Energy-momentum Tensor Research Articles

Proton’s gluon GPDs at large skewness and gravitational form factors from near threshold heavy quarkonium photoproduction

We study the exclusive near threshold photoproduction of heavy quarkonium in the framework of the generalized parton distribution (GPD) factorization, taking the J/ψ production as an example. Because of the threshold kinematics, the Compton-like amplitudes are related to gluon GPDs at large skewness ξ, distinct from the common kinematics in asymptotic high energy where the skewness is typically small. We discuss the nature of large-ξ expansion of these amplitudes in terms of the moments of gluon GPDs in the large-ξ limit. Based on that, we propose several ways to extract the first few moments of the gluon GPDs from these amplitudes, with the leading ones corresponding to the gluonic gravitational or energy-momentum tensor form factors (GFFs). We apply these methods to analyze the recent near threshold J/ψ production measurements by the J/ψ 007 experiment and GlueX Collaboration and find that the ξ scaling of the measured differential cross sections is consistent with the asymptotic behavior. However, the current data are not accurate enough yet for a complete determination of the gluonic GFFs, and therefore we consider some prospects for better extractions in the future. Published by the American Physical Society 2024

Measures of Distance in Quantum Mechanics

Combining gravity with quantum theory is still a work in progress. On the one hand, classical gravity is the geometry of space-time determined by the energy–momentum tensor of matter and the resulting nonlinear equations; on the other hand, the mathematical description of a quantum system is Hilbert space with linear equations describing evolution. In this paper, various measures in Hilbert space will be presented. In general, distance measures in Hilbert space can be divided into measures determined by energy and measures determined by entropy. Entropy measures determine quasi-distance because they do not satisfy all the axioms defining distance. Finding a general rule to determine such a measure unambiguously seems to be fundamental.

Energy densities in quantum mechanics

Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin-12 particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydrodynamic energy in the Madelung representation of quantum dynamics, which includes the quantum potential. Moreover, we find a new form of spin-related energy that is finite in the non-relativistic limit, emerges from the rest energy, and is (separately) locally conserved, though it does not contribute to the global energy budget. This form of energy has a holographic character, i.e., its value for a given volume is expressed via the surface of this volume. Our results apply to situations where local energy representation is essential; e.g. we show that the energy transfer velocity for a large class of free wave-packets (including Gaussian and Airy wave-packets) is larger than its group (i.e. coordinate-transfer) velocity.

Gravitational form factors of the nucleon and one pion graviproduction in chiral EFT

In the framework of chiral effective field theory of delta resonances, nucleons, and pions interacting with background gravitational field we calculate the gravitational form factors of the nucleon up to fourth order in the small scale expansion and obtain the long-range behavior of the corresponding contributions to the energy, spin, pressure, and shear force distributions. By comparing nucleon gravitational form factors with and without delta contributions we conclude that explicit inclusion of deltas plays an important role. Next we explore the Lorentz structure of the N↦Nπ transition matrix element of the conserved symmetric energy-momentum tensor and introduce its parametrization in terms of twelve transition form factors. We use the chiral effective field theory to calculate the tree-order contributions to the gravitational transition form factors of the pion graviproduction off the nucleon up to third order. Published by the American Physical Society 2024

Trace and diffeomorphism anomalies of the classical Liouville theory, Virasoro algebras, Weyl-gauging and all that

To fully clarify the invariance of the classical Liouville field theory under the Virasoro algebra, we first elucidate in detail the concept of classical anomaly, discuss the occurrence of two symmetry algebras associated to this theory, and provide some new formulae to compute the classical center in a general fashion. We apply this to the study of the symmetries of the free boson in two dimensions. Moving to Liouville, we see how this gives rise to an energy-momentum tensor with non-tensorial conformal transformations, in flat space, and a non-vanishing trace, in curved space. We provide a variety of improvements of the (local) theory, that restore Weyl invariance. With explicit computations, we show that the covariant conservation of the Weyl-invariance-improved energy-momentum tensor is lost, in general, and relate the chosen improvement with the corresponding subset of preserved diffeomorphisms. The non-tensorial transformation rule of the Weyl-invariance-improved energy-momentum tensor in curved space is explicitly back-traced to the Virasoro center.

Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String

In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1+D)-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated.

Hadrons, superconductor vortices, and cosmological constant

We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. It is shown that the energy-equilibrium correspondence of hadrons infers an equation of state where the trace anomaly matrix element, emerging from the glue condensate in the vacuum, gives a negative constant pressure that leads to confinement, much like the confinement mechanism for the vortices in type II superconductors where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that both the trace anomaly in the QCD energy-momentum tensor and the cosmological constant in Einstein's equation are associated with the metric term which contributes to both energy and pressure. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.

Lower bound on the radii of light rings in traceless black-hole spacetimes

Photonspheres, curved hypersurfaces on which massless particles can perform closed geodesic motions around highly compact objects, are an integral part of generic black-hole spacetimes. In the present compact paper we prove, using analytical techniques, that the innermost light rings of spherically symmetric hairy black-hole spacetimes whose external matter fields are characterized by a traceless energy-momentum tensor cannot be located arbitrarily close to the central black hole. In particular, we reveal the physically interesting fact that the non-linearly coupled Einstein-matter field equations set the lower bound rγ≥65rH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {r}_{\\gamma}\\ge \\frac{6}{5}{r}_H $$\\end{document} on the radii of traceless black-hole photonspheres, where rH is the radius of the outermost black-hole horizon.

Bianchi Type V Cosmological Scenario In f(R,T) Gravity Theory With Special Form Of Scale Factor

In this study, we have examined the exact solutions of the field equations for a Bianchi type V universe filled with bulk viscous fluid within the framework of theory, where and and represent the Ricci scalar and the trace of the energy momentum tensor, respectively. We used a combination of exponential and hyperbolic scale factors to determine the physical parameters and metric potentials in the space-time. We also investigated the geometrical and physical parameters of the model, as well as the energy conditions. Additionally, we found that the state finder diagnostic pair falls within an acceptable range.

Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein–Cartan Theory with Background Fields

Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy–momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking.

Non-minimal unimodular inflation

We study an extension of the unimodular cosmological inflation in the context of the non-minimal coupling of a generic scalar field with gravitational sector. We consider the non-minimal coupling of the scalar field and gravity as the only source of energy–momentum tensor in this setup. Without introducing new particles other than those already existing in electroweak theory, the generic scalar field’s non-minimal coupling is responsible for the generation of the seeds of perturbations for structure formation and the observed Cosmic Microwave Background anisotropies in this scenario. We calculate inflation parameters in both the Jordan and Einstein frames, and then we study primordial spectral indices for slow-roll parameters in Einstein’s frame at the first and second orders. The numerical results of this model are consistent with the Planck2018 and BICEP/Keck joint data sets in some subspaces of the model parameters space. By considering a sufficient amount of inflation, we estimate the strength of the non-minimal coupling parameter, ξ, to find appropriate new constraints on the values of this parameter. By comparing the numerical values of the inflation observables in two frames and also with observation, we comment on the issue of frames in this framework.

What is a real black hole?

Abstract Four dimensional Einstein equation with non-vanishing energy momentum tensor is solved to give a solution where the event horizon of a celestial body is outside of the body, which corresponds to a black hole by definition. There is no singularity at the center of the object unlike the case of Schwarzschild solution. We do not have the gravitational collapse. We do not have the gravitational collapse thus avoiding the Penrose-Hawking singularity theorems. The main feature of our black hole solution is that it has the horizon inside the black hole in addition to the usual outside horizon. This inner horizon singularity is not removable by a coordinate transformation because the determinant of metric tensor is singular at this point but there is no singularity neither in the density nor in the pressure indicating there is no gravitational collapse.

More on the fact that Rastall = GR

Rastall gravity is the same as General Relativity, with a simple algebraic redefinition of what is called the energy–momentum tensor. Despite it having been very clearly explained by M. Visser several years go, there are still many papers claiming big differences between the two formulations of gravitational equations and trying to use them for problems of physics. When going this way, the totally ignored task is to explain why the conserved energy–momentum quantities and the quantities used for other purposes are different from each other. Moreover, when researchers are using the non-conserved energy density and pressure for determining the sound speed, it is just inconsistent with the Rastall gravity. I carefully explain all this, and also show how one could construct a variational principle for producing equations in the Rastall form.

On curvature related geometric properties of Hayward black hole spacetime

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F⋅F=LQ(g,F) for F=W,C,K with a smooth scalar function L), and it also possesses the relation R⋅R−LQ(g,C)=Q(S,R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η-Ricci soliton as well as an almost η-Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc.

On higher-spin points and infinite distances in conformal manifolds

Distances in the conformal manifold, the space of CFTs related by marginal deformations, can be measured in terms of the Zamolodchikov metric. Part of the CFT Distance Conjecture posits that points in this manifold where part of the spectrum becomes free, called higher-spin points, can only be at infinite distance from the interior. There, an infinite tower of operators become conserved currents, and the conformal symmetry is enhanced to a higher-spin algebra. This proposal was initially motivated by the Swampland Distance Conjecture, one of pillars of the Swampland Program. In this work, we show that the conjecture can be tackled using only methods from the conformal toolkit, and without relying on the existence of a weakly-coupled gravity dual. Via conformal perturbation theory combined with properties of correlators and of the higher-spin algebra, we establish that higher-spin points are indeed at infinite distance in the conformal manifold. We make no assumptions besides the usual properties of local CFTs, such as unitarity and the existence of an energy-momentum tensor. In particular, we do not rely on a specific dimension of spacetime (although we assume d > 2), nor do we require the presence of supersymmetry.

From Scalar Clouds to Rotating Hairy Black Holes

First, we review the solutions of a complex-valued scalar field, termed scalar clouds, with and without electric charge, when coupled to a rotating Kerr–Newman (electrically charged) or Kerr (neutral) black hole (BH), respectively. To this aim, we determine the conditions and parameters that characterize the existence of solutions that represent bound states, with an energy-momentum tensor that respect the symmetries of the underlying spacetimes, even if the backreaction of the field is not taken into account at this stage. In particular, we show that in the extremal Kerr scenario the cloud solutions exist only when the mass of the BH satisfies certain bounds, which are obtained by analyzing an effective potential associated with the radial dependency of the scalar clouds that leads to a Schrödinger-like equation. Second, when the backreaction of the field in the spacetime is taken into account, we present a family of stationary, axisymmetric and asymptotically flat solutions of the Einstein–Klein–Gordon system that represent genuine rotating hairy black holes (RHBHs) and provide different values of some global quantities associated with them, such as the Komar mass and the Komar angular momentum. We also compute RHBH solutions with nodes in the radial part of the scalar field and also for a higher azimuthal number m.

Axially symmetric exponential metric

We present a new family of vacuum axially symmetric static solutions to Einstein’s field equations. This solution is a geometrically modified version of the Yilmaz exponential metric (YEM) which has recently been shown to represent a traversable wormhole. This vacuum solution is a one-parameter static singular solution with its singularity located at r=0. Furthermore, it is shown that both the YEM and its geometrically modified version, introduced in this work i.e., the Axially Symmetric Exponential metric (ASEM) belong to a general 2-parameter class of solutions supported by an anisotropic fluid. Depending on the parameters the generic energy–momentum tensor represents either an exotic or a normal fluid. Concerning the ASEM, the circular stable orbit does not exist for a null particle, however, for a massive particle such orbit exists provided its radius is larger than a minimum radius. This is in analogy with the Schwarzschild black hole as well as the YEM.

On the Anomalous Dimension in QCD

The anomalous dimension γm=1 in the infrared region near the conformal edge in the broken phase of the large Nf QCD has been shown by the ladder Schwinger–Dyson equation and also by the lattice simulation for Nf=8 and for Nc=3. Recently, Zwicky made another independent argument (without referring to explicit dynamics) for the same result, γm=1, by comparing the pion matrix element of the trace of the energy-momentum tensor π(p2)|(1+γm)·∑i=1Nfmfψ¯iψi|π(p1)=π(p2)|θμμ|π(p1)=2Mπ2 (up to trace anomaly) with the estimate of π(p2)|2·∑i=1Nfmfψ¯iψi|π(p1)=2Mπ2 through the Feynman–Hellmann theorem combined with an assumption Mπ2∼mf characteristic of the broken phase. We show that this is not justified by the explicit evaluation of each matrix element based on the dilaton chiral perturbation theory (dChPT): π(p2)|2·∑i=1Nfmfψ¯iψi|π(p1)=2Mπ2+[(1−γm)Mπ2·2/(1+γm)]=2Mπ2·2/(1+γm)≠2Mπ2 in contradiction with his estimate, which is compared with π(p2)|(1+γm)·∑i=1Nfmfψ¯iψi|π(p1)=(1+γm)Mπ2+[(1−γm)Mπ2]=2Mπ2 (both up to trace anomaly), where the terms in [] are from the σ (pseudo-dilaton) pole contribution. Thus, there is no constraint on γm when the σ pole contribution is treated consistently for both. We further show that the Feynman–Hellmann theorem is applied to the inside of the conformal window where dChPT is invalid and the σ pole contribution is absent, and with Mπ2∼mf2/(1+γm) instead of Mπ2∼mf, we have the same result as ours in the broken phase. A further comment related to dChPT is made on the decay width of f0(500) to ππ for Nf=2. It is shown to be consistent with the reality, when f0(500) is regarded as a pseudo-NG boson with the non-perturbative trace anomaly dominance.

Cosmological models in [formula omitted] gravity and the dynamical system analysis

The study addresses matter-coupled modified gravity, particularly f(T,T) gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of critical points to understand these models’ viability better. The dynamical system analysis of the cosmological models in f(T,T) gravity, where T and T respectively represent the torsion scalar and trace of the energy–momentum tensor has been investigated. It demonstrates how first-order autonomous systems can be treated as cosmological equations and analyzed using standard dynamical system theory techniques. Two forms of the function f(T,T) are considered (i) one with the product of trace and higher order torsion scalar and the other (ii) linear combination of linear trace and squared torsion. By employing this methodology, the research aims to uncover the actual behavior of the Universe. The findings emphasize the graphical representation of these insights, enriching our understanding of cosmological scenarios.

Revisiting [formula omitted] cosmologies

We review the status of f(R,T) cosmological models, where T is the trace of the energy momentum tensor Tμν. We start focusing on the modified Friedmann equations for the minimally coupled gravitational Lagrangian of the type f(R,T)=R+αeβT+γnTn. We show that in such a minimally coupled case there exists a useful constraining relation between the effective fractionary total matter density with an arbitrary equation of state parameter and the modified gravity parameters. With this association the modified gravity sector can be independently constrained using estimations of the gas mass fraction in galaxy clusters. Using cosmological background cosmic chronometers data and demanding the universe is old enough to accommodate the existence of Galactic globular clusters with ages of at least ∼14 Gyrs we find a narrow range of the modified gravity free parameter space in which this class of theories remains viable for the late time cosmological evolution. This preferred parameter space region accommodates the ΛCDM limit of f(R,T) models. We also work out the non-minimally coupled case in the metric-affine formalism and find that there are no viable cosmologies in the latter situation. However, when analyzing the cosmological dynamics including a radiation component, we find that this energy density interacts with the matter field and it does not scale according to the typical behavior. We conclude stating that f(R,T) gravity is not able to provide a full cosmological scenario and should be ruled out as a modified gravity alternative to the dark energy phenomena.