Homothetic symmetries of static plane symmetric spacetimes: A comparative study of energy-momentum tensor representations

This research explores homothetic matter collineations of static plane symmetric space-times through a comprehensive analysis of the stress-energy tensor's contravariant, co-variant and mixed representations. When dealing with non-degenerate energy-momentumtensors, the contravariant formulation produces finite-dimensional Lie algebras of dimen-sion 4, 5, 6, and 11, while the mixed tensor form consistently generates infinite-dimensional Lie algebras. For degenerate cases, the solution of homothetic matter collineations equations reveals infinite-dimensional Lie algebras for both tensor representations. Further-more, the present study provides a comparative analysis between the homothetic mattercollineations obtained for contravariant and mixed representations of energy-momentumtensors and those obtained for the covariant formulation in an earlier work, identifying significant distinctions among the three approaches used for studying homothetic matter collineations.