Classical Weyl transverse gravity

Abstract

We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge-fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally invariant scalar tensor gravity and the WTDiff gravity is a "fake" symmetry. We find it possible to extend this proof to all matter fields, i.e. the Weyl-invariant scalar, vector and spinor fields. Fourthly, it is explicitly shown that in the WTDiff gravity the Schwarzschild black hole metric and a charged black hole one are classical solutions to the equations of motion only when they are expressed in the Cartesian coordinate system. Finally, we consider the Friedmann-Lemaitre-RobertsonWalker (FLRW) cosmology and provide some exact solutions.

Weinberg’s no go theorem in quantum gravity

“…To tell the truth, a hidden motivation behind this article has lain in a primitive question of the present author: If some gravitational theory does not possess the GL(4) symmetry that survives as a vestige of diffeomorphisms when the fields are restricted to be constants, can such a gravitational theory evade Weinberg's no go theorem? As such a gravitational theory, we have had in mind the transverse Weyl gravity which is not invariant under GL(4) but is equivalent to general relativity at least at the classical level [19]. The result obtained in this article also answers this question in a negative way: The transverse Weyl gravity cannot evade the Weinberg theorem since although there is no the GL(4) symmetry there is a BRST symmetry in this gravitational theory as well.…”

Gravity with more or less gauging

“…From this point of view, DG seems a perverse complication of the description of GR. In the literature, this point of view is represented for example in [11,14,15], where the Weyl invariance of DG is viewed as 'fake'. The characterisation of the Weyl invariance as fake was based on the vanishing of the Noether current.…”

Quartet-metric/multi-component gravity: scalar graviton as emergent dark substance

“…But the latter should not fulfill in a general case. The specific form of the second FE, which looks like a continuity condition, is due to L G 7 For WTDiff, see, e.g., [12]- [16]. Stress that in distinction with WTDiff, ω in qWTDiff is a dynamical variable, ω = ω(ω a ).…”

“…For the CC problems, see, e.g [21],. and for some recent (far from being exhaustive) attempts at solving them, cf., e.g.,[14]-[16] and[22]-[25].…”