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 Localized Energetics of Linear Gravity: Theoretical Development


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We recently developed a local description of the energy, momentum and angular momentum carried by the linearized gravitational field, wherein the gravitational energy-momentum tensor displays positive energy-density and causal energy-flux, and the gravitational spin-tensor describes purely spatial spin. We now investigate the role these tensors play in a broader theoretical context, demonstrating for the first time that a they do indeed constitute Noether currents associated with the symmetry of the linearized gravitational field under translation and rotation, and b they are themselves a source of gravity, analogous to the energy-momentum and spin of matter. To prove a we construct a Lagrangian for linearized gravity a covariantized Fierz-Pauli Lagrangian for a massless spin-2 field and show that our tensors can be obtained from this Lagrangian using a standard variational technique for calculating Noether currents. This approach generates formulae that uniquely generalize our gravitational energy-momentum tensor and spin tensor beyond harmonic gauge: we show that no other generalization can be obtained from a covariantized Fierz-Pauli Lagrangian without introducing second derivatives in the energy-momentum tensor. We then construct the Belinfante energy-momentum tensor associated with our framework combining spin and energy-momentum into a single object and as our first demonstration of b we establish that this Belinfante tensor appears as the second-order contribution to a perturbative expansion of the Einstein field equations. By considering a perturbative expansion of the Einstein-Cartan field equations, we then demonstrate that b can be realized without forming the Belinfante tensor: our energy-momentum tensor and spin tensor appear as the quadratic terms in separate field equations, generating gravity as distinct entities. Finally, we examine the role of

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Author: Luke M. Butcher; Michael Hobson; Anthony Lasenby

Source: https://archive.org/



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