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The search for the gravitational energy-momentum tensor is often qualified as an attempt of looking for ``the right answer to the wrong question''. This position does not seem convincing to us. We think that we have found the right answer…

General Relativity and Quantum Cosmology · Physics 2009-10-31 S V Babak , L P Grishchuk

We investigate the second-order gravitational scalar perturbations for a barotropic fluid. We derive the effective energy-momentum tensor described by the quadratic terms of the gravitational and the matter perturbations. We show that the…

General Relativity and Quantum Cosmology · Physics 2020-09-09 Inyong Cho , Jinn-Ouk Gong , Seung Hun Oh

A set of lattice operators for the energy-momentum (EM) tensor in the Ising CFT is derived in the spin variables. Our expression works under arbitrary affine transformation both on triangular and hexagonal lattices (where the former…

High Energy Physics - Lattice · Physics 2025-05-14 Richard C. Brower , George T. Fleming , Nobuyuki Matsumoto , Rohan Misra

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane parallel conducting plates is derived. A perturbative expansion, to first order in the constant…

High Energy Physics - Theory · Physics 2008-11-26 Giuseppe Bimonte , Enrico Calloni , Giampiero Esposito , Luigi Rosa

We clarify the relation among canonical, metric and Belinfante's energy-momentum tensors for general tensor field theories. For any tensor field T, we define a new tensor field $\til {\bm T}$, in terms of which the Belinfante tensor is…

Mathematical Physics · Physics 2016-08-16 Ricardo E. Gamboa Saraví

Starting from covariant expressions, a gauge independent separation of orbital and spin angular momentum for electrodynamics is presented. This results from the non-symmetric canonical energy momentum tensor of the electromagnetic field.…

Optics · Physics 2017-06-27 Richard T. Hammond

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In…

General Relativity and Quantum Cosmology · Physics 2023-06-06 Salvatore Capozziello , Maurizio Capriolo , Gaetano Lambiase

In the literature one often finds the claim that there is no such thing as an energy-momentum tensor for the gravitational field, and consequently, that the total energy-momentum conservation can only be defined in terms of a gravitational…

General Relativity and Quantum Cosmology · Physics 2014-08-08 H. Nikolic

The current paper is devoted to the investigation of the general form of the energy-momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general…

General Relativity and Quantum Cosmology · Physics 2020-10-15 R. V. Ilin , S. A. Paston

A constraint of vanishing energy-momentum tensor is motivated by a variety of perspectives on quantum gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which quantum gravity emerges as…

High Energy Physics - Theory · Physics 2017-04-26 Christopher D. Carone , Joshua Erlich , Diana Vaman

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field…

Optics · Physics 2015-02-12 Michael E. Crenshaw , Thomas B. Bahder

General classical theories of material fields in an arbitrary Riemann-Cartan space are considered. For these theories, with the help of equations of balance, new non-trivially generalized, manifestly generally covariant expressions for…

General Relativity and Quantum Cosmology · Physics 2014-03-10 Robert R. Lompay

In this tutorial, we provide the natural derivation of symmetrical, gauge-invariant canonical energy-momentum tensor for the abelian gauge field, i.e., the electromagnetic field.

Classical Physics · Physics 2025-03-20 Peir-Ru Wang , Yen-Cheng Chang

Weinberg's energy-momentum pseudotensor is obtained for Schwarzschild metric in harmonic coordinates. On the horizon it possesses unintegrable singularities. For this reason the total energy of a collapsar can't be obtained by integrating…

General Relativity and Quantum Cosmology · Physics 2007-05-23 A. I. Nikishov

Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor…

General Relativity and Quantum Cosmology · Physics 2012-10-23 J. Navarro , J. B. Sancho

Due to proton spin crisis it is necessary to understand the gauge invariant definition of the spin and orbital angular momentum of the quark and gluon from first principle. In this paper we derive the gauge invariant Noether's theorem by…

High Energy Physics - Phenomenology · Physics 2018-03-30 Gouranga C Nayak

We provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and…

High Energy Physics - Phenomenology · Physics 2015-09-30 Cédric Lorcé

Recent research has highlighted the non-uniqueness problem of energy-momentum tensors in linearized gravity; many different tensors are published in the literature, yet for particular calculations a unique expression is required. It has…

General Relativity and Quantum Cosmology · Physics 2021-04-13 Mark Robert Baker

General relativity and its extensions including torsion identify stress energy momentum as being proportional to the Einstein tensor, thus ensuring both symmetry and conservation. Here we visualize stress energy and momentum by identifying…

General Relativity and Quantum Cosmology · Physics 2025-02-26 Adam Marsh

A framework is developed which quantifies the local exchange of energy and momentum between matter and the linearized gravitational field. We derive the unique gravitational energy-momentum tensor consistent with this description, and find…

General Relativity and Quantum Cosmology · Physics 2010-11-26 Luke M. Butcher , Michael Hobson , Anthony Lasenby