Related papers: Energy in Gravitation and Noether's Theorems
Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the…
We investigate the possibility that dark energy does not couple to gravitation in the same way than ordinary matter, yielding a violation of the weak and strong equivalence principles on cosmological scales. We build a transient mechanism…
A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…
Einstein's theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aether theories. Moreover, any theoretical…
The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar…
For Einstein's General Relativity (GR) or the alternatives suggested up to date the vacuum energy gravitates. We present a model where a new measure is introduced for integration of the total action in the D-dimensional space-time. This…
With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincar\'e group as the…
We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. The extension links seamlessly to the action integral for the gravitational field. The demand…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
The present paper continues the work of the authors [arXiv:1306.6887 [gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity presented more concretely, setting that their Lagrangians are \emph{manifestly} generally…
According to Einstein's principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energy-momentum conservation has been established. Here, we show that…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
The null energy condition has sweeping consequences in general relativity. I argue here that it has been misunderstood as a property exclusively of matter, when in fact it arises only in a theory of both matter and gravity. I then derive an…
When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…
We work out the most general theory for the interaction of spacetime geometry and matter fields -- commonly referred to as geometrodynamics -- for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i)…
We exploit an ambiguity somewhat hidden in Noether's theorem to derive systematically, for relativistic field theories, the stress-energy tensor's improvement terms that are associated with additional spacetime symmetries beyond…
The Noether currents are derived in a generic metric-affine theory of gravity, and the holographic nature of the gravitational entropy and energy-momentum is clarified. The main result is the verification of the canonical resolution to the…
The conserved charges associated to gauge symmetries are defined at a boundary component of space-time because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is…
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…
Using Noether's identities, we define a superpotential with respect to a background for the Einstein Gauss-Bonnet theory of gravity. As an example, we show that its associated conserved charge yields the mass-energy of a D-dimensional…