Reissner-Nordstrom Solution from Weyl Transverse Gravity

Abstract

We study classical solutions in the Weyl-transverse (WTDiff) gravity coupled to an electro-magnetic field in four space-time dimensions. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known to be equivalent to general relativity at least at the classical level (perhaps even in the quantum regime). In particular, we find that only in four space-time dimensions, the charged Reissner-Nordstrom black hole metric is a classical solution when it is expressed in the Cartesian coordinate system.

11 pages. arXiv admin note: text overlap with arXiv:1607.06562

References in corpus (6)

• Quantum scale invariance, cosmological constant and hierarchy problem
• Unimodular cosmology and the weight of energy
• Longitudinal diffeomorphisms obstruct the protection of vacuum energy
• Ultraviolet behavior of transverse gravity
• Classically Scale-invariant B-L Model and Dilaton Gravity
• Conformal Higgs Inflation

Cited by in corpus (1)

• Weinberg's No Go Theorem in Quantum Gravity