Abstract
New general spherically symmetric solutions have been derived with a cosmological ``constant'' Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.
Highlights
The hope that spacetime singularities in classical General Relativity are just an artifact of the high degree of symmetries assumed in the solutions was soon lost when the singularity theorems of Hawking and Penrose appeared
Concerning models on continuous spacetimes, one line of thought like String theory suggests to search for new symmetries and new degrees of freedom in order to succeed an Ultra Violet (UV) completion of General Relativity
General branches of new spherically symmetric solutions have been obtained in the context of Quantum Einstein Gravity
Summary
The hope that spacetime singularities in classical General Relativity are just an artifact of the high degree of symmetries assumed in the solutions was soon lost when the singularity theorems of Hawking and Penrose appeared. Another research path is to keep the same fields and symmetries from General Relativity and work on the belief that the associated gravitational action is a fundamental part of the complete theory at the non-perturbative level This is the idea behind the Asymptotic Safety scenario [4,5,6] which was first proposed by Weinberg [7, 8]. The scope of our work is to investigate the structure of spacetime at high energies and in particular the spherically symmetric configurations in the asymptotic safety scenario in the vicinity of the center This is why we have chosen to study the modified Einstein vacuum equations where only Λ(k) appears. Which of these solutions is the physically acceptable one will be determined by the demand to match smoothly with the classical Schwarzschild solution at larger length scales
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
