Einstein field equations extended to fractal manifolds: A fractal perspective

Khalili Golmankhaneh A., Jørgensen P. E., Schlichtinger A. M.

Journal of Geometry and Physics, vol.196, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 196
  • Publication Date: 2024
  • Doi Number: 10.1016/j.geomphys.2023.105081
  • Journal Name: Journal of Geometry and Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH
  • Keywords: Fractal arc length, Fractal Einstein field equation, Fractal manifolds, Fractal Riemannian manifold
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper provides a framework for understanding and analyzing non-differentiable fractal manifolds. By introducing specialized mathematical concepts and equations, such as the Metric Tensor, Curvature Tensors, Analogue Arc Length, and Inner Product, it enables the study of complex patterns that exhibit self-similarity across different scales and dimensions. The Analogue Geodesic and Einstein Field Equations, among others, offer practical applications in physics, highlighting the relevance and potential of fractal geometry.