Almost Riemann Solitons in f(r,T)-Gravity: Extensions to Anisotropic Fluids and Field-Based Sources

This research paper studies almost Riemann solitons and almost gradient Riemann solitons on space-times obeying the $$f(r,T)$$ -gravity field equations. First, we obtain the divergence of the potential vector field of an almost Riemann soliton in terms of the scalar curvature on a perfect-fluid space-time in $$f(r,T)$$ -gravity. We then discuss almost Riemann solitons on special perfect fluids (dark fluid, dust, radiation). As a natural generalization, we extend the framework to anisotropic-fluid and field-based matter sources (e.g., scalar and electromagnetic fields), indicating how the soliton structure equations adapt in $$f(r,T)$$ -gravity beyond the perfect-fluid ansatz.