Abstract
This paper explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity, focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles with a star product structure determined by R-flux deformations in string theory. For the nonassociative vacuum Einstein equations we consider both real and complex effective sources. In order to analyze the nonassociative vacuum Einstein equations we develop the anholonomic frame and connection deformation methods, which allows one to decoupled and solve these equations. The metric coefficients can depend on both space-time coordinates and energy-momentum. By imposing conditions on the integration functions and effective sources we find physically important, exact solutions: (1) 6-d Tangherlini BHs, which are star product and R-flux distorted to 8-d black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE configurations generalizing Schwarzschild-de Sitter metrics. We also investigate the concept of Bekenstein-Hawking entropy and find it applicable only for very special classes of nonassociative BHs with conventional horizons and (anti) de Sitter configurations. Finally, we show how analogs of the relativistic Perelman W-entropy and related geometric thermodynamic variables can be defined and computed for general classes of off-diagonal solutions with nonassociative R-flux deformations.
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Acknowledgments
This work is elaborated in the framework of a research program supported to a Fulbright senior fellowship of SV and hosted by DS at physics department at California State University at Fresno, USA. It develops for nonassociative geometry and gravity some former research projects on geometry and physics supported by fellowships and grants at the Perimeter Institute and Fields Institute (Ontario, Canada), CERN (Geneva, Switzerland) and Max Planck Institut für Physik / Werner Heisenberg Institut, München (Germany) and DAAD. The sections 3 and 4 are related also to research programs proposed for visiting at CASLMU München, and PNRR-Initiative 8 of the Romanian Ministry of RID. SV is also grateful to professors D. Lüst, N. Mavromatos, J. Moffat, Yu. A. Seti, P. Stavrinos, M.V. Tkach, and E. V. Veliev for respective hosting visits and collaborations.
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Address for post correspondence in 2022–2023 as a visitor senior researcher at YF CNU Ukraine: Vokzal’na (former Yu. Gagarin) street, 37-3, Chernivtsi, 58008, Ukraine. (Sergiu I. Vacaru)
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Bubuianu, L., Singleton, D. & Vacaru, S.I. Nonassociative black holes in R-flux deformed phase spaces and relativistic models of Perelman thermodynamics. J. High Energ. Phys. 2023, 57 (2023). https://doi.org/10.1007/JHEP05(2023)057
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DOI: https://doi.org/10.1007/JHEP05(2023)057