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

TL;DR

This paper constructs nonassociative deformations of Schwarzschild black holes into ellipsoid shapes with accretion disks, incorporating string theory effects and anisotropic features, providing new exact solutions in modified gravity.

Contribution

It introduces a method to generate nonassociative, anisotropic black hole and accretion disk solutions using off-diagonal metrics and star products influenced by R-fluxes from string theory.

Findings

Derived nonassociative black ellipsoid solutions with string-inspired sources.

Analyzed properties of anisotropic accretion disks around distorted black holes.

Extended solution-generating techniques to modified gravity and general relativity.

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 $ (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.