Stress-energy Tensor Research Articles

Conservative wormholes in generalized [formula omitted]- function

We present an exhaustive study of wormhole configurations in κ(R,T) gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a constant redshift function that leads to a wormhole (WH) which is asymptotically non-flat. The remaining solutions were explored in two cases. Firstly, assuming a linear equation of state p(r)=ωρ(r) along with different forms of κ(R,T)-function. This proved enough to derive a shape function of the form b(r)=r0(r0r)1/ω. Secondly, by assuming specific choices of the shape function consistent with the wormhole configuration requirements. All the solutions fulfill flare-out condition, asymptotically flat and supported by phantom energy. Further, the embedding surface and its revolution has been generated using numerical method to see how the length of the throat is affected of the coupling parameters through κ(R,T) function. At the end, we have also calculated the average null energy condition, which is satisfied by all the WH models signifying minimum exotic matter is required to open the WH throats.

Spin-2 operators in two-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (4, 0) quivers from massive type IIA

In this work we revisit the problem of studying spin-2 fluctuations around a class of solutions in massive type IIA that is given by a warped AdS3 × S2 × T4 × Iρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{I}}_{\\rho } $$\\end{document} and with N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (4, 0) supersymmetry. We were able to identify a class of fluctuations, which is known as the “minimal universal class” that is independent of the background data and saturates the bound on the mass related to the field theory unitarity bound. These operators have conformal dimension ∆ = 2(ℓ + 1), with ℓ being the quantum number of the angular momentum on the S2. We also computed the normalisation of the 2-point function of stress-energy tensors from the effective 3-dimensional graviton action. We comment on the relation of our results to the related AdS3 and AdS2 solutions in massive type IIA and type IIB theories respectively.

Existence of remnants of regular black holes with de Sitter centers

We address the question of the end point of the quantum evaporation of regular black holes with the de Sitter centers specified by the algebraic structure of their stress–energy tensors [Formula: see text]. Most of the presented in the literature regular solutions belong to this class. In the case of a nonzero background cosmological constant stress–energy tensors with [Formula: see text] connect smoothly two de Sitter vacua, in the center and at infinity, and generate regular solutions to the Einstein equations, which describe the spacetime structure of regular black holes and their remnants. We show that for this class black holes their spacetime symmetry prevents a complete evaporation and provides the existence of thermodynamically stable remnants.

Spacetime symmetry breaking on nongeodesic leaves and a new form of matter

We examine the permanent damage caused by the historical breakdown of full diffeomorphism invariance induced by a foliation. We focus on the case where the foliation is allowed to be nongeodesic after the interactions with the foliation switch off. Gravity and other forms of matter recover full diffeomorphism invariance only at the expense of introducing a new matterlike component, carrying the nonvanishing Hamiltonian (and momentum, as it turns out) left over from the violating past interactions. This matter form must be stress-free in the preferred frame; this is the only way a matter action can mimic the evolution of the leftover Hamiltonian (and momentum) driven by the Dirac hypersurface deformation algebra. Hence, if the preferred frame is nongeodesic, the equivalent matter component must have energy and a momentum current in this frame, but still no spatial stresses: an unusual form of “matter.” It is equivalent to a fluid with anisotropic stress in some regimes, reducing to dust in others, or even displaying completely new features in extreme situations. Its stress energy tensor is conserved. We provide two examples based on accelerated frames: Rindler space-time and the canonical Schwarzchild frame. Published by the American Physical Society 2024

Unravelling the Enigmatic Nexus: Black Holes, Dark Matter, and the Interplay of Light, Gravity, and Electromagnetic Forces in Astrophysics and Astronomy

This research introduces a mathematical model positioning our physical reality within a ten-dimensional hyperspace, in which time acts as the unifying coordinate linking three-dimensional electric, magnetic, and gravitational spaces. Each domain is characterized by its respective field—electric, magnetic, or gravitational—and governed by intrinsic divergences and rotations, leading to a universal property known as Force Density, expressed in [N/m³]. This Force Density facilitates interactions among the distinct spaces while adhering to the principle of equilibrium, which posits that cumulative force densities from disturbances must consistently sum to zero. Building upon Einstein's General Relativity—which describes the curvature of spacetime by gravitational fields and assumes a constant light speed—this study proposes a perspective wherein light speed may vary during coherent laser beam interactions, prompting a re-examination of gravitational and luminous interactions across scales. The proposed model integrates the Stress-Energy Tensor and Gravitational Tensor, introducing a new tensor representation for black holes, termed Gravitational Electromagnetic Confinements, incorporating electromagnetic energy gradients and Lorentz transformations. This framework transcends traditional General Relativity, particularly evident in gravitational lensing. By reinterpreting Einstein's incorporation of the Gravitational Constant within the Energy-Stress Tensor, this work harmonizes gravity and light, offering insights into black hole solutions resonating with John Archibald Wheeler's 1955 research. Empirical data from Galileo satellites and MASER frequency measurements underscore discrepancies between established theories and this new model, enhancing the precision of gravitational observations. Through the confluence of Quantum Physics and General Relativity, as seen in approaches like String Theory, this interdisciplinary endeavor revisits the gravitational constant "G," redefining it while bridging theoretical frameworks, thus paving the way for breakthroughs in astronomical and astrophysical sciences.

Inconsistency of modified gravity in cosmology

We show that there is a fundamental flaw in the application of modified gravity theories in cosmology, taking f(R) gravity as a paradigmatic example. This theory contains a scalar degree of freedom that couples to the matter stress-energy tensor but not to gravitational energy. However, when applied to cosmology this theory is unable to distinguish between gravitational and non-gravitational energy. Hence the cosmological version of the theory does not coincide with its own macroscopic average, and we show that this leads to order-one discrepancies. We argue that the same inconsistency is common to many other modified gravity theories with extra degrees of freedom. Our results put into question whether these theories can make sense as the cosmological average of a fundamental theory, hence challenging their physical significance.

The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor

Given a Cauchy surface in a curved spacetime and a suitably defined quantum state on the CCR algebra of the Klein-Gordon quantum field on that surface, we show, by expanding the squared spacetime geodesic distance and the 'U' and 'V' Hadamard coefficients (and suitable derivatives thereof) in sufficiently accurate covariant Taylor expansions on the surface that the renormalized expectation value of the quantum stress-energy tensor on the surface is determined by the geometry of the surface and the first 4 time derivatives of the metric off the surface, in addition to the Cauchy data for the field's two-point function. This result has been anticipated in and is motivated by a previous investigation by the authors on the initial value problem in semiclassical gravity, for which the geometric initial data corresponds, a priori, to the spatial metric on the surface and up to 3 time derivatives off the surface, but where it was argued that the fourth derivative can be obtained with aid of the field equations on the initial surface.

A Quantization for the Toy Model of Black Hole and a Suggestion to the Unification Theory

In my previous paper about the correlations between quantum mechanics and the four different natural forces, I suggested that there may be a fifth force or even the existence of a new particle. However, it remains a mystery to physicists, even after nearly a hundred years, that they cannot unify these four natural forces. This may be because there are indeed too many variables for them to consider. Also, there is a possibility that quantum mechanics may coexist with quantum field theory. In the present paper, this author proposes that there may be a misconception in the computational equation for relative time or gaps in the system for measuring time between quantum mechanics and general relativity. Hence, one may still not be able to unify these natural forces. This author suggests that we may need to rewrite parts of quantum mechanics – the Schrödinger equation – or even the general relativity equation. Additionally, this author proposes that there may be a bridge equation converting between quantum mechanics and general relativity. Moreover, this author has employed the non-trivial zeta zeros to simulate the black hole or the so-called black hole toy model. In practice, there may be an electromagnetic field surrounding the boundary of the black hole, as well as the existence of a continuum along the boundary contour. This author hopes that, in such a case, we may decode those high-frequency electromagnetic waves into useful information and take a further step toward verifying Stephen Hawking’s famous theory on black hole radiation and information entropy. In fact, this author has used the HKLam statistical model theory to express the electromagnetic field energy-stress tensor (with the possibility of quantization) to analogically establish a quantized model for the Einstein Gravitational Field Equation. Hence, the problem of quantum gravity may then be solved. Last but not least, this author also expects that humanity may finally find a way to unify quantum mechanics and general relativity through modifications to the current quantum gravity theory, such as my proposed bridge-converting equation, etc.

Geometric Formulation of Generalized Root-TT[over ¯] Deformations.

We develop a generic geometric formalism that incorporates both TT[over ¯]-like and root-TT[over ¯]-like deformations in arbitrary dimensions. This framework applies to a wide family of stress-energy tensor perturbations and encompasses various well-known field theories. Building upon the recently proposed correspondence between Ricci-based gravity and TT[over ¯]-like deformations, we further extend this duality to include root-TT[over ¯]-like perturbations. This refinement extends the potential applications of our approach and contributes to a deeper exploration of the interplay between stress tensor perturbations and gravitational dynamics. Among the various original outcomes detailed in this Letter, we have also obtained a deformation of the flat Jackiw-Teitelboim gravity action.

Holographic reconstruction of flat spacetime

The flat/CFT dictionary between the bulk gravitational theory and boundary conformal field theory is systematically developed in this paper. Asymptotically flat spacetime is built up by asymptotically AdS hyperboloid slices in terms of Fefferman Graham coordinates together with soft modes propagating between different slices near the null boundary. Then we construct the flat holography dictionary based on studying the Einstein equation at zero and first order and it turns out that these correspond to the description of hard and soft sector for the field theory from the boundary point of view. The explicit expression for energy-stress tensor is also determined by performing holographic renormalisation on the Einstein Hilbert action. By studying the anomalies of the energy-stress tensor, we obtain the leading and subleading contribution to the central charge. Einstein equations in the bulk are related to the Ward identities of the boundary theory and we find that the boundary CFT energy-stress tensor is not conserved due to the existence of radiative soft modes which will generate the energy flow through the null boundary.

Quantum instability of the Cauchy horizon in a charged de-Sitter spacetime with dark matter

The strong cosmic censorship conjecture (SCCC) requires that spacetime cannot be extended beyond the Cauchy horizon. This ensures the predictability of spacetime. In this paper, we investigate the SCCC for a spherically symmetric charged de-Sitter black hole surrounded by dark matter using classical and quantum scalar fields. At the classical level, we analyze the behavior of scalar waves near the Cauchy horizon using the method developed by Hintz and Vasy. We find a relationship between the Sobolev regularity of scalar waves and the spectral gap of quasinormal modes. In the nearly extremal region, this may lead to a violation of the SCCC. At the quantum level, we first provide a proof of the renormalizability of the quantum scalar field in dark-matter black holes. Using numerical methods, we then demonstrate that the renormalized quantum stress-energy tensor for any Hadamard state exhibits quadratic divergence near the Cauchy horizon in the nearly extremal region. The quadratic divergence of the renormalized quantum stress-energy tensor is sufficient to convert the Cauchy horizon into a singularity. Thus, the SCCC is preserved by quantum effects. Since the quadratic divergence is more singular than the behavior of classical scalar field perturbations near the Cauchy horizon, it means there is a region where physics is dominated by quantum effects. We study the influence of dark matter on quantum effects in this region and we find there is a monotonic relationship between the dark matter and the strength of quantum effects. The numerical results show that the quantum effects will become stronger as dark matter increases.

Beyond N = ∞ in large N conformal vector models at finite temperature

We investigate finite-temperature observables in three-dimensional large N critical vector models taking into account the effects suppressed by 1N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N} $$\\end{document}. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalar O(N) model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in 1N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N} $$\\end{document}, which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infinite N, while in special cases the discrepancies only start to appear at the next-to-subleading order.

Conservation laws of stress–energy tensor in Yang–Mills theory

In this paper we present a new identity to associate the conservation laws of stress–energy tensor with the field equations in Yang–Mills theory. The Lorentz force is included with a consistent formulation as in Maxwell theory.

A hidden 2d CFT for self-dual Yang-Mills on the celestial sphere

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this paper, we propose to derive an explicit 2d realization of the algebra by performing a particular gauge transformation on the twistor action for self-dual Yang-Mills. The gauge parameter used in the transformation generates pure gauge connections corresponding to large gauge transformations on 4d Minkowski space, which localises part of the twistor action to a ℂℙ1 on ℂ* reduction of twistor space. Under a projection, it can be mapped to the celestial sphere at the light-cone cut of the origin on I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{I} $$\\end{document}. Geometrically, this is the common boundary celestial sphere shared by Euclidean AdS3 or Lorentzian dS3 slices of Minkowski space. We comment on the geometric meaning of the derivation from the perspective of minitwistor spaces of the 3d slices embedded in 4d Minkowski space. Using the action functional of this 2d CFT, we compute its stress-energy tensor and central charge. By a further marginal deformation, we calculate correlation functions of current algebra generators purely from the 2d side which reproduce full 4d tree-level form factors.

A relativistic scalar model for fractional interaction between dark matter and gravity

Abstract In a series of recent papers we put forward a “fractional gravity”
framework striking an intermediate course between a modified gravity theory and an
exotic dark matter (DM) scenario, which envisages the DM component in virialized
halos to feel a non-local interaction mediated by gravity. The remarkable success
of this model in reproducing several aspects of DM phenomenology motivates us to
look for a general relativistic extension. Specifically, we propose a theory, dubbed
Relativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stressenergy tensor couples to the scalar curvature via a non-local operator constructed with
a fractional power of the d’Alembertian. We derive the field equations starting from
an action principle, and then we investigate their weak field limit, demonstrating that
in the Newtonian approximation the fractional gravity setup of our previous works is
recovered. We compute the first-order post-Newtonian parameter γ and its relation
with weak lensing, showing that although in RSFG the former deviates from its GR
values of unity, the latter is unaffected. We also perform a standard scalar-vectortensor-decomposition of RSFG in the weak field limit, to highlight that gravitational
waves propagate at the speed of light, though also an additional scalar mode becomes
dynamical. Finally, we derive the modified conservation laws of the DM stress energy
tensor in RSFG, showing that a new non-local force emerges, and hence that the DM
fluid deviates from the geodesic solutions of the field equations.

Shear-free inhomogeneous energy density in 4D Einstein-Gauss-Bonnet spherical systems

We explore the inhomogeneity factors for the initially regular relativistic spheres in 4D-Einstein-Gauss-Bonnet (EGB) theory. The corresponding equations of motion are derived once the generic expressions for the kinematical variables are obtained for spherically symmetric self-gravitating system. By using the non-zero divergence of the stress-energy tensor, the independent components of Bianchi identities are constructed. To enable a thorough explanation of the inhomogeneity of the particular shear free matter distribution, we computed two distinct components of evolution equations employing the Weyl tensor. We then investigate the requisite variables for the irregularity by looking at particular scenarios in both the adiabatic and non-adiabatic domains. These instances demonstrate how, in addition to other factors, the Gauss-Bonnet terms contribute to the regularity requirements of the collapsing fluid.

Wormhole Restrictions from Quantum Energy Inequalities

Wormhole solutions, bridges that connect different parts of spacetime, were proposed early in the history of General Relativity. Soon after, it was shown that all wormholes violate classical energy conditions, which are non-negativity constraints on contractions of the stress–energy tensor. Since these conditions are violated by quantum fields, it was believed that wormholes can be constructed in the context of semiclassical gravity. But negative energies in quantum field theory are not without restriction: quantum energy inequalities (QEIs) control renormalized negative energies averaged over a geodesic. Thus, QEIs provide restrictions on the construction of wormholes. This work is a review of the relevant literature, thus focusing on results where QEIs restrict traversable wormholes. Both ‘short’ and ‘long’ (without causality violations) wormhole solutions in the context of semiclassical gravity are examined. A new result is presented on constraints on the Maldacena, Milekhin, and Popov ‘long’ wormhole from the recently derived doubled smeared null energy condition.

Stress and Geometry for Isotropic Singularities.

We develop the mathematics needed to treat the interaction of geometry and stress at any isotropic spacetime singularity. This enables us to handle the Einstein equations at the initial singularity and characterize allowed general relativistic stress-energy tensors. Their leading behaviors are dictated by an initial hypersurface conformal embedding. We also show that an isotropic big bang determines a canonical nonsingular metric on and about the initial hypersurface as well as a cosmological time. This assigns a volume and energy to the initial point singularity.

Geometrical interpretation of isospin subalgebras in SU(3)

Ever since new tetrads in four-dimensional Lorentzian curved spacetimes were introduced, many outstanding properties and results have been proven regarding Riemannian geometry, gauge theory or group theory. These tetrads might carry spacetime-kinematic information about particle multiplets. Among other properties, these new tetrads, locally and covariantly diagonalize stress–energy tensors. In the case where particles have an electromagnetic field, the local planes of gauge symmetry served as a tool in order to propose a new gravitational-kinematic interpretation of particle multiplets. The core reason stems from the mathematical fact that all local gauge symmetries associated to the Standard Model have been proven to be isomorphic to local groups of tetrad transformations in four-dimensional Lorentzian spacetimes. Therefore, the different stress–energy tensors have been proven to determine the local gauge geometry as a natural part of Riemannian geometry. The stress–energy tensors determine locally the orthogonal planes such that the rotation on either of them of the local tetrad vectors that span these planes is isomorphic to local tetrad gauge transformations. All these properties put together allow for a reinterpretation presented previously of particle states as particle gravitational-kinematic-spacetime tetrad states in the asymptotically flat limit. We proceed in this paper to study the case where there are [Formula: see text], [Formula: see text] and [Formula: see text] isospin subalgebras or submultiplets within the context of this new Riemannian interpretation of gauge symmetries.

Holographic entanglement renormalisation for fermionic quantum matter

We demonstrate the emergence of a holographic dimension in a system of 2D non-interacting Dirac fermions placed on a torus, by studying the scaling of multipartite entanglement measures under a sequence of renormalisation group (RG) transformations applied in momentum space. Geometric measures defined in this emergent space can be related to the RG beta function of the spectral gap, hence establishing a holographic connection between the spatial geometry of the emergent spatial dimension and the entanglement properties of the boundary quantum theory. We prove, analytically, that changing the boundedness of the holographic space involves a topological transition accompanied by a critical Fermi surface in the boundary theory. We go on to show that this results in the formation of a quantum wormhole geometry that connects the UV and the IR of the emergent dimension. The additional conformal symmetry at the transition also supports a relation between the emergent metric and the stress-energy tensor. In the presence of an Aharonov–Bohm flux, the entanglement gains a geometry-independent piece which is shown to be topological, sensitive to changes in boundary conditions, and related to the Luttinger volume of the system. Upon the insertion of a strong transverse magnetic field, we show that the Luttinger volume is linked to the Chern number of the occupied single-particle Landau levels.