Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks

Abstract

We construct nonassociative quasi-stationary solutions describing deformations of Schwarzschild black holes, BHs, to ellipsoid configurations, which can be black ellipsoids, BEs, and/or BHs with ellipsoidal accretion disks. Such solutions are defined by generic off-diagonal symmetric metrics and nonsymmetric components of metrics (which are zero on base four dimensional, 4-d, Lorentz manifold spacetimes but nontrivial in respective 8-d total (co) tangent bundles). Distorted nonassociative BH and BE solutions are found for effective real sources with terms proportional to $$\hbar \kappa $$ ħ κ (for respective Planck and string constants). These sources and related effective nontrivial cosmological constants are determined by nonlinear symmetries and deformations of the Ricci tensor by nonholonomic star products encoding R-flux contributions from string theory. To generate various classes of (non) associative /commutative distorted solutions we generalize and apply the anholonomic frame and connection deformation method for constructing exact and parametric solutions in modified gravity and/or general relativity theories. We study properties of locally anisotropic relativistic, optically thick, could and thin accretion disks around nonassociative distorted BHs, or BEs, when the effects due to the rotation are negligible. Such configurations describe angular anisotropic deformations of axially symmetric astrophysical models when the nonassociative distortions are related to the outer parts of the accretion disks.

Nonassociative Ricci Flows, Star Product and R‐flux Deformed Black Holes, and Swampland Conjectures

“…Here we emphasize that to elaborate on rigorous algebraic and geometric approaches to mathematical particle physics and QG, we have to consider models of nonassociative quantum mechanics, QM, [ 28–31 ] and further developments with nonassicative and noncommutative algebras. [ 15,32–36 ] We cite [ 12,13,37–41 ] for reviews and recent results on nonassociative and noncommutative geometry and physics. An important task in string and M‐theory, and modern quantum field theory, QFT, and QG, is to extend the swampland program in a form incorporating geometric and physical models with nonassociative/noncommutative structures.…”

“…We proved a general splitting and integration property for quasi‐stationary configurations (with Killing symmetry on a time like coordinate) of such nonassociative nonlinear dynamical systems and shown how to construct nonassociative four dimensional, 4‐d, and 8‐d, black hole, BH, and black ellipsoid, BE, solutions in refs. [13, 40, 41]. Generic off‐diagonal quasi‐stationary solutions can be generated for κ‐linear parametric decompositions transforming the real part of () into associative and commutative modified Einstein equations (see appendix 2.1.1), $$$$\begin{equation} \ ^{\shortmid }\widehat{\mathbf {R}}_{\ \ \gamma _{s}}^{\beta _{s}}={\delta } _{\ \ \gamma _{s}}^{\beta _{s}}\ _{s}^{\shortmid }\mathcal {K}.$$…”

“…[13] and, for respective 4‐d and 8‐d BH/BE solutions, in refs. [40, 41]. In result, we generate parametric solutions for nonassociative vacuum Einstein equations () if we restrict the geometric constructions for a subclass of generating functions when the distortion s‐tensor $$\ ^{\shortmid }\widehat{\mathbf {Z}}_{\gamma _{s}}$$ () is constrained to zero and $$\ ^{\shortmid }\widehat{\mathbf {D}}_{\gamma _{s}}\rightarrow \ ^{\shortmid }\nabla _{\gamma _{s}}$$.…”

“…This work is a natural and logical development of a series of articles on nonassociative geometry and physics [ 37–39 ] and a new research program on nonassociative geometric and quantum information flows and gravity. [ 12,13,40,41 ] It is related to the swampland program [ 19–21 ] and revised conjectures [ 23–27 ] following such five aims:…”

“…Then, the third aim, in Section 4, is to extend the AFCDM [ 13,16,17,40,41 ] in such forms which allow us to decouple and integrate the nonassociative R. Hamilton equations in certain generalized forms describing the geometric evolution of quasi‐stationary Ricci soliton and vacuum gravitational structures (with effective sources encoding star product and R‐flux deformations). We analyze a class of nonlinear symmetries relating different types of generating functions, generating (effective) sources and cosmological constants running on temperature like geometric flow parameter.…”