Gödel-type universes with closed timelike curves are exact vacuum solutions in nonlocal gravity for a special class of form factors.
Spacetime completeness of non-singular black holes in conformal gravity
5 Pith papers cite this work, alongside 98 external citations. Polarity classification is still indexing.
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abstract
We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the $r=0$ point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.
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Weyl symmetry of gravity is restored if masses transform as m → Ω^{-1}m under conformal changes, allowing any matter to couple invariantly and potentially accounting for dark energy and dark matter.
The conformal frame problem in scalar-tensor theories stems from incomplete transformation rules for parameters and overlooked Ward identities; active conformal transformations provide the suitable framework while passive ones do not.
If Hawking's area law is taken as exact, nonlocal and Stelle quantum-gravity theories are forced to drop R^2 and (Riemann)^2 terms (or use singular Ricci-flat black holes), and the standard entropy-area law follows as a consequence.
Kasner spacetime is singularity-free in conformal gravity because its curvature invariants are regular and geodesics for massive, massless, and conformally coupled particles are complete.
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Approaching a spacetime singularity in conformal gravity
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