Stress-energy Tensor Research Articles

Angular momentum at null infinity in Einstein-Maxwell theory

On Minkowski spacetime, the angular momentum flux through null infinity of Maxwell fields, computed using the stress-energy tensor, depends not only on the radiative degrees of freedom, but also on the Coulombic parts. However, the angular momentum also can be computed using other conserved currents associated with a Killing field, such as the Noether current and the canonical current. The flux computed using these latter two currents is purely radiative. A priori, it is not clear which of these is to be considered the true flux of angular momentum for Maxwell fields. This situation carries over to Maxwell fields on non-dynamical, asymptotically flat spacetimes for fluxes associated with the Lorentz symmetries in the asymptotic Bondi-Metzner-Sachs (BMS) algebra. We investigate this question of angular momentum flux in the full Einstein-Maxwell theory. Using the prescription of Wald and Zoupas, we compute the charges associated with any BMS symmetry on cross-sections of null infinity. The change of these charges along null infinity then provides a flux. For Lorentz symmetries, the Maxwell fields contribute an additional term, compared to the Wald-Zoupas charge in vacuum general relativity, to the charge on a cross-section. With this additional term, the flux associated with Lorentz symmetries, e.g., the angular momentum flux, is purely determined by the radiative degrees of freedom of the gravitational and Maxwell fields. In fact, the contribution to this flux by the Maxwell fields is given by the radiative Noether current flux and not by the stress-energy flux.

Expectation value of mathrm{T}overline{mathrm{T}} operator in curved spacetimes

We study the expectation value of the mathrm{T}overline{mathrm{T}} operator in maximally symmetric spacetimes. We define an diffeomorphism invariant biscalar whose coinciding limit gives the expectation value of the mathrm{T}overline{mathrm{T}} operator. We show that this biscalar is a constant in flat spacetime, which reproduces Zamolodchikov’s result in 2004. For spacetimes with non-zero curvature, we show that this is no longer true and the expectation value of the mathrm{T}overline{mathrm{T}} operator depends on both the one- and two-point functions of the stress-energy tensor.

Expanding 3d mathcal{N} = 2 theories around the round sphere

We study a perturbative expansion of the squashed 3-sphere left({s}_b^3right) partition function of 3d mathcal{N} = 2 gauge theories around the squashing parameter b = 1. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit b → 0 (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data (F, CT, CJJ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.

A possible semiclassical bounce instead of a Schwarzschild singularity

We have previously shown that the singularity in a Schwarzschild black hole of stellar or larger mass may be avoided in a semiclassical manner by using as a source of gravity the stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, with a minimum spherical radius a few orders of magnitude larger than the Planck length. In this note we estimate the nonlocal contribution to the total SET due to particle creation from vacuum. We show that this contribution is negligibly small as compared to vacuum polarization and does not affect the previously suggested scenario.

Renormalized quantum stress–energy tensor for massive spinor fields around global monopoles

The renormalized quantum stress–energy tensor [Formula: see text] for a massive spinor field around global monopoles is constructed within the framework of Schwinger–DeWitt approximation, valid whenever the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry. The results obtained show that the quantum massive spinor field in the global monopole spacetime violates all the pointwise energy conditions.

Regular quantum states on the Cauchy horizon of a charged black hole

We consider the expectation value of the stress–energy tensor for a massless quantum scalar field near the Cauchy horizon interior to the Reissner–Nordström black hole spacetime. We construct the quantum state by considering the two-point function on a negative definite metric obtained by a double analytic continuation from the Lorentzian manifold, complexifying both the t and polar coordinates. We enforce periodicity in the Euclideanized t coordinate with periodicity equal to the reciprocal of the temperature of the Cauchy horizon, a necessary condition for avoiding a conical singularity at the inner horizon. We show by explicit construction that our quantum state satisfies the Hadamard condition on the Cauchy horizon. The expectation value of the quantum stress–energy tensor on the Cauchy horizon is given in closed form.

Traversable wormhole solutions in Rastall teleparallel gravity

Abstract In this manuscript we consider the traversable wormhole solutions in teleparallel gravity formalism with and without Rastall constraint on stress–energy tensor of dark energy. We have studied the isotropic and non-isotropic form of stress–energy tensor of dark energy which the equation of state (EoS) between density and the radial components of pressure is used. This work is done for a diagonal tetrad and we have found some geometries which could describe a traversable wormhole, but the null energy and weak energy conditions were not violated for some sets of parameters.

Stability of charged rotating (2 + 1)-dimensional wormholes

This paper investigates the effects of charge on linearized stability of rotating thin-shell wormholes (WHs) filled with a barotropic fluid. We use Visser cut and paste technique to construct thin-shell from charged rotating Bañados–Teitelboim–Zanelli (BTZ) black holes (BHs). The components of stress-energy tensor are evaluated through Israel thin-shell formalism. The angular momentum for both interior as well as exterior region at the WH throat remains the same but opposite in direction, i.e. thin-shell WH at the throat is counter-rotated. It is found that the geometrical structure of WHs is more stable for highly charged and fast rotating thin-shell. We conclude that the stability regions of charged rotating WHs are larger than the uncharged rotating WHs.

Noncommutative-geometry wormholes without exotic matter

A fundamental property of Morris-Thorne wormholes is the so-called flare-out condition that automatically results in a violation of the null energy condition (NEC) in classical general relativity. By contrast, in $f(R)$ modified gravity, the material threading the wormhole may actually satisfy the NEC, while, at the same time, the effective stress-energy tensor arising from the modified theory violates the NEC, thereby sustaining the wormhole. It is shown in this paper that noncommutative geometry, an offshoot of string theory, can be viewed as a special case of $f(R)$ gravity and can therefore sustain a wormhole without the use of exotic matter. It also provides a motivation for the choice of $f(R)$ in the modified gravitational theory.

Small sphere limit of the quasi-local energy with anti de-Sitter space reference

In [13], a new quasi-local energy is introduced for spacetimes with a non-zero cosmological constant. In this article, we study the small sphere limit of this newly defined quasi-local energy for spacetimes with a negative cosmological constant. For such spacetimes, the anti de-Sitter space is used as the reference for the quasi-local energy. Given a point $p$ in a spacetime $N$, we consider a canonical family of surfaces approaching $p$ along its future null cone and evaluate the limit of the quasi-local energy. The optimal embedding equation which identifies the critical points of the quasi-local energy is solved in order to evaluate the limit. Using the optimal embedding, we show that the limit recovers the stress-energy tensor of the matter field at $p$. For vacuum spacetimes, the quasi-local energy vanishes to a higher order. In this case, the limit of the quasi-local energy is related to the Bel-Robinson tensor at $p$.

Dark Future for Dark Matter

The prevailing cosmological constant and cold dark matter (ΛCDM) cosmic concordance model accounts for the radial expansion of the universe after the Big Bang. The model appears to be authoritative because it is based on the Einstein gravitational field equation. However, a thorough scrutiny of the underlying theory calls into question the suitability of the field equation, which states that the Einstein tensor Gμv is a constant multiple of the stress-energy tensor Tμv when they both are evaluated at the same 4D space-time point: Gμv = 8πkTμv, where k is the gravitational constant. Notwithstanding its venerable provenance, this equation is incorrect unless the cosmic pressure is p = 0; but then all that remains of the Einstein equation is the Poisson equation which models the Newtonian gravity field. This shortcoming is not resolved by adding the cosmological constant term to the field equation, Gμv +Λ gμv =8πkTμv, as in the ΛCDM model, because then p = Λ, so the pressure is a universal constant, not a variable. Numerous studies support the concept of a linearly expanding universe in which gravitational forces and accelerations are negligible because the baryonic mass density of the universe is far below its critical density. We show that such a coasting universe model agrees with SNe Ia luminosity vs. redshift distances just as well or even better than the ΛCDM model, and that it does so without having to invoke dark matter or dark energy. Occam’s razor favors a coasting universe over the ΛCDM model.

Baryon Physics and Tight Coupling Approximation in Boltzmann Codes

We provide two derivations of the baryonic equations that can be straightforwardly implemented in existing Einstein–Boltzmann solvers. One of the derivations begins with an action principle, while the other exploits the conservation of the stress-energy tensor. While our result is manifestly covariant and satisfies the Bianchi identities, we point out that this is not the case for the implementation of the seminal work by Ma and Bertschinger and in the existing Boltzmann codes. We also study the tight coupling approximation up to the second order without choosing any gauge using the covariant full baryon equations. We implement the improved baryon equations in a Boltzmann code and investigate the change in the estimate of cosmological parameters by performing an MCMC analysis. With the covariantly correct baryon equations of motion, we find 1 % deviation for the best fit values of the cosmological parameters that should be taken into account. While in this paper, we study the Λ CDM model only, our baryon equations can be easily implemented in other models and various modified gravity theories.

, , JT and deformations

The light-cone gauge approach to deformed models is generalised to models deformed by U(1) conserved currents , , stress–energy tensor , and their various quadratic combinations of the form . It is then applied to derive a ten-parameter deformed Hamiltonian for a system of scalars with an arbitrary potential, the flow equations for the Hamiltonian density, and the flow equations for the energy of the deformed model. The flow equations disagree with the ones recently proposed in Le Floch and Mezei (2019 (arXiv:1903.07606)). The results obtained are applied to analyse a CFT with left- and right-moving conserved currents deformed by these operators. It is shown that with a proper choice of the parameter of the deformation the deformed CFT Hamiltonian density is independent of the parameters of the and deformations. This leads to the existence of two extra relations which generalise the and relations of the undeformed CFT. The spectrum of the deformed CFT is found and shown to satisfy the flow equations.

Ingoing Eddington-Finkelstein metric of an evaporating black hole

We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.

Gravitational wave polarization in exponential forms of f(R) gravity with coupling to matter

We investigate polarizations of gravitational waves in generalized theories of gravity whose action contains a nonminimal coupling (NMC) between an exponential function of [Formula: see text] gravity and the matter field. Specifically, we consider two classes of such models. In the first case, we assume an explicit NMC between the matter Lagrangian density and curvature while in the second case, we consider the exponential [Formula: see text] gravity coupled to the trace of the stress-energy tensor of a scalar field. Using the Newman–Penrose quantities, we show that these models can be considered as suitable choices in order to produce new polarization modes.

The type III stress-energy tensor: ugly duckling of the Hawking–Ellis classification

We present some advances in the understanding of type III stress-energy tensors as per the Hawking–Ellis classification. Type I and type II naturally appear in classical situations, and can also describe semiclassical effects. Type IV often shows up in semiclassical gravity. Type III is much more subtle. We focus our attention on type III0 stress-energy tensors, which capture the essence (‘essential core’) of type III. Reflecting on known purely phenomenological examples, (‘gyratons’), we are able to generalize the geometry generated by those type III0 stress-energy tensors. Moreover, we also succeed in extending work by Griffiths based on massless Weyl spinors by finding a fundamental classical bosonic Lagrangian description of these type III0 stress-energy tensors. To the best of our knowledge this is the first time in the literature that a consistent classical bosonic Lagrangian formulation for type III0 stress-energy has been found.

Bootstrapping the 3d Ising model at finite temperature

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions 〈σσ〉 and 〈ϵϵ〉. As a result, we estimate the one-point functions of the lowest-dimension ℤ2-even scalar ϵ and the stress energy tensor Tμν. Our result for 〈σσ〉 at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

Inhomogeneous perturbations and stability analysis of the Einstein static universe in $f(R,T)$ gravity

The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy tensor, respectively). The static and perturbed field equations are constructed for perfect fluid parameterized by linear equation of state parameter. We obtain solutions manifesting the Einstein static state by considering peculiar $f(R,T)$ forms for vanishing and non-vanishing conservation of the stress-energy tensor. It is observed that stable static Einstein regions exist for both closed as well as open FLRW universe models for an appropriate choice of parameters. We conclude that this theory is efficient for presenting such cosmological solutions leading to emergent universe scenario.

Einstein\u2013Cartan\u2013Dirac gravity with U(1) symmetry breaking

Einstein–Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein–Cartan–Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the U(1) gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).

Ghost-free modification of the Polyakov action and Hawking radiation

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.