Energy-momentum Tensor Research Articles

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.

A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry

We study magnetohydrodynamics using holography. The gravity model is closely related to the STU supergravity in five dimensions and admits an analytical black brane solution carrying the conserved charge dual to the magnetic 1-form symmetry of the magnetohydrodynamic system. The black brane solution features a fortuitous SO(3) symmetry, providing a new symmetry principle for describing the magnetohydrodynamics. Since the bulk theory contains multiple 2-form gauge fields, the resistivity becomes matrix-valued. We find that the antisymmetric part of the resistivity matrix exhibits novel features depending on the UV cut-off of the theory. We also compute the shear and bulk viscosities and find that the bulk viscosity is proportional to the shear viscosity. Remarkably, the proportionality constant is exactly what is required for conformality, despite the zeroth-order energy-momentum tensor not being trace-free.

A comprehensive analysis of cosmic evolution in f(Q,T) theory

This paper examines the bouncing cosmology in f(Q,T) theory, where Q represents non-metricity and T denotes the trace of energy-momentum tensor. The aim of this research is to study the phenomenon of a cosmic bounce, where contraction, bounce point and expansion occur at t < 0, t = 0 and t > 0, respectively. In this perspective, we consider Bianchi Type-I spacetime with perfect matter configuration to study the mysterious universe. Further, we analyze the behavior of cosmological parameters such as scale factor, Hubble parameter, deceleration parameter and equation of state parameter using three distinct functional forms of f(Q,T) theory. A comprehensive examination of energy conditions is analyzed to study the matter bounce in this modified framework. Our findings indicate that the acceleration takes place in the vicinity of the bouncing point and ensures the presence of a nonsingular bounce in this theory.

Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries

We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant boundary conditions, is related to the dimensions of boundary operators by Cardy, the actual spectra of lattice models are affected by both bulk and boundary perturbations and contain non-universal boundary energies. We obtain a general expression of the finite-size energy levels in the presence of bulk and boundary perturbations. In particular, a generic boundary perturbation related to the energy-momentum tensor gives rise to a renormalization of the effective system size. We verify our field-theory formulation by comparing the results with the exact solution of the critical transverse-field Ising chain and with accurate numerical results on the critical three-state Potts chain obtained by Density-Matrix Renormalization Group.

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.

Infinite Family of Integrable Sigma Models Using Auxiliary Fields.

We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field g, these models include an auxiliary field v_{α} which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor.

Constraints on anisotropic properties of the universe in f(Q,T) gravity theory

Motivated by anomalies in cosmic microwave background observations, we investigate the implications of f(Q,T) gravity in Bianchi type-I spacetime, aiming to characterize the universe's spatially homogeneous and anisotropic properties. By using a linear combination of non-metricity Q and the energy-momentum tensor trace T, we parametrize the deceleration parameter and derive the Hubble solution, which we then impose in the Friedmann equations of f(Q,T) gravity. Bayesian analysis is employed to find the best-fit values of model parameters, with 1−σ and 2−σ contour plots illustrating the constraints from observational data, including H(z) data and the Pantheon+ sample. Our analysis reveals a transition from a decelerated to an accelerated expansion phase, with the present deceleration parameter indicating an accelerating universe. The energy density gradually decreases over time, approaching zero for the present and future, indicating continuous expansion. The anisotropic pressure, initially notably negative, transitions to slightly negative values, suggesting the presence of dark energy. The evolving equation of state parameter ω exhibits behavior akin to phantom energy, influenced by spacetime anisotropy. Violations of the null energy condition and the strong energy condition imply phantom-like behavior and accelerated expansion.

Spin-orbit correlations in the nucleon in the large- Nc limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-Nc limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024

Casimir energy with perfect electromagnetic boundary conditions and duality: A field-theoretic approach

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral and once as the vacuum expectation value of the 00 component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation. Published by the American Physical Society 2024

Note on holographic torus stress tensor correlators in AdS3 gravity

In the AdS3/CFT2 framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system’s dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

Physical characteristics of anisotropic solutions in f(Q,T) gravity under the vanishing complexity, embedding class one, conformally flat and conformally Killing conditions

The foundation of this paper is to present a comparative study of the properties of anisotropic solutions for compact stars in the framework of modified f(Q,T) gravity for the first time under the schemes of vanishing complexity, embedding class one, conformally flat and conformally Killing, where Q is the nonmetricity scalar and T is the trace of the energy-momentum tensor. The model f(Q,T)=ϕQ+αQn+1−γ(1−e−Q/γ)+βT is chosen in order to compare the results of the various forms f(Q,T) and f(Q) gravity theories. The f(Q,T) and f(Q) gravities in this model are then further simplified to depend on parameters ϕ,α,γ&β. Then, we discussed several approaches to determining the spherically symmetric spacetime components. Schwarzschild geometry represents the exterior spacetime, while a Tolman-Kuchowiz spacetime is used to examine the spherically symmetric spacetime inside the interior geometry. Many properties of compact stars are investigated, like energy density, energy conditions, pressure profiles, sound speeds, gradients, adiabatic index, TOV equation, mass function, compactness, and redshift function are all carefully examined in order to complete the analysis. We have compiled results for both stable and unstable scenarios, derived from gravity theories categorized into various cases, with solutions considered under different frameworks such as Tolman-Kuchowiz spacetime, embedding class 1 spacetime, the vanishing complexity condition, the conformally flat condition, and the conformal Killing vector condition.

Laws of conservation of mass and momentum for an ideal fluid in the inertial framework of special relativity

In the realm of Newtonian fluids, fundamental conservation laws such as those governing mass, momentum, and energy are rigorously upheld within absolute reference frames. However, within the framework of special relativity and the concept of space -time, the notions of separate conservation of mass and momentum no longer hold. Instead, the theory relies on Lorentz transformations and relative reference systems, typically denoted as S and S', moving uniformly relative to each other, each with its own temporal framework. Within the context of special relativity, particularly in the study of particles, significant findings pertain to the energy-momentum vector. These findings underscore the necessity, when studying fluids within inertial frames, to apply conservation principles to the energy-momentum tensor.

Pion gravitational form factors in the QCD instanton vacuum. I

The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024

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.

Evidence for universal flow and characteristics of early time thermalization in a scalar field model for heavy ion collisions

We study numerically the evolution of an expanding strongly self-coupled real scalar field. We use a conformally invariant action that gives a traceless energy-momentum tensor and is better suited to model the early time behavior of a system such as QCD, whose action is also conformally invariant. We consider asymmetric initial conditions and observe that when the system is initialized with nonzero spatial eccentricity, the eccentricity decreases and the elliptic flow coefficient increases. This behavior is characteristic of a hydrodynamic system in which pressure gradients are converted into fluid velocities, and therefore spatial anisotropy decreases while momentum anisotropy is generated. We look at a measure of transverse pressure asymmetry that has been shown to behave similarly to the elliptic flow coefficient in hydrodynamic systems and show that in our system their behavior is strikingly similar. We show that the derivative of the transverse velocity is proportional to the gradient of the energy in Milne coordinates and argue that this result means that transverse velocity initially develops in the same way that it does in hydrodynamic systems. We conclude that some aspects of the early onset of hydrodynamic behavior that has been observed in quark-gluon plasmas are seen in our numerical simulation of strongly coupled scalar fields. Published by the American Physical Society 2024

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.