Components Of Energy-momentum Tensor Research Articles

Emergence of negative mass in general relativity

We investigate a symmetric traversable wormhole model, integrating Einstein’s gravitational coupling phantom field and a nonlinear electromagnetic field. This work indicates the emergence of negative ADM mass within a specific parameter range, coinciding with distinct alterations in the wormhole’s spacetime properties. Despite violating the Null Energy Condition (NEC) and other energy conditions, the solution exhibits unique characteristics in certain energy-momentum tensor components, potentially accounting for the manifestation of negative mass.

Is dark energy necessary for the sustainability of traversable wormholes?

Abstract Dark energy is usually the principal ingredient needed for traversability of wormholes by providing the negative gravity effect to keep the throat open. But can the same be achieved without dark energy? It turns out that if we couple the trace of energy-momentum with the standard Einstein-Hilbert Lagrangian and utilise a specific equation of state then dark energy may be obviated. The Casimir stress energy is known to result in the violation of the null energy condition (NEC) on the energy momentum tensor. This phenomenon makes such an equation of state (EoS) an ideal candidate to generate traversable wormhole (WH) geometries. The laboratory proven phenomenon provides a natural mechanism to sustain an open WH throat without having to appeal to dark energy. We generate two classes of WH solutions with this in energy-momentum trace-coupling gravity.
 For the specific choice of the Casimir EoS relating the energy-momentum tensor components [ Kar and Sahdev: Phys. Rev D {\bf 52} 2030 (1995)] and different choices for redshift functions, we determine the WH geometry completely. The obtained WH solutions violate the NECs and all qualitative constraints demanded of physically realisable WHs are satisfied. This is demonstrated via graphical plots for a suitably chosen range of values of the coupling parameter. Furthermore, our study involved an investigation into the repulsive effect of gravity, which revealed that its presence leads to a negative deflection angle for photons traveling along null geodesics. Notably, we observed a consistent pattern of negative values for the deflection angle across all values of $r_0$ in the three scenarios considered, thus indicating the clear manifestation of the repulsive gravity effect. All of this is possible without invoking the existence of dark energy.

Vacuum instability in QED with an asymmetric x step: New example of an exactly solvable case

We present a new exactly solvable case in strong-field QED with a one-dimensional step potential (x-step). The corresponding x-step is given by an analytic asymmetric with respect to the axis x reflection function. The step can be considered as a certain analytic “deformation” of the symmetric Sauter field. Moreover, it can be treated as a new regularization of the Klein step field. We study the vacuum instability caused by this x-step in the framework of a nonperturbative approach to strong-field QED. Exact solutions of the Dirac equation used in the corresponding nonperturbative calculations are represented in the form of stationary plane waves with special left and right asymptotics and identified as components of initial and final wave packets of particles. We show that in spite of the fact that the symmetry with respect to positive and negative bands of energies is broken, the distribution of created pairs and other physical quantities can be expressed via elementary functions. We consider the processes of transmission and reflection in the ranges of the stable vacuum and study physical quantities specifying the vacuum instability. We find the differential mean numbers of electron-positron pairs created from the vacuum, the components of current density and energy-momentum tensor of the created electrons and positrons leaving the area of the strong field under consideration. Besides, we study the particular case of the particle creation due to a weakly inhomogeneous electric field and obtain explicitly the total number, the current density and energy-momentum tensor of created particles. Unlike the symmetric case of the Sauter field the asymmetric form of the field under consideration causes the energy density and longitudinal pressure of created electrons to be not equal to the energy density and longitudinal pressure of created positrons. Published by the American Physical Society 2024

Physical properties and maximum allowable mass-radius relation of complexity-free compact stellar objects within modified gravity formalism* *The authors MKJ and SKM acknowledge that this work is carried out under TRC Project (BFP/RGP/CBS/22/014). This study is also supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2024/R/1445). The authors are thankful to the Deanship of Graduate Studies and Scientific

This paper investigates the physical properties and predicted radii of compact stars generated by the Tolman-IV complexity-free model within the background of modified gravity theory, particularly the -gravity theory, under complexity formalism for a spherically symmetric spacetime proposed by L. Herrera [Phys Rev D 97: 044010, 2018]. By solving the resulting set of differential equations, we obtain the explicit forms of the energy-momentum (EM) tensor components, including the density, radial pressure, and tangential pressure. The influence of the parameter χ on various physical properties of the star is thoroughly investigated. The model undergoes a series of rigorous tests to determine its physical relevance. The findings indicate that the model exhibits regularity, stability, and a surface with vanishing pressure. The boundary of this surface is determined by carefully selecting the parameter space. The complexity method employed in gravity offers an interesting approach for developing astrophysical models that are consistent with observable events as demonstrated by recent experiments. In this regard, we use observational data from the GW190814 event, detected by the LIGO and Virgo observatories, to investigate the validity of the Tolman-IV model in gravity. The analysis includes comparing the model's predictions with the observed characteristics of the compact object involved in the merger. In addition, data from two-millisecond pulsars, PSR J1614-2230 and PSR J0952-0607, are incorporated to further constrain the theoretical theories. However, we present a diagram depicting the relationship between the total mass and radius of the compact object candidates for different values of χ.

Irreversible Geometrothermodynamics of Open Systems in Modified Gravity.

In this work, we explore the formalism of the irreversible thermodynamics of open systems and the possibility of gravitationally generated particle production in modified gravity. More specifically, we consider the scalar-tensor representation of f(R,T) gravity, in which the matter energy-momentum tensor is not conserved due to a nonminimal curvature-matter coupling. In the context of the irreversible thermodynamics of open systems, this non-conservation of the energy-momentum tensor can be interpreted as an irreversible flow of energy from the gravitational sector to the matter sector, which, in general, could result in particle creation. We obtain and discuss the expressions for the particle creation rate, the creation pressure, and the entropy and temperature evolutions. Applied together with the modified field equations of scalar-tensor f(R,T) gravity, the thermodynamics of open systems lead to a generalization of the ΛCDM cosmological paradigm, in which the particle creation rate and pressure are considered effectively as components of the cosmological fluid energy-momentum tensor. Thus, generally, modified theories of gravity in which these two quantities do not vanish provide a macroscopic phenomenological description of particle production in the cosmological fluid filling the Universe and also lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy.

Hydrodynamic attractors for the speed of sound in holographic Bjorken flow

The time evolution of the averaged energy momentum tensor as well as its variation with energy density are calculated in a far-from-equilibrium state of $\mathcal{N}=4$ SYM theory undergoing a Bjorken expansion. The calculation is carried out holographically where we consider a collection of trajectories of the energy density in the space of solutions by small changes to the initial conditions of the bulk spacetime. We argue that the proper interpretation of the variation of the diagonal energy momentum tensor components with respect to the energy density is that of a far-from-equilibrium speed of sound. We demonstrate remarkable agreement with a corresponding hydrodynamic prediction. We find by Borel resummation that the holographic system has one attractor for this speed of sound longitudinal, and another transverse to the direction of Bjorken expansion. Attractor times for various initial flow conditions show that reaching an attractor does not imply or require local thermal equilibrium. In the cases studied, reaching an attractor implies hydrodynamization (quantities evolve approximately according to hydrodynamics), justifying the name \emph{hydrodynamic attractor }

Gravitationally induced particle production in scalar-tensor f(R,T) gravity

We explore the possibility of gravitationally generated particle production in the scalar-tensor representation of $f(R,T)$ gravity. Due to the explicit nonminimal curvature-matter coupling in the theory, the divergence of the matter energy-momentum tensor does not vanish. We explore the physical and cosmological implications of this property by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, temperature evolution, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy-momentum tensor. We also consider specific models, and compare the scalar-tensor $f(R,T)$ cosmology with the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ scenario and the observational data for the Hubble function. The properties of the particle creation rates, of the creation pressures, and entropy generation through gravitational matter production are further investigated in both the low and high redshift limits.

Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating Systems

The post-Newtonian Jeans equation for stationary self-gravitating systems is derived from the post-Newtonian Boltzmann equation in spherical coordinates. The Jeans equation is coupled with the three Poisson equations from the post-Newtonian theory. The Poisson equations are functions of the energy-momentum tensor components which are determined from the post-Newtonian Maxwell–Jüttner distribution function. As an application, the effect of a central massive black hole on the velocity dispersion profile of the host galaxy is investigated and the influence of the post-Newtonian corrections are determined.

Role of structure scalars on the evolution of compact objects in Palatini [formula omitted] gravity

The utmost concern of this article is the construction of modified scalar functions (structure scalars) by taking Palatini f(R) gravitational theory into account. At first, a general formalism is established in which we assess gravitational stellar equations by putting into use the Palatini’s technique. Later, from the perspective of tilted observer, we Lorentz boosted the components of energy-momentum tensor using relative velocity ω. To examine the physical as well as mathematical aspects of the fluid source, we carry out a detailed analysis of kinematical variables by evaluating shear tensor and scalar, four-acceleration and expansion scalar. For the fluid content inside our spherical star, we inferred the mass function (geometric mass) and the active gravitational mass. Raychaudhuri equation, Bianchi identities in addition to few other equations are worked out to discern the structure formation and analyze the object’s evolutionary stages. The Riemann tensor is then broken up orthogonally to set up few scalar functions connected with fundamental physical characteristics of the fluid source like energy density, effects of tidal forces and anisotropic stresses etc.

Charged dust solutions for the warp drive spacetime

The Alcubierre warp drive metric is a spacetime construction where a massive particle located inside a spacetime distortion, called warp bubble, travels at velocities arbitrarily higher than the velocity of light. This theoretically constructed spacetime geometry is a consequence of general relativity where global superluminal velocities, also known as warp speeds, are possible, whereas local speeds are limited to subluminal ones as required by special relativity. In this work we analyze the solutions of the Einstein equations having charged dust energy-momentum tensor as source for warp velocities. The Einstein equations with the cosmological constant are written and all solutions having energy-momentum tensor components for electromagnetic fields generated by charged dust are presented, as well as the respective energy conditions. The results show an interplay between the energy conditions and the electromagnetic field such that in some cases the former can be satisfied by both positive and negative matter density. In other cases the dominant and null energy conditions are violated. A result connecting the electric energy density with the cosmological constant is also presented, as well as the effects of the electromagnetic field on the bubble dynamics.

Quagnetic Field Part (II)

In continuation of article quagnetic field part (I), acknowledgement of quagnetic field is further exercised theoretically. Among the present theoretical methods, introduced generalized Coulomb and Newtonian four forces suggest existence of quagnetic field and other two new fields. The new fields are for both Electromagnetic and gravitoquagnetic systems named as super curvilinear vector fields. Other theoretical approach is based on energy momentum tensor components for macroscopic system. Extended Maxwell equations are discussed regarding gravitational and quagnetic fields and their quagnetization and gravitational inductions.

The thermodynamics of the FRW universe in scalar-twist gravitational theories

In this paper, we study the validity of the laws of thermodynamics in the form of a far parallel gravitational theory with an incomplete coupling between curves and scalar fields. To this end, we consider the FRW flat world, showing that the first and second laws of thermodynamics lie in its dynamic apparent horizon. We further assume that the universe is enclosed by the cosmological event horizon, such that in this case the first law of thermodynamics is valid, but the second law of thermodynamics is applied to the selected incomplete model, depending on the energy-momentum tensor components derived.

Exact wormholes solutions without exotic matter in f(R,T) gravity

This paper is aimed to evaluate the existence of wormholes in viable [Formula: see text] gravity models (where [Formula: see text] is the scalar curvature and [Formula: see text] is the trace of stress–energy tensor of matter). The exact solutions for energy–momentum tensor components depending on different shapes and redshift functions are calculated without some additional constraints. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic fluid and formulate the Einstein field equations for three different [Formula: see text] models. For each model, we derive expression for weak and null energy conditions and graphically analyzed its violation near the throat. It is really interesting that wormhole solutions do not require the presence of exotic matter — like that in general relativity. Finally, the stability of the solutions for each model is presented using equilibrium condition.

Spinor fields in spherically symmetric space-time

Within the scope of a spherically symmetric space-time we study the role of a nonlinear spinor field in the formation of different configurations with spherical symmetries. The presence of the non-diagonal components of energy-momentum tensor of the spinor field leads to some severe restrictions on the spinor field itself. Since spinor field is the source of the gravitational one, the metric functions also changes in accordance with it. The system as a whole possesses solutions only in case of some additional conditions on metric functions.

Antigravitating braneworld solutions for a de Sitter brane in scalar-tensor gravity

In the context of a five-dimensional theory with a scalar field nonminimally coupled to gravity, we look for solutions that describe novel black-string or maximally symmetric solutions in the bulk. The brane line element is found to describe a Schwarzschild--(anti)--de Sitter spacetime, and, here, we choose to study solutions with a positive four-dimensional cosmological constant. We consider two different forms of the coupling function of the scalar field to the bulk scalar curvature, a linear one and a quadratic one. In the linear case, we find solutions where the theory, close to our brane, mimics an ordinary gravitational theory with a minimally coupled scalar field giving rise to an exponentially decreasing warp factor in the absence of a negative bulk cosmological constant. The solution is characterized by the presence of a normal gravity regime around our brane and an antigravitating regime away from it. In the quadratic case, there is no normal-gravity regime at all; however, scalar field and energy-momentum tensor components are well defined and an exponentially decreasing warp factor emerges again. We demonstrate that, in the context of this theory, the emergence of a positive cosmological constant on our brane is always accompanied by an antigravitating regime in the five-dimensional bulk.

Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media

Applying a quantum mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy–momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham’s symmetric energy–momentum-tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular momentum (spin) of an electro-magnetic field in the medium. Only the Minkowski tensor leads to the experimentally confirmed spin values that are multiples of ħ, providing the grounds for choosing the Minkowski representation as the proper form for the momentum density of a transverse electromagnetic field in a transparent medium, in both classical and quantum descriptions of the field. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasistatic and static fields.

Bianchi type-VIII spinor solutions

Within the scope of Bianchi type-VIII space-time the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that, unlike the diagonal Bianchi models, in this case the components of energy-momentum tensor of spinor field along the principal axis are not the same, i.e. $T_{1}^{1} \ne T_{2}^{2} \ne T_{3}^{3}$ , even in the absence of spinor field nonlinearity. The presence of nontrivial non-diagonal components of energy-momentum tensor of the spinor field imposes severe restrictions both on geometry of space-time and on the spinor field itself. While the energy-momentum with diagonal components alone allows only locally rotational symmetry, say $a_{1} \sim a_{2}$ , in this case there might be a second case with $a_{1} \sim a_{2} \sim a_{3}$ . It was found that, like a Bianchi type-IX case, a positive $\lambda_{1}$ gives rise to an oscillatory mode of expansion, while a trivial $\lambda_{1}$ leads to rapid expansion at the early stage of evolution.

Nonlinear Gravitational Waves as Dark Energy in Warped Spacetimes

We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers of the subsequent orders of the scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution due to the suppression of the n-dependency in the energy momentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This contribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations of about 180 ∘ . The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure T z z for discrete values of the azimuthal-angle. There could be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and this could be evidence for the existence of cosmic strings. Careful comparison of this spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available. It turns out that, for late time, the vacuum 5D spacetime is conformally invariant if the warp factor fulfils the equation of a vibrating “drum”, describing standing normal modes of the brane.

Alignment of Quasar Polarizations on Large Scales Explained by Warped Cosmic Strings. PART II: The Second Order Contribution

We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectrum of azimuthal-angle dependent wavelike modes without the need of conventional density perturbations in standard 4D cosmological models. Carefully com-parison of the spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available.

Nonlinear spinor field in isotropic space-time and dark energy models

Within the scope of isotropic FRW cosmological model the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that unlike in anisotropic cosmological models in the present case the spinor field does not possess nontrivial non-diagonal components of energy-momentum tensor, consequently does not impose any additional restrictions on the components of the spinor field or metric function. The spinor description of different matter was given and evolution of the Universe corresponding to these sources is illustrated. In the framework of a three fluid system the utility of spinor description of matter is established.