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

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.

LIFTS OF GOLDEN STRUCTURES ON THE TANGENT BUNDLE

The present paper aims to study the complete lift of golden structure on tangent bundles. Integrability conditions for complete lift and third-order tangent bundle are established.

On the completeness of total spaces of horizontally conformal submersions

In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.