The Robinson-Trautman Type III Prolongation Structure Contains K₂
classification
🌀 gr-qc
nlin.SIsolv-int
keywords
algebraprolongationrobinson-trautmanstructuretypeacklundallowalways
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The minimal prolongation structure for the Robinson-Trautman equations of Petrov type III is shown to always include the infinite-dimensional, contragredient algebra, K$_2$, which is of infinite growth. Knowledge of faithful representations of this algebra would allow the determination of B\"acklund transformations to evolve new solutions.
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