Stress-energy Tensor Research Articles

Cosmological sudden singularities in f(R, T) gravity

In this work, we study the possibility of finite-time future cosmological singularities appearing in f(R, T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We present the theory in both the geometrical and the dynamically equivalent scalar–tensor representation and obtain the respective equations of motion. In a background Friedmann–Lemaître–Robertson–Walker (FLRW) universe with an arbitrary curvature and for a generic C^infty function f(R, T), we prove that the conservation of the stress-energy tensor prevents the appearance of sudden singularities in the cosmological context at any order in the time-derivatives of the scale factor. However, if this assumption is dropped, the theory allows for sudden singularities to appear at the level of the third time-derivative of the scale factor a(t), which are compensated by divergences in either the first time-derivatives of the energy density rho (t) or the isotropic pressure p(t). For these cases, we introduce a cosmological model featuring a sudden singularity that is consistent with the current measurements for the cosmological parameters, namely, the Hubble constant, deceleration parameter, and age of the universe, and provide predictions for the still unmeasured jerk and snap parameters. Finally, we analyse the constraints on a particular model of the function f(R, T) that guarantees that the system evolves in a direction favorable to the energy conditions at the divergence time.

Tidal forces in dirty black hole spacetimes

Black holes can be inserted in very rich astrophysical environments, such as accretion disks. Although isolated black holes are simple objects in general relativity, their accretion disks may significantly enrich the field configurations of their surroundings. Alternative theories of gravity can lead to novel black hole solutions, which can be represented by small deviations in the metric due to an effective stress-energy tensor. Among the key aspects of the interaction of black holes with their surroundings, stand tidal forces phenomena. We study the tidal forces of spherically symmetric black holes in the presence of effective matter fields, dubbed as dirty black holes. These effective fields can generically represent usual or exotic matter associated to a variety of gravity theories. We show that this dirtiness leads to characteristic imprints in the tidal forces, which are absent in the case of a black hole surrounded by vacuum. We apply our results to particular cases, such as black holes coupled to linear and nonlinear electrodynamics theories and a Schwarzschild black hole surrounded by a spherical shell.

Quantum vacuum fluctuations and the principle of virtual work in inhomogeneous backgrounds

We discuss several aspects of the stress-energy tensor for a quantum scalar field in an inhomogeneous background, the latter being modeled by a variable mass. Using a perturbative approach, dimensional regularization, and adiabatic subtraction, we present all-order formal expressions for the stress-energy tensor. Importantly, we provide an explicit proof of the principle of virtual work for Casimir forces, taking advantage of the conservation law for the renormalized stress-energy tensor. We discuss also discontinuity-induced divergences. For the particular case of planar inhomogeneities, we corroborate the perturbative results with a WKB-inspired expansion.

Null cosmic strings: Scattering by black holes, optics, and spacetime content

Equations of motion of null cosmic strings near black holes, or other massive sources, are solved exactly in the weak field approximation. The stress-energy tensor of a null string in a curved spacetime is introduced and used to show how scattering by black holes transforms linear and angular momenta of the string. The corresponding recoil effect of a black hole and change of its angular momentum caused by a null cosmic string are calculated. For a null string, its energy $\mu$ per unit length evolves along the null direction of the string trajectory. The evolution of $\mu$ is connected with a string optical scalar $Z$. Optical properties of null strings are that their energy is concentrated on caustics, where $Z$ has poles. String parameters $\mu$ and $Z$ capture important features of the spacetime where strings move. Explicit dependence of $\mu$ and $Z$ on the strain and Bondi news tensors of gravitational wave background, mass and angular momentum aspects are established, near the future null infinity, up to the 4-th order in expansion in an inverse null parameter in asymptotically flat spacetimes.

Signature-Causality Reflection in An Imperfect Fluid with Vorticity Generated by Tetrad Abelian Gauge Transformations

We will address the possibility of a change in signature-causality in an imperfect fluid when we consider four-velocity gauge-like transformations in the case when the fluid has vorticity. An analogous tetrad formulation as to the Einstein-Maxwell spacetimes formalism introduced previously. The curl of the four-velocity and also the metric tensor will be invariant under the group of four-velocity gauge-like local transformations. The Einstein-Maxwell stress-energy tensor is invariant under local electromagnetic gauge transformations, similarly the imperfect fluid stress-energy tensor will also be invariant under the group of four-velocity gauge-like local transformations when we consider additional variable transformations in the stress-energy tensor. However, there is a relevant local causality scalar that undergoes a change in sign due to reflections under appropriate local Abelian tetrad gauge transformations. In this note we will study how to produce a signature-causality reflection in a region of spacetime bounded by a closed null surface using this same kind of transformations. This will be an important result since it is a physical result obtained through the use of a new local scalar quantity.

Gravity from symmetry: duality and impulsive waves

We show that we can derive the asymptotic Einstein’s equations that arises at order 1/r in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provide a definition of conserved charges parametrizing the non-radiative corner phase space. These observables, related to the Weyl scalars, reveal a duality symmetry and a spin-2 generator which allow us to recast the asymptotic evolution equations in a simple and elegant form as conservation equations for a null fluid living at null infinity. Finally we identify non-linear gravitational impulse waves that describe transitions among gravitational vacua and are non-perturbative solutions of the asymptotic Einstein’s equations. This provides a new picture of quantization of the asymptotic phase space, where gravitational vacua are representations of the asymptotic symmetry group and impulsive waves are encoded in their couplings.

Electromagnetic influence on hyperbolically symmetric sources in f(T) gravity

The present study aims to see how gravitational modification, specifically, the f(T) gravitational field, where T is torsion scalar, impacts static fluid content with hyperbolic symmetry and electromagnetic field. We enlarge Herrera’s strategy (Herrera et al. in Phys Rev D 103:024037, 2021) to analyze the impact of electromagnetic field on f(T) gravity. We distinguish the stress–energy tensor by considering the ingredients of the tetrad field in the Minkowski co-ordinate frame, commencing with modified field equations. With the advent of negative density, this sort of fluid is supposed to surpass extreme physical conditions, enabling quantum impacts to be detected. We calculate a viable formulation of mass utilizing the Tolman mass from the viewpoint of f(T) gravity along with the electromagnetic field. The gravitational interference is repulsive, as made evident by the negative value of the Tolman mass. Also, we explored the structure scalars in f(T) gravity and found significant solutions in presence of electric charge.

Analytic and asymptotically flat hairy (ultra-compact) black-hole solutions and their axial perturbations

In this work, we consider a very simple gravitational theory that contains a scalar field with its kinetic and potential terms minimally coupled to gravity, while the scalar field is assumed to have a coulombic form. In the context of this theory, we study an analytic, asymptotically flat, and regular (ultra-compact) black-hole solutions with non-trivial scalar hair of secondary type. At first, we examine the properties of the static and spherically symmetric black-hole solution — firstly appeared in [109] — and we find that in the causal region of the spacetime the stress-energy tensor, needed to support our solution, satisfies the strong energy conditions. Then, by using the slow-rotating approximation, we generalize the static solution into a slowly rotating one, and we determine explicitly its angular velocity ω(r). We also find that the angular velocity of our ultra-compact solution is always larger compared to the angular velocity of the corresponding equally massive slow-rotating Schwarzschild black hole. In addition, we investigate the axial perturbations of the derived solutions by determining the Schrödinger-like equation and the effective potential. We show that there is a region in the parameter space of the free parameters of our theory, which allows for the existence of stable ultra-compact black hole solutions. Specifically, we calculate that the most compact and stable black hole solution is 0.551 times smaller than the Schwarzschild one, while it rotates 2.491 times faster compared to the slow-rotating Schwarzschild black hole. Finally, we present without going into details the generalization of the derived asymptotically flat solutions to asymptotically (A)dS solutions.

Physical viability of anisotropic compact stars solutions under Karmarkar condition in f(ℛ,𝒯) theory of gravity

In this paper, we investigate the generalized symmetric, static compact objects under anisotropic fluid in the background of Karmarkar embedding class-1 condition. To find the exact solutions of the modified field equations, we consider the gravitational Lagrangian as a linear function of the Ricci scalar and the trace of the stress–energy tensor, i.e. [Formula: see text], where [Formula: see text] is a constant. By employing the concept of Karmarkar condition, we calculate a [Formula: see text] metric component, while for a specific form of [Formula: see text], the gravitational potential is chosen. To attain the closed-form solutions of the modified field equations, we match the interior spacetime metric with the exterior Schwarzschild metric at the boundary and using the numerical values of mass and radius of the compact stars like PSR J1903+327, 4U 1820-30, LMC X-4, and EXO 1785-248, we constraint some unknown parameters. We have discussed physical stability of the stellar configuration by adopting the energy bounds, Tolman–Oppenheimer–Volkov (TOV) equation, adiabatic index, central density and pressure as well. It is concluded that our resulting anisotropic solutions did well behave and a reasonable degree of precision with recent observations.

Relative Cauchy Evolution for Linear Homotopy AQFTs

This paper develops a concept of relative Cauchy evolution for the class of homotopy algebraic quantum field theories (AQFTs) that are obtained by canonical commutation relation quantization of Poisson chain complexes. The key element of the construction is a rectification theorem proving that the homotopy time-slice axiom, which is a higher categorical relaxation of the time-slice axiom of AQFT, can be strictified for theories in this class. The general concept is illustrated through a detailed study of the relative Cauchy evolution for the homotopy AQFT associated with linear Yang-Mills theory, for which the usual stress-energy tensor is recovered.

Lorentzian 2D CFT from the pAQFT Perspective

We provide a detailed construction of the quantum theory of the massless scalar field on two-dimensional, globally hyperbolic (in particular, Lorentzian) manifolds using the framework of perturbative algebraic quantum field theory. From this we obtain subalgebras of observables isomorphic to the Heisenberg and Virasoro algebras on the Einstein cylinder. We also show how the conformal version of general covariance, as first introduced by Pinamonti as an extension of the construction due to Brunetti, Fredenhagen and Verch, may be applied to natural Lagrangians, which allow one to specify a theory consistently across multiple spacetimes, in order to obtain a simple condition for the conformal covariance of classical dynamics, which is then shown to quantise in the case of a quadratic Lagrangian. We then compare the covariance condition for the stress-energy tensor in the classical and quantum theory in order to obtain a transformation law involving the Schwarzian derivative of the new coordinate, in accordance with a well-known result in the Euclidean literature.

Relativistic quantum fluid with boost invariance

We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable non-equilibrium problem. For the free quantum field, we calculate the exact form of the expectation values of the stress-energy tensor and the entropy current. For the stress-energy tensor, we find that a finite value can be obtained only by subtracting the vacuum of the density operator at some fixed proper time \tau_0. As a consequence, the stress-energy tensor acquires non-trivial quantum corrections to the classical free-streaming form.

Galactic dynamo seeds and black hole singularities driven by Einstein–Cartan QCD walls

Torsion spin polarised wall solution of Einstein–Cartan equations as torsion defects (Garcia de Andrade, Ann Phys 432 (2021)) where spin is distributed orthogonally to the wall has recently been obtained. Moreover, torsional inflating defect [Class and Quantum Gravity, 16 (1999) 2097] in the form of a dilatonic domain wall has also been found. Our goal in this paper is to obtain thin torsion wall solutions as teleparallel and Riemann–Cartan (RC) spacetime walls, with Einstein–Cartan stress–energy tensor, similar to Kalb–Ramond torsion fields. In thin teleparallel wall, we show that torsion is proportional to a time Dirac delta function which possesses a time singularity at the wall like Big Bang and black hole GR ones. This magnetic field has a torsional contribution of BQCD∼1017G in RC walls, which is suitable for dynamo amplification from a seed field of Bseed∼1012G as Big Bang Nucleosynthesis (BBN). From QCD cosmic time scale of tQCD∼10−6s torsion of the order of J0∼10−11cm−1 is obtained. From a 1 MeV torsion and seed field of Bseed∼10−32G, found by Barrow et al [PRD] in the framework of general relativity (GR) which is suitable to seed galactic dynamo field. In this case a domain wall magnetic field of BDW∼10−28G which is stronger, and more suitable as a galactic dynamo seed, is obtained. Magnetic field seed of 10−14G, quite close to orders of magnitude of O(10−15−10−18G) obtained by Atrayed et al. (EPJC (2018) 78: 1027) on a torsionless GR domain wall, generates a wall (DW) magnetic field of order of BDW∼1018G obtained at 1 kpc scales. These similarities between GR results and teleparallel one were expected due to the fact that the teleparallel theory of gravity considered in this paper is the teleparallel equivalent to GR or (TEGR). Chiral dynamos in dilatonic conformally flat metric are also discussed.

The Coupling effects of f(R,Tϕ) gravity on axial gravitational waves

The motive of this paper is to study the axial type gravitational waves within flat FRW universe and in the context of f ( R , T ϕ ) gravity (where T ϕ corresponds to the trace of stress energy tensor of ϕ , a scalar field). For this purpose, we consider the famous Regge–Wheeler axial perturbation scheme for geometry as well as assume the corresponding perturbations in the scalar field. We derived the field equations for both unperturbed and axially perturbed scenarios. The simultaneous solution of both sets of field equations lead to some expressions for unknown perturbation parameters. In view of these expressions, we concluded that the propagation of axial gravitational waves is influenced by the scalar field potential and the coupling of geometry and scalar field. The plots of conformal time function emanating from axial metric perturbations, for different values of λ and β , indicate this impact. • Our work is in Modified gravity. • Many researchers which are working in GR not appreciated the Modified gravity.

Cosmological perturbation theory in f(Q,T) gravity

We developed the cosmological linear theory of perturbations for f(Q,T) gravity, which is an extension of symmetric teleparallel gravity, with Q the non-metricity and T the trace of the stress-energy tensor. By considering an ansatz of f(Q,T) = f 1(Q)+f 2(T), which has been broadly studied in the literature and the coincident gauge where the connection vanishes, we got equations consistent with f(Q) gravity when fT = 0. In the case of the tensor perturbations, the propagation of gravitational waves was found to be identical to f(Q), as expected. For scalar perturbations, outside the limit fT = 0, we got that the coupling between Q and T in the Lagrangian produces a coupling between the perturbation of the density and the pressure. This coupling is preserved when considering the weak coupling limit between Q and T. On the other hand, in the strong coupling limit with a generic function of the form f 2(T) = αT + β T 2, the perturbative equations are heavily driven by the f 2(T) derivatives when β ≠ 0. However, when β = 0, the perturbative equations are identical to the weak coupling limit even though this case is a non-minimally coupling one. The presence of T in the Lagrangian breaks the equation of the conservation of energy, which in turn breaks the standard ρ' + 3\U0001d4d7 (ρ+p) = 0 relation. We also derived a coupled system of differential equations between δ, the density contrast and v in the \U0001d4d7 ≪ k limit and with negligible time derivative of the scalar perturbation potentials, which will be useful in future studies to see whether this class of theories constitute a good alternative to dark matter. These results might also enable to test f(Q,T) gravity with CMB and standard siren data that will help to determine if these models can reduce the Hubble constant tension and if they can constitute an alternative to the ΛCDM model.

Fractional formulation of Podolsky Lagrangian density

Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.

On the light-ray algebra in conformal field theories

We analyze the commutation relations of light-ray operators in conformal field theories. We first establish the algebra of light-ray operators built out of higher spin currents in free CFTs and find explicit expressions for the corresponding structure constants. The resulting algebras are remarkably similar to the generalized Zamolodchikov’s W∞ algebra in a two-dimensional conformal field theory. We then compute the commutator of generalized energy flow operators in a generic, interacting CFTs in d > 2. We show that it receives contribution from the energy flow operator itself, as well as from the light-ray operators built out of scalar primary operators of dimension ∆ ≤ d − 2, that are present in the OPE of two stress-energy tensors. Commutators of light-ray operators considered in the present paper lead to CFT sum rules which generalize the superconvergence relations and naturally connect to the dispersive sum rules, both of which have been studied recently.

Black tsunamis and naked singularities in AdS

We study the evolution of the Gregory-Laflamme instability for black strings in global AdS spacetime, and investigate the CFT dual of the formation of a bulk naked singularity. Using an effective theory in the large D limit, we uncover a rich variety of dynamical behaviour, depending on the thickness of the string and on initial perturbations. These include: large inflows of horizon generators from the asymptotic boundary (a ‘black tsunami’); a pinch-off of the horizon that likely reveals a naked singularity; and competition between these two behaviours, such as a nakedly singular pinch-off that subsequently gets covered by a black tsunami. The holographic dual describes different patterns of heat flow due to the Hawking radiation of two black holes placed at the antipodes of a spherical universe. We also present a model that describes, in any D, the burst in the holographic stress-energy tensor when the signal from a bulk self-similar naked singularity reaches the boundary. The model shows that the shear components of the boundary stress diverge in finite time, while the energy density and pressures from the burst vanish.

On the Significance of the Stress–Energy Tensor in Finsler Spacetimes

We revisit the physical arguments that led to the definition of the stress–energy tensor T in the Lorentz–Finsler setting (M,L) starting with classical relativity. Both the standard heuristic approach using fluids and the Lagrangian one are taken into account. In particular, we argue that the Finslerian breaking of Lorentz symmetry makes T an anisotropic 2-tensor (i.e., a tensor for each L-timelike direction), in contrast with the energy-momentum vectors defined on M. Such a tensor is compared with different ones obtained by using a Lagrangian approach. The notion of divergence is revised from a geometric viewpoint, and, then, the conservation laws of T for each observer field are revisited. We introduce a natural anisotropic Lie bracket derivation, which leads to a divergence obtained from the volume element and the non-linear connection associated with L alone. The computation of this divergence selects the Chern anisotropic connection, thus giving a geometric interpretation to previous choices in the literature.

(5+1)-dimensional analytical braneworld models: Intersecting thick branes

Two codimensional thick braneworlds are investigated in quite general terms for two intersecting scalar fields generating the extra dimension defect. In general, when one considers two codimensional thick braneworlds, the warp factor is constructed as a stringlike defect. Considering a twofold warp factor constructed from two intersecting warp factors, an alternative bulk configuration is examined. With the brane localization thus driven by two crossing scalar fields, the possible solvable models obtained from such a two codimensional setup are systematically discussed. The obtained solutions are classified as five different models organized into two subsets, for which some of their physical properties are evaluated. For models $I$ and $II$, in the first subset, Einstein equation solutions are rigidly defined, up to some arbitrary constant. For models $III$, $IV$, and $V$, in the second subset, an additional degree of freedom not constrained by Einstein equations is admitted. The solutions are all obtained from a departure statement of assuming a conformally flat metric for the internal space, which is concomitant to the proper choice of coordinates. Eventual singularities in the curvature are identified, however, without affecting the physical appeal of the solutions described in terms of the stress energy tensor patterns, which are shown to be free of singularities for model $IV$, besides admitting straightforward reductions to ($4+1$) dimensions. In particular, from the framework of models $III$ and $IV$, one is able to achieve braneworld solutions over two different geometries of ${\mathbb{S}}^{2}$ which, as demonstrated, can be reduced to trivial and nontrivial extensions of the well-known ($4+1$)-dimensional braneworlds. Therefore, our ($5+1$)-dimensional results point to a consistent and expanded generalization of a ($4+1$)-dimensional braneworld which naturally admits the possibility of an enlarged and maybe more accurate phenomenology.