# Deforming Black Hole and Cosmological Solutions by Quasiperiodic and/or Pattern Forming Structures in Modified and Einstein Gravity

## TL;DR

This paper introduces a method for constructing exact solutions with quasiperiodic structures in modified gravity and general relativity, revealing potential implications for dark energy, dark matter, and nonlinear astrophysical phenomena.

## Contribution

It develops the anholonomic frame deformation method (AFDM) to generate off-diagonal quasiperiodic solutions in gravity theories, expanding the toolkit beyond numerical approaches.

## Key findings

- Quasiperiodic structures can transform black hole solutions into cosmological metrics.
- The method provides exact solutions with off-diagonal metrics and effective matter sources.
- Implications for dark energy and dark matter physics are discussed.

## Abstract

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.