Abstract
We study geometric relativistic flow and Ricci soliton equations which (for respective nonholonomic constraints and self-similarity conditions) are equivalent to the gravitational field equations of R2 gravity and/or to the Einstein equations with scalar field in general relativity, GR. Perelman’s functionals are generalized for modified gravity theories, MGTs, which allows to formulate an analogous statistical thermodynamics for geometric flows and Ricci solitons. There are constructed and analyzed generic off-diagonal black ellipsoid, black hole and solitonic exact solutions in MGTs and GR encoding geometric flow evolution scenarios and nonlinear parametric interactions. Such new classes of solutions in MGTs can be with polarized and/or running constants, nonholonomically deformed horizons and/or embedded self-consistently into solitonic backgrounds. They exist also in GR as generic off-diagonal vacuum configurations with effective cosmological constant and/or mimicking effective scalar field interactions. Finally, we compute Perelman’s energy and entropy for black ellipsoids and evolution solitons in R2 gravity.
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.
