approaches to cosmology, and to the gravitational phenomena.

Maxwell–Dirac system in cosmology

Within the scope of a Bianchi type-I (BI) cosmological model, we study the interacting system of spinor and electromagnetic fields and its role in the evolution of the Universe. In some earlier studies, it was found that in the case of a pure spinor field, the presence of nontrivial nondiagonal components of energy–momentum tensor (EMT) leads to some severe restrictions both on the space–time geometry and/or spinor field itself, whereas in the case of electromagnetic field with induced nonlinearity, such components impose severe restrictions on metric functions and the components of the vector potential. It is shown that in the case of interacting spinor and electromagnetic fields, the restrictions are not as severe as in the other cases and in this case, a nonlinear and massive spinor field with different components of vector potential can survive in a general Bianchi type-I space–time.

Phase space properties of cosmological models in f(Q, T) gravity

The Weyl type f(Q, T) gravity is the modification of f(Q) gravity and f(Q, T) theories, where non-metricity is denoted by Q and T is the trace of the energy–momentum tensor. Together with a geometric explanation for dark energy, the theory can provide an exact interpretation of the transformation of the late-time Universe and the observable data. In this study, we present an accelerated cosmic model of the Universe in f(Q, T) gravity. We consider the model of f(Q, T) gravity as, f(Q,T)=-Q+ϕ(Q,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q,T) = -Q+\\phi (Q,T)$$\\end{document}. We examine the energy condition for the model of f(Q, T) gravity and find out that our model satisfies the null and strong energy conditions at the same time, it violates the weak and dominant energy conditions. After that, we perform the phase-space study of our cosmological model with and without interaction independently. In case of the absence of interaction, we get six critical points out of which three critical points are stable critical points while the rest three critical points are saddle. When we perform the stability analysis in the presence of interaction, we get three critical points out of which one critical point is stable while the rest two are saddle points. The phase-plot analysis also shows the cosmological models in f(Q, T) gravity.

General relativistic gravitational induction and causal temperatures

Abstract In this paper, we describe the process of general relativistic gravitational induction in spherically symmetric spacetimes by defining an energy momentum tensor for the induction process, which is divergence-free and hence conserved. The aforementioned tensor explicitly describes how the matter-free gravity, as measured by the geometrical Weyl curvature, interacts with the matter. This tensor is clearly different from the energy momentum tensor of the standard matter and we transparently show that in spherical symmetry, the Bianchi identities reduce to the conservation laws for these two such energy momentum tensors. Working with a semitetrad covariant formalism in spherically symmetric spacetimes, we then demonstrate the process of constructing a consistent causal thermodynamical picture for the free gravity and matter interaction via the general non-truncated Israel-Stewart heat transport equation. As an illustrative example, we consider the Lemaître-Tolman-Bondi spacetime to highlight the relationship between the shear and the Weyl curvature in determining the inductive heat flux.

Boosted Kerr–Newman black holes

Abstract In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr–Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr–Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson–Trautman coordinates to Bondi–Sachs, including the perturbation term of the boosted Robinson–Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy–momentum tensor the boosted Kerr–Newman solution. To this end, we consider the electromagnetic energy–momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy–momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr–Newman metric. To proceed, we examine the causal structure of the boosted Kerr–Newman black hole in Bondi–Sachs coordinates as in a preferred timelike foliation. We show that the ultimate effect of a nonvanishing charge is to shrink the overall size of the event horizon and ergosphere areas when compared to the neutral boosted Kerr black holes. Considering the preferred timelike foliation we obtain the electromagnetic fields for a proper nonrotating frame of reference. We show that while the electric field displays a pure radial behavior, the magnetic counterpart develops an involved structure with two intense lobes of the magnetic field observed in the direction opposite to the boost.

Morris–Thorne-type wormholes with global monopole charge and the energy conditions

In this paper, we investigate Morris–Thorne-type wormholes with global monopole charge using various shape function forms known in the literature. We solve the Einstein field equations incorporating an anisotropic energy–momentum tensor and obtain different physical quantities associated with the matter-content. A crucial aspect of this study is the non-exotic matter distribution, examined through the evaluation of energy conditions, and exploring how different shape functions impact these conditions. Additionally, the anisotropy parameter is calculated to quantify the extent of attractive or repulsive behavior. Our study demonstrates that for different types of shape function forms, the energy conditions are influenced by the global monopole parameter. Our findings provide valuable insights for further theoretical explorations of these fascinating hypothetical structures in the realm of general relativity and beyond.

Finite temperature fermionic condensate and energy–momentum tensor in cosmic string spacetime

Here we analyze the expectation value of the fermionic condensate and the energy–momentum tensor associated with a massive charged fermionic quantum field with a nonzero chemical potential propagating in a magnetic-flux-carrying cosmic string in thermal equilibrium at finite temperature T. The expectation values of the fermionic condensate and the energy–momentum tensor are expressed as the sum of vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitation. The thermal expectations values of the fermionic condensate and the energy–momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Because the analyses of vacuum expectation of the fermionic condensate and energy–momentum tensor have been developed in literature, here we are mainly interested in the investigation of the thermal corrections. In this way we explicitly study how these observable behaves in the limits of low and high temperatures, and also for points near the string. Besides the analytical discussions, we included some graphs that exhibit the behavior of these observable for different values of the physical parameters of the model.

Braneworld black bounce to transversable wormhole

We provide a way for embedding a 4-dimensional geometry corresponding to the Simpson-Visser (SV) spacetime — which is capable of representing a traversable wormhole, a one-way wormhole, or a regular black hole — into a Randall-Sundrum setup. To achieve this, we linearly deform the bulk geometry and the bulk matter distribution concerning a coupling constant. These deformations induce a transition from a 5D vacuum AdS state to an anisotropic matter distribution. The latter results in the induced geometry on the brane transitioning from a singular Schwarzschild spacetime to a regularized SV spacetime. Since there are no sources or matter fields on the brane, we can assert that the induced SV geometry on the brane arises from the influence of geometrical and matter deformations in the bulk. Thus, the central singularity is suppressed. We determine the cases where the energy conditions are either satisfied or violated. Our spacetime is asymptotically radial AdS, which is intriguing given the absence of a global AdS box that would prevent instability under larger wavelength perturbations. Therefore, it is no longer appropriate to claim that instability exists for very small perturbations near the AdS horizon. Thus, we propose that the stability of the solution can be analyzed by examining the speed of sound due to the presence of matter fields in the energy momentum tensor.

Energy–momentum tensor of a causally disconnected region of the Universe, the cosmological constant, and the inflationary model

Energy–momentum tensor of a causally disconnected region of the Universe, the cosmological constant, and the inflationary model

Growth of cosmic perturbations in the modified [formula omitted] gravity

We explore the generalized f(R,T) modified theory of gravity, where the gravitational Lagrangian is a function of Ricci scalar R and the trace of the energy–momentum tensor T. We derive modified field equations to the linear order of perturbations in the context of f(R,T) model. We then investigate the growth of perturbations in the context of f(R,T) modified gravity. Primary numerical investigations based on matter power spectra diagrams indicate a structure growth suppression in f(R,T) gravity, which exhibits consistency with local measurements. Also, we notice that matter-geometry interaction in f(R,T) model would results in the specific feature named as ”matter acoustic oscillations” appeared in matter power spectra diagrams. Moreover, we put constraints on the cosmological parameters of f(R,T) model, utilizing current observations, chiefly cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results based on MCMC calculations imply that f(R,T) is a qualified theory of modified gravity in reconciling Planck CMB data with local probes of large scale structures, by reporting lower values for the structure growth parameter σ8 compared to the standard model of cosmology.

Cosmological bouncing solutions in f(𝒬,𝒯) theory

This paper examines the behavior of the universe around the bouncing point in the background of [Formula: see text] theory, where [Formula: see text] is the non-metricity and [Formula: see text] is the trace of the energy–momentum tensor. We derive the field equations that describe gravitational phenomena in the existence of non-metricity and matter source terms. By applying the reconstruction method for the Hubble parameter, a phenomenon of the bouncing universe for homogeneous spacetime filled with perfect fluid is studied. We consider specific models of this modified theory to evaluate the behavior of various cosmic parameters such as the Hubble, deceleration, equation of state and fluid parameters. When the null energy condition is violated, it follows a bouncing behavior. It is found that spacetime is composed of isotropic fluid, where a big bounce can occur and the universe turns into extremely unstable. We conclude that [Formula: see text] gravity successfully explains the early and late time cosmic expansion and evolution.

Stability and viability of charged anisotropic pulsar SAX J1748.9-2021 in extended symmetric teleparallel gravity

This manuscript aims to study the viability and stability of a pulsar SAX J1748.9-2021, containing a charged anisotropic matter configuration within the framework of f(Q,T) theory (Q and T are the non-metricity scalar and energy–momentum tensor, respectively). We employ a non-singular solution and a specific model of this gravitational theory and use junction conditions to determine the unknown constants in the metric coefficients. We explore different geometric and physical properties using astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. This framework establishes relationships between various physical quantities, including fluid parameters, anisotropy, mass–radius relation, redshift, the Zeldovich condition, energy conditions, causality conditions, adiabatic index, Tolman–Oppenheimer–Volkoff equation, equation of state parameter and compactness. Our findings affirm the feasibility and stability of the proposed charged pulsar within this theoretical framework.

Equivalence of magnetic flux and energy

Magnetic flux and energy equivalence is the principle that everything that has magnetic flux has an equivalent amount of energy, and vice versa. The main methods used: transformation of natural units, algebra, analogy. The equivalence of magnetic flux and energy, despite its widespread use in describing the principles of physics, has not yet been formulated. This paper presents the formula for this equivalence. This is done based on known measurement systems, parameters and principles of physics. Five examples (Stoney units, Planck units, standard gravitational parameter, Lorentz force, and Ampere force) of the algebraic representation of this principle show its universality. Five examples should justify the universality of the new principle and its use in physics and astrophysics. Using the equivalence of magnetic flux and energy, new physical units of mass and magnetic flux are proposed, each of which is suitable for measuring both mass and magnetic flux. Natural values of electric current and voltage, linear density of electric capacitance and inductance, linear density of magnetic flux, linear density of electric charge, as well as natural units of electric voltage and current, electrical resistance, magnetic flux, electrical capacitance and inductance are also described. The article presents the Einstein field equation (additional magnetic stress–energy–momentum tensor) and a standard astrophysical parameter for refining the orbits of celestial bodies.

Charged wormhole solutions in 4D Einstein-Gauss-Bonnet gravity

In the present work, we construct models of static wormholes in 4-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity with an (an)isotropic energy momentum tensor (EMT) and a Maxwell field as supporting matters for the wormhole geometry assuming a constant redshift function. We obtain exact spherically symmetric wormhole solutions in 4D EGB gravity for isotropic and anisotropic matter sources under the effect of electric charge. The solutions are more generalized in the sense of incorporating the charge contributions. Furthermore, we examine the null, weak and strong energy conditions at the wormhole throat of radius r=r0. We demonstrate that at the wormhole throat, the classical energy conditions are violated by arbitrary small amount. Additionally, we analyze the wormhole geometry incorporating semiclassical corrections through embedding diagrams. We discover that the wormhole solutions are in equilibrium as the anisotropic and hydrostatic forces cancel each other.

Possible wormholes in f(R) gravity sourced by solitonic quantum wave and cold dark matter halos and their repulsive gravity effect

In this paper, we present new generalized wormhole (WH) solutions within the context of f(R) gravity. Specifically, we focus on f(R) gravitational theories formulated in the metric formalism, with our investigation centered on a power-law form represented by f(R)=ϵRχ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R) = \\epsilon R^{\\chi }$$\\end{document}. Here, ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document} is an arbitrary constant, and χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document} is a real number. Notably, this form possesses the advantageous property of reducing to Einstein gravity when ϵ=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon =1$$\\end{document} and χ=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi =1$$\\end{document}. To obtain these novel WH solutions, we establish the general field equations for any f(R) theory within the framework of Morris–Thorne spacetime, assuming metric coefficients that are independent of time. By utilizing an anisotropic matter source and a specific type of energy density associated with solitonic quantum wave (SQW) and cold dark matter (CDM) halos, we calculate two distinct WH solutions. We thoroughly investigate the properties of the exotic matter (ExoM) residing within the WH geometry and analyze the matter contents through energy conditions (ECs). Both analytical and graphical methods are employed in this analysis to examine the validity of different regions. Notably, the calculated shape functions for the WH geometry satisfy the necessary conditions in both scenarios, emphasizing their reliability. Our investigations into specific parameter ranges in both scenarios revealed the presence of ExoM. This ExoM is characterized by an energy–momentum tensor that violates the null energy condition (NEC) and, consequently, the weak energy condition as well, in the vicinity of the WH throats. Furthermore, we investigated the repulsive effect of gravity and discovered that its presence results in a negative deflection angle for photons following null geodesics. Importantly, we observed that the deflection angle consistently exhibits negative values across all r0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0$$\\end{document} values in both scenarios, indicating the manifestation of the repulsive gravity effect. Finally, we compare the obtained WH solutions utilizing both distributions, as well as the f(R) power-law-like models, in order to assess the feasibility of energetic configurations for WHs within SQW and CDM systems.

Compatibility of Gravitational Baryogenesis with theoretical framework of [formula omitted] Gravity

The primary goal of this article is to analyze the disproportion between matter and antimatter in the Universe using the phenomenon of gravitational baryogenesis under the framework of f(R,G,T) gravity, where R, G and T are Ricci Scalar, Gauss–Bonnet invariant and the trace of energy momentum tensor. This phenomenon based on charge parity violation interactions and in this article we generate it through the coupling between the baryon matter current (Jν) and ∂ν(R+G+T) as well as for generalized case with (Jν) and ∂νf(R+G+T). We evaluate the ratio ηBS (baryon to entropy) of the propose model of f(R,G,T) gravity for gravitational baryogenesis and generalized gravitational baryogenesis with power-law form consideration for the scale factor in different eras of the Universe. We notice that the results of (ηBS) are compatible with its observational bound under the optimal choice of model parameters and hence we say that this gravity is good for gravitational baryogenesis under certain constraints of model parameters.

Relativistic fluids interacting through gravitational decoupling in f(T,𝒯) theory

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use [Formula: see text] modified gravity, which is characterized by the trace of an energy–momentum tensor as [Formula: see text] and torsion scalar [Formula: see text], Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics.

Collapsing scenarios of K-essence generalized Vaidya spacetime under [formula omitted] gravity

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of f(R̄,T̄) gravity, specifically in K-essence theory. In this study, the Dirac–Born–Infeld type non-standard Lagrangian is used to calculate the emergent metric Ḡμν, which is not conformally equivalent to the conventional gravitational metric. We use the function f(R̄,T̄) to reflect the additive nature of the emergent Ricci scalar (R̄) and the trace of the emergent energy–momentum tensor (T̄). Our study demonstrates that certain choices of f(R̄,T̄) may result in the existence of a naked singularity caused by gravitational collapse. The alternative f(R̄,T̄) values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. In addition, when a certain amount of kinetic energy is present in the K-essence scalar field, mass is entirely converted into energy, indicating that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena.