Hyperbolic Octonion Formulation of Gravitational Field Equations

Demir S.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, vol.52, no.1, pp.105-116, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1007/s10773-012-1307-3
  • Journal Name: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.105-116
  • Keywords: Octonion, Gravitational field equations, Proca-Maxwell equations, Monopole, MAGNETIC MONOPOLES, MAXWELL EQUATIONS, CONIC SEDENIONS, ELECTRODYNAMICS, GRAVITY, DYONS, ELECTROMAGNETISM, RELATIVITY, ALGEBRA
  • Anadolu University Affiliated: Yes

Abstract

In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation.