Spacetime completeness of non-singular black holes in conformal gravity
  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.
