A Matrix Formulation of Einstein's Vacuum Field Equations

1998/12/31 by Walter J. Wild, Wild, Walter J.
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research #gr-qc

paper · pdf · doi:10.48550/arxiv.gr-qc/9812095

8 pages

arxiv created 1998/12/31 · openalex publication_date 1998/12/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a correspondence between arbitrary tensors and matrices based on the use of Kronecker products and associated identities. Utilizing the rules of matrix differentiation we derive the vacuum Einstein field equations as a differential-matrix equation. This formulation may facilitate their efficient use in numerical relativistic models.

Related

• Matrix Representation of Special Relativity
• A formalism for analyzing vacuum spacetimes
• Solving the Einstein field equations
• Mathematical matrix theory of the field in n-dimensional metric space: rigorous derivation of the equations of the field with application in electromagnetic-gravitational fields
• A Unified Invariant Formulation, by Frames, from General Relativity to the Atomic Scale