#### strangerep

Science Advisor

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Yes, the literature on this is quite sparse, and mostly poor.In response to this I was searching for information about fractional linear transforms. All of them that I saw were mappings from the complex plane to the complex plane. I didn’t see anything on FL transforms as a mapping from R4 to R4.

In Fock & Kemmer, [Ref: FK64, Appendix A] there's a derivation of the most general transformations that map solutions of the free EoMs among themselves.I am not sure how they are even applicable here.

Stepanov [Ref: Step99, Appendix 1] gives a simplified derivation in 1+1D (although the main body of that paper is rather poor, IMHO).

These transformations are also known as "Fock-Lorentz" transformations (which coincidenally has the same initials "FL"). But you can mostly ignore the Wikipedia page on that subject, since it gives an impression that FL transformations necessarily involve a varying (local) speed of light, which is a false claim.

Kerner [Ref: Ker76] also attempted some work on this, but he didn't get very far and (in subsequent publications) develops an increasingly aggressive/desperate tone. He progresses to de Sitter, but doesn't get very far beyond that.

Manida [Ref: Man99], also derives Fock-Lorentz transformations, duplicating some of Kerner's early work (though apparently without citing him). But his attempts to develop this into a cosmoglogy are (imho) fruitless, with shortcomings reminiscent of Milne's work.

References:

**FK64:**V. Fock, N. Kemmer (translator),

*The theory of space, time and gravitation.*

2nd revised edition. Pergamon Press, Oxford, London, New York, Paris (1964).

**Step99:**S. S. Stepanov,

*Fundamental Physical Constants & the Principle of Parametric Incompleteness*,

arXiv:physics/9909009.

**Ker76:**E. H. Kerner,

*An extension of the concept of inertial frame and of Lorentz transformation,*

Proc. Nat. Acad. Sci. USA, Vol. 73, No. 5, pp. 1418-1421, May 1976 .

**Man99:**S. N. Manida,

F

*ock-Lorentz transformations and time-varying speed of light*,

Available as: arXiv:gr-qc/9905046 .

(Ignore the 2nd part of the title: he's

*not*talking about a varying

**local**speed of light.)

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