Abstract
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein’s gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein’s gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase.
Highlights
In conformal gravity, the theory is invariant under a conformal transformation of the metric tensor gμν → gμ∗ν = 2gμν, (1)where = (x) is a function of the point of the spacetime
We study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein’s gravity with an effective energymomentum tensor
We investigate the domains in which the null energy condition (NEC) holds and is violated in the regular non-rotating black hole spacetime in conformal gravity
Summary
[6,7], the authors found singularity-free black hole solutions in conformal gravity. For the theory in (3), the actual energy-momentum tensor vanishes, because the singularityfree black hole metrics are vacuum solutions, so we consider an effective energy-momentum tensor. These energy conditions may be used as a selection criterion to choose the right vacuum in the broken phase by requiring the minimum possible violation. As we have already pointed out, our black hole metrics are solutions in an infinite class of conformal gravity theories.
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