Second Gravity

Details Second Gravity Second Gravity

2010-04-16

arxiv.org/abs/1004.2816v1

Journal of Mathematical Physics Vol.51, Issue 4, online 5 April 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

published in Journal of Mathematical Physics (Vol.51, Issue 4, online 5 April 2010) online at: http://jmp.aip.org/jmapaq/v51/i

Scientific paper

10.1063/1.3352935

A theory of a new gravitational interaction is described. This theory follows naturally from a new Lagrangian formulation of Maxwell's theory for photons and electrons (and positrons) whose associated Euler Lagrange equations imply the conventional Maxwell equations, but which possesses new \textbf{\emph{bosonic}} spinor degrees of freedom that may be associated with a new type of fundamental gravitational interaction. The precise character of this gravitational interaction with a photon vector potential is explicitly defined in terms of a local U(1)-invariant Lagrangian in Eq.[\ref{Lagrangian3}]. However in Section \ref{ssec:Simple-Cosmolo-Model}, in order to parallel the well known Friedmann model in cosmology, a phenomenological description of the new gravitational interaction coupled to Newton-Einstein gravity that is sourced by an ideal fluid is discussed. % % To lay the foundation for a description of the new gravitational interaction our new formulation of Maxwell's theory must first be described. It is cast on the real, eight dimensional pseudo-Euclidean vector space defined by the split octonion algebra, regarded as a vector space over $\mathbb{R}$, and denoted $ \mathbb{R}^{4,4} \cong M_{3,1} \oplus {}^*M_{3,1}$. (Here $M_{3,1}$ denotes real four-dimensional Minkowski space-time and $ {}^*M_{3,1}$ denotes its dual; $\mathbb{R}^{4,4}$ resembles the phase space of a single relativistic particle.) The new gravitational interaction is carried by a field that defines an algebraically distinguished element of the split octonion algebra, namely, the multiplicative unit element. We call this interaction the "unit" interaction, and more descriptively refer to it as "second gravity."

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