Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity, it is highly reminiscent of the tetrad formalism although there are significant conceptual differences. Most notably, the background in GTG is flat, Minkowski spacetime. The equivalence principle is not assumed, but instead follows from the fact that the gauge covariant derivative is minimally coupled. As in general relativity, equations structurally identical to the Einstein field equations are derivable from a variational principle. A spin tensor can also be supported in a manner similar to Einstein–Cartan–Sciama–Kibble theory. GTG was first proposed by Lasenby, Doran, and Gull in 1998[1] as a fulfillment of partial results presented in 1993.[2] The theory has not been widely adopted by the rest of the physics community, who have mostly opted for differential geometry approaches like that of the related gauge gravitation theory.
^Lasenby, Anthony; Chris Doran; Stephen Gull (1998), "Gravity, gauge theories and geometric algebra", Philosophical Transactions of the Royal Society A, 356 (1737): 487–582, arXiv:gr-qc/0405033, Bibcode:1998RSPTA.356..487L, doi:10.1098/rsta.1998.0178, S2CID 119389813
^Doran, Chris; Anthony Lasenby; Stephen Gull (1993), "Gravity as a Gauge Theory in the Spacetime Algebra", in F. Brackx; R. Delanghe; H. Serras (eds.), Clifford Algebras and their Applications in Mathematical Physics, pp. 375–385, doi:10.1007/978-94-011-2006-7_42, ISBN 978-0-7923-2347-1
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