Advanced principles in Mathematics, IT and Business Sciences

This study investigates a static plane symmetric spacetime within the framework of f(Q)-Gravity, an advanced extension of gravitational theory offering new insights into spacetime geometry. We analyzed 12 distinct linear and nonlinear cases to identify homothetic vector fields (HVFs), which are crucial for understanding spacetime symmetries. Through direct integration, we discovered that in cases (ii), (vi), (viii), and (xii), HVFs reduce to four-dimensional Killing Vector Fields (KVFs). Conversely, cases (i), (iii), (iv), (v), (vii), (ix), (x), and (xi) exhibit HVFs with dimensions of five, seven, ten, and eleven. These results underscore the diversity in vector field dimensions, encouraging further exploration of the implications of f(Q)-Gravity.