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 Schwarzshild 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-Robertson-Walker (FLRW) cosmology and provide some exact solutions.

Dedicated to the memory of Mario Tonin, 39 pages

References in corpus (13)

• Quantum scale invariance, cosmological constant and hierarchy problem
• Fake Conformal Symmetry in Conformal Cosmological Models
• Unimodular cosmology and the weight of energy
• Two-loop scale-invariant scalar potential and quantum effective operators
• Ultraviolet behavior of transverse gravity
• Classically Scale-invariant B-L Model and Dilaton Gravity
• Fake Conformal Symmetry in Unimodular Gravity
• Newton law in covariant unimodular $F(R)$ gravity
• Topological Induced Gravity
• Reissner-Nordstrom Solution from Weyl Transverse Gravity
• Conformal Higgs Inflation
• Schwarzschild Solution from WTDiff Gravity
• Cosmology in Weyl Transverse Gravity

Cited by in corpus (15)

• Gravity with more or less gauging
• Noether charge formalism for Weyl invariant theories of gravity
• Noether charge formalism for Weyl transverse gravity
• Quadratic Gravity and Restricted Weyl Symmetry
• Modified gravity from Weyl connection and the $f(R,\mathcal{A})$ extension
• Quantum Theory of Weyl Invariant Scalar-tensor Gravity
• Weinberg's No Go Theorem in Quantum Gravity
• Cosmological Solutions from a Multi-Measure Model with Inflaton Field
• Thermodynamics as a tool for (quantum) gravitational dynamics
• Quartet-metric/multi-component gravity: scalar graviton as emergent dark substance
• Vanishing Noether Current in Weyl Invariant Gravities
• Asymptotic conformal symmetry at spatial infinity
• Multiscalar-metric gravity: cosmological constant screening and emergence of massive-graviton dark components
• Higgs Potential from Wick Rotation in Conformal BSM
• Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants