Spacetime completeness of nonsingular black holes in conformal gravity
Abstract
We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or nonlocal gravitational theory. Moreover, we yield explicit examples of local and nonlocal theories enjoying Weyl and diffeomorphism symmetry (in short cocovariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularityfree spherically symmetric and axisymmetric 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 NewmanJanis transformation just as in standard general relativity (based on EinsteinHilbert 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 cocovariant 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 =0more »
 Authors:

 Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China)
 Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China)
 Publication Date:
 OSTI Identifier:
 22676235
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Cosmology and Astroparticle Physics
 Additional Journal Information:
 Journal Volume: 2017; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 14757516
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; CONFORMAL INVARIANCE; EQUATIONS; EXACT SOLUTIONS; EXPANSION; GENERAL RELATIVITY THEORY; GRAVITATION; MASSLESS PARTICLES; METRICS; SINGULARITY; SPACETIME; SYMMETRY; TRANSFORMATIONS
Citation Formats
Bambi, Cosimo, Rachwał, Lesław, and Modesto, Leonardo. Spacetime completeness of nonsingular black holes in conformal gravity. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/05/003.
Bambi, Cosimo, Rachwał, Lesław, & Modesto, Leonardo. Spacetime completeness of nonsingular black holes in conformal gravity. United States. https://doi.org/10.1088/14757516/2017/05/003
Bambi, Cosimo, Rachwał, Lesław, and Modesto, Leonardo. 2017.
"Spacetime completeness of nonsingular black holes in conformal gravity". United States. https://doi.org/10.1088/14757516/2017/05/003.
@article{osti_22676235,
title = {Spacetime completeness of nonsingular black holes in conformal gravity},
author = {Bambi, Cosimo and Rachwał, Lesław and Modesto, Leonardo},
abstractNote = {We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or nonlocal gravitational theory. Moreover, we yield explicit examples of local and nonlocal theories enjoying Weyl and diffeomorphism symmetry (in short cocovariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularityfree spherically symmetric and axisymmetric 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 NewmanJanis transformation just as in standard general relativity (based on EinsteinHilbert 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 cocovariant 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 singularityfree and geodesicallycomplete black hole spacetimes.},
doi = {10.1088/14757516/2017/05/003},
url = {https://www.osti.gov/biblio/22676235},
journal = {Journal of Cosmology and Astroparticle Physics},
issn = {14757516},
number = 05,
volume = 2017,
place = {United States},
year = {2017},
month = {5}
}