2016/11/30 by Cosimo Bambi, Leonardo Modesto, Lesław Rachwał +1 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Conformal gravity #Conformal symmetry #Cosmology and Gravitation Theories #General relativity #Geodesic #Kerr metric #Noncommutative and Quantum Gravity Theories #Ring singularity #Schwarzschild radius #Singularity #Spacetime #astro-ph.CO #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1475-7516/2017/05/003
published as JCAP 1705:003,2017 · 24 pages, 13 figures. v2: refereed version
openalex created_date 2016/11/11 · arxiv created 2017/05/02 · openalex publication_date 2017/05/02 · arxiv updated 2017/05/04 · openalex updated_date 2026/08/05
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.