  This paper systematically explores new classes of black hole (BH) solutions
in nonassociative and noncommutative gravity by focusing on features that
generalize to higher dimensions. The theories we study are modelled on (co)
tangent Lorentz bundles (i.e. eight dimensional phase spaces) with a star
product structure determined by R-flux deformations in string theory. The
nonassociative vacuum Einstein equations involve real and complex effective
sources with coefficients which are proportional to the Planck and string
constants or their products. We develop the anholonomic frame and connection
deformation method and prove that such systems of nonlinear partial
differential equations can be decoupled and integrated in general form for a
generic off-diagonal ansatz for symmetric and non-symmetric metrics. The
coefficients of such metrics may depend on all phase space coordinates
(space-time coordinates plus energy-momentum). Conditions are given when the
generating and integration functions and effective sources define two classes
of physically important exact and parametric solutions with R-flux sources
related via nonlinear symmetries to effective cosmological constants: (1) 6D
Tangherlini BHs, which are star product and R-flux distorted to
quasi-stationary configurations and 8D 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 argue that
the concept of Bekenstein-Hawking entropy is applicable only for very special
classes of nonassociative BHs encoding conventional horizons and (anti) de
Sitter configurations. Finally, we show how analogs of the relativistic G.
Perelman geometric thermodynamic variables can be defined and computed for
general classes of off-diagonal solutions encoding nonassociative R-flux
deformations.
