The Bekenstein-Sanders tensor-vector-scalar theory of
gravitation (TeVeS) has been shown to account for the galactic rotation curves,
lensing, and other cosmological phenomena without the significant presence of
dark matter.
Treating the Bekenstein-Sanders field Bµ, for which Bµ Bµ
= −1 as a gauge field requires that the field be non-Abelian. This
structure was worked out in a previous publication by Horwitz, Gershon and
Schiffer, where an equivalent Kaluza-Klein metric was found for an extended
(5D) spacetime. In this paper, we study a quaternionic formulation of this
theory with quaternionic gauge fields and quaternionic wave functions (as discussed
in two seminal books by S.L. Adler), thereby establishing a connection between
quaternionic quantum mechanics and general relativity. It was shown that TeVeS
gravitational theory theory can be derived by a conformal transformation from a
Hamiltonian form on a curved space for which the Bekenstein-Sanders vector
field Bµ is a non-Abelian gauge field.
Author(s)details:-
Lawrence
Horwitz
School of Physics, Tel Aviv University, Ramat Aviv, Israel and Department
of Physics, Bar Ilan University, Ramat Gan, Israel and Department of Physics,
Ariel University, Ariel, Israel.
Please See
the book here :-https://doi.org/10.9734/bpi/crpps/v1/47
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