Showing papers on "Stress–energy tensor published in 2023"

Notes on higher-derivative conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string

Abstract: A bstract I investigate the higher-derivative conformal theory which shows how the Nambu-Goto and Polyakov strings can be told apart. Its energy-momentum tensor is conserved, traceless but does not belong to the conformal family of the unit operator. To implement conformal invariance in such a case I develop the new technique that explicitly accounts for the quantum equation of motion and results in singular products. I show that the conformal transformations generated by the nonprimary energy-momentum tensor form a Lie algebra with a central extension which in the path-integral formalism gives a logarithmically divergent contribution to the central charge. I demonstrate how the logarithmic divergence is canceled in the string susceptibility and reproduce the previously obtained deviation from KPZ-DDK at one loop.

The energy–momentum complex in non-local gravity

Abstract: In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator [Formula: see text] are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

Induced energy-momentum tensor in de Sitter scalar QED and its implication for induced currents

Abstract: The aim of this research is to investigate the vacuum energy-momentum tensor of a quantized, massive, nonminimally coupled scalar field induced by a uniform electric field background in a four-dimensional de Sitter spacetime (${\mathrm{dS}}_{4}$). We compute the expectation value of the energy-momentum tensor in the in-vacuum state and then regularize it using the adiabatic subtraction procedure. The correct trace anomaly of the induced energy-momentum tensor that confirmed our results is significant. The nonconservation equation for the induced energy-momentum tensor imposes the renormalization condition for the induced electric current of the scalar field. The findings of this research indicate that there are significant differences between the two induced currents which are regularized by this renormalization condition and the minimal subtraction condition.

Physical aspects of ${f}(R,G_{\mu \nu}T^{\mu \nu})$ modified gravity theories

Abstract: The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the space--time geometry and the matter fields. The fundamental Einstein--Hilbert action is extended by considering a generic function ${f}(R,G_{\mu u}T^{\mu u})$ which is further decomposed into its main constituents, a geometric component which depends on the scalar curvature, and a second element embedding the interplay between geometry and matter fields. Specific cosmological models are established at the level of background dynamics, based on particular couplings between the matter energy--momentum tensor and the Einstein tensor. After deducing the resulting field equations, the physical aspects for the cosmological model are investigated by employing a dynamical system analysis for various coupling functions. The investigation showed that the present model is compatible with different epochs in the evolution of our Universe, possible explaining various late time historical stages.

Gravitational wave energy-momentum tensor and radiated power in a strongly curved background

Abstract: Allowing for the possibility of extra dimensions, there are two paradigms: either the extra dimensions are hidden from observations by being compact and small as in Kaluza-Klein scenarios, or the extra dimensions are large/non-compact and undetectable due to a large warping as in the Randall-Sundrum scenario. In the latter case, the five-dimensional background has a large curvature, and Isaacson's construction of the gravitational energy-momentum tensor, which relies on the assumption that the wavelength of the metric fluctuations is much smaller than the curvature length of the background spacetime, cannot be used. In this paper, we construct the gravitational energy-momentum tensor in a strongly curved background such as Randall-Sundrum. We perform a scalar-vector-tensor decomposition of the metric fluctuations with respect to the $SO(1,3)$ background isometry and construct the covariantly-conserved gravitational energy-momentum tensor out of the gauge-invariant metric fluctuations. We give a formula for the power radiated by gravitational waves and verify it in known cases. In using the gauge-invariant metric fluctuations to construct the gravitational energy-momentum tensor we follow previous work done in cosmology. Our framework has applicability beyond the Randall-Sundrum model.

Induced energy-momentum tensor in de Sitter scalar QED and its implication for induced current

Abstract: The aim of this research is to investigate the vacuum energy-momentum tensor of a quantized, massive, nonminimally coupled scalar field induced by a uniform electric field background in a four-dimensional de Sitter spacetime ($\dsf$). We compute the expectation value of the energy-momentum tensor in the in-vacuum state and then regularize it using the adiabatic subtraction procedure. The correct trace anomaly of the induced energy-momentum tensor that confirmed our results is significant. The nonconservation equation for the induced energy-momentum tensor imposes the renormalization condition for the induced electric current of the scalar field. The findings of this research indicate that there are significant differences between the two induced currents which are regularized by this renormalization condition and the minimal subtraction condition.

Energy–momentum tensor: Noether vs Hilbert

Abstract: Several definitions of the energy–momentum tensor in classical field models on differential manifolds are examined in this work. We specifically talk about the connection between - Hilbert’s symmetric and Noether’s asymmetric energy–momentum tensors. We consider a matter field Lagrangian on a manifold endowed with a teleparallel (coframe) structure. The associated 3-form of coframe conserved current can be viewed as a link between Noether’s and Hilbert’s energy–momentum tensors. In these circumstances, we are able to show the complete equivalence of Hilbert’s and Noether’s currents for the matter field.

Modified gravity and cosmology with nonminimal direct or derivative coupling between matter and the Einstein tensor

Abstract: We construct new classes of modified theories in which the matter sector couples with the Einstein tensor, namely we consider direct couplings of the latter to the energy-momentum tensor, and to the derivatives of its trace. We extract the general field equations, which do not contain higher-order derivatives, and we apply them in a cosmological framework, obtaining the Friedmann equations, whose extra terms give rise to an effective dark energy sector. At the background level we show that we can successfully describe the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the dark-energy equation-of-state parameter can lie in the phantom regime, tending progressively to $-1$ at present and future times. Furthermore, we confront the theory with Cosmic Chronometer data, showing that the agreement is very good. Finally, we perform a detailed investigation of scalar and tensor perturbations, and extracting an approximate evolution equation for the matter overdensity we show that the predicted behavior is in agreement with observations.

ANEC on stress-tensor states in perturbative λ ϕ4 theory

Abstract: A bstract We evaluate the Average Null Energy Condition (ANEC) on momentum eigenstates generated by the stress tensor in perturbative λ ϕ 4 and general spacetime dimension. We first compute the norm of the stress-tensor state at second order in λ ; as a by-product of the derivation we obtain the full expression for the stress tensor 2-point function at this order. We then compute the ANEC expectation value to first order in λ , which also depends on the coupling of the stress-tensor improvement term ξ . We study the bounds on these couplings that follow from the ANEC and unitarity at first order in perturbation theory. These bounds are stronger than unitarity in some regions of coupling space.

Conformal Symmetry

Abstract: The trace or conformal anomalies are the second important family of anomalies. They affect the trace of the energy-momentum tensor of a theory and represent the violation of a classical property: the on shell vanishing of the trace of the energy-momentum tensor when the (classical) theory is conformal invariant. This chapter is devoted to an introduction to conformal symmetry and conformal field theories.

Freedom near lightcone and ANEC saturation

Abstract: Averaged Null Energy Conditions (ANECs) hold in unitary quantum field theories. In conformal field theories, ANECs in states created by the application of the stress tensor to the vacuum lead to three constraints on the stress-tensor three-point couplings, depending on the choice of polarization. The same constraints follow from considering two-point functions of the stress tensor in a thermal state and focusing on the contribution of the stress tensor in the operator product expansion (OPE). One can observe this in holographic Gauss-Bonnet gravity, where ANEC saturation coincides with the appearance of superluminal signal propagation in thermal states. We show that, when this happens, the corresponding generalizations of ANECs for higher-spin multi-stress tensor operators with minimal twist are saturated as well and all contributions from such operators to the thermal two-point functions vanish in the lightcone limit. This leads to a special near-lightcone behavior of the thermal stress-tensor correlators -- they take the vacuum form, independent of temperature.

The energy-momentum complex in non-local gravity

Abstract: In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here we generalize the Einstein gravitational energy-momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator $\Box^{-1}$ are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy-momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy-momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy-momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

The Fundamental Choice in Physics between a non-linear and non-divergence Free “Stress-Energy Tensor” and the linear Divergence-Free “Stress-Energy Tensor” in the 4-dimensional Minkowski Space

Abstract: This article describes a new theory in physics which has been based on the “divergence-free linear 4-dimensional stress-energy tensor in the Minkowski Space”. The difference between Einstein’s General Relativity and this theory is the different approach. Einstein has deformed (non-linear and non-divergence free) the “4-dimensional Stress-Energy Tensor” by introducing the curved 4-dimensional Riemannian Manifold to explain the interaction between Gravity and Light. The new theory describes the interaction between different fields (Electric, Magnetic and Gravitational) by identical interaction terms, generated by the separate divergence and the separate rotation of the different fields. (equation 24) The conclusion of the new theory is that “divergence-free” and “rotation-free” fields do not interact.When Isaac Newton published his 3 famous equations which became the foundation of Classical Dynamics, he was not aware that he was building the first elemental blocks for the Stress-Energy Tensor in the 4-dimensional Minkowski Space.When James Clerk Maxwell published his 4 famous equations which became the foundation for Classical Electrodynamics, he was not aware that he was building new blocks for the Stress-Energy Tensor in the 4-dimensional Minkowski Space.When Paul Dirac published his famous equation which became the foundation of Relativistic Quantum Physics, he was not aware that he was building further on blocks for the Stress-Energy Tensor in the 4-dimensional Minkowski Space.It was Albert Einstein who was one of the first physicists who discovered the importance of the Stress-Energy Tensor to describe in a mathematical way the interaction between Electromagnetic Radiation and a Gravitational Field.But because there was no match, Einstein deformed the Divergence-Free Linear “Stress-Energy Tensor” by deforming Space and Time. He deformed this Tensor in such a way that he found a very special Mathematics to describe the interaction between Electromagnetic Radiation (Light) and a Gravitational Field. The Theory of General Relativity. And that became a problem. Because Einstein deformed the fundamental building block in physics (the Divergence-Free Linear “Stress-Energy Tensor), nothing fits anymore. Classical Mechanics has no match with Classical Electrodynamics. Classical Electrodynamics has no match with Relativistic Quantum Physics. Relativistic Quantum Physics has no match with General Relativity.It is important to distinguish the “Physical Reality” from a Mathematical Description of it (which is in general an approach). The scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. Einstein used a curved Riemannian manifold to describe “Gravitational-Electromagnetic Interaction”. But the physics beyond this is the interaction between the different fields. It is possible to describe this in different ways. This new theory demonstrates a more direct approach in the force densities acting between different fields expressed by equation (24).This new theory starts with the Divergence-Free Linear “Stress-Energy Tensor” in the 4-dimensional Minkowski Space. And from this unique Divergence-Free “Stress-Energy Tensor” follows Classical Mechanics, Classical Electrodynamics, Relativistic Quantum Physics and General Relativity. Bringing back the necessary unity in physics.Theories which unify Quantum Physics and General Relativity, like “String Theory”, predict the non-constancy of natural constants. Accurate observations of the NASA Messenger [11] observe in time a value for the gravitational constant “G” which constrains until ( /G to be < 4 × 10-14 per year) . One of the characteristics of the New Theory is the “Constant Value” in time for the Gravitational Constant “G”. A second experiment to test the New Theory is the effect of “Gravitational RedShift” [2].The “Gravitational RedShift” between an observatory on Earth (Radius = 6 106 [m]) and a Satellite in a Galileo Orbit (Radius = 23222 103 [m]) according “General Relativity”: The “Gravitational RedShift” between an observatory on Earth (Radius = 6 106 [m]) and a Satellite in a Galileo Orbit (Radius = 23222 103 [m]) according “The Proposed Theory”:

Energy-momentum tensor in the scalar diquark model

Abstract: We compute all the gravitational form factors in the scalar diquark model at the one-loop level using two different regularization methods. We check explicitly that all the Poincar\'e sum rules are satisfied and we discuss in detail the results for the trace of the energy-momentum tensor. Finally we discuss the spatial distributions of energy and pressure in two and three dimensions.

Classical gravitational anomalies of Liouville theory

Abstract: We show that for classical Liouville field theory, diffeomorphism invariance, Weyl invariance and locality cannot hold together. This is due to a genuine Virasoro center, present in the theory, that leads to an energy\hyp{}momentum tensor with non-tensorial conformal transformations, in flat space, and with a non-vanishing trace, in curved space. Our focus is on a field-independent term, proportional to the square of the Weyl gauge field, $W_\mu W^\mu$, that makes the action Weyl-invariant and was disregarded in previous investigations of Weyl and conformal symmetry. We show this term to be related to the classical center of the Virasoro.

Irreversible Geometrothermodynamics of Open Systems in Modified Gravity

Abstract: 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.

The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories

Abstract: The first order variation of the matter energy-momentum tensor $T_{\mu u}$ with respect to the metric tensor $g^{\alpha \beta}$ plays an important role in modified gravity theories with geometry-matter coupling, and in particular in the $f(R,T)$ modified gravity theory. We obtain the expression of the variation $\delta T_{\mu u}/\delta g^{\alpha \beta}$ for the baryonic matter described by an equation given in a parametric form, with the basic thermodynamic variables represented by the particle number density, and by the specific entropy, respectively. The first variation of the matter energy-momentum tensor turns out to be independent on the matter Lagrangian, and can be expressed in terms of the pressure, the energy-momentum tensor itself, and the matter fluid four-velocity. We apply the obtained results for the case of the $f(R,T)$ gravity theory, where $R$ is the Ricci scalar, and $T$ is the trace of the matter energy-momentum tensor, which thus becomes a unique theory, also independent on the choice of the matter Lagrangian. A simple cosmological model, in which the Hilbert-Einstein Lagrangian is generalized through the addition of a term proportional to $T^n$ is considered in detail, and it is shown that it gives a very good description of the observational values of the Hubble parameter up to a redshift of $z\approx 2.5$.

Spacetime Admitting Semiconformal Curvature Tensor in f(ℛ) Modify Gravity

Abstract: The primary goal of this paper is to examine spacetimes admitting semiconformal curvature tensor in [Formula: see text] modify gravity. The semiconformal flatness of general spacetime and spacetime in [Formula: see text] gravity with perfect fluid, has been analyzed. For this consideration, we generate the forms of isotropic pressure [Formula: see text] and energy density [Formula: see text]. After that, a few energy conditions are taken into account. Finally, we study the divergence-free semiconformal curvature tensor in [Formula: see text] gravity in presence of perfect fluid. We emphasize that for recurrent or bi-recurrent energy–momentum tensor, Ricci tensor of this spacetime is semi-symmetric and consequently, the resulting spacetimes either accomplish inflation or possess fixed isotropic pressure and energy density.

Representation of Physical Fields as Einstein Manifold

Abstract: In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

Abstract: We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu-Goldstone modes of higher-form symmetries.