Solitonic structures in a relativistic thermodynamical fluid spacetime and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e22"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>r</m

In this present work, we discuss Yamabe solitons and hyperbolic Ricci solitons within the framework of relativistic thermodynamical fluid spacetime endowed with a cosmological constant. We study the variation in the nature of soliton subjected to certain types of vector fields. Furthermore, we establish the conditions under which the spacetime exhibits accelerated expansion. An example was given corresponding to our results. Finally, we present a comprehensive classification of hyperbolic Ricci solitons in a relativistic thermodynamical fluid spacetime governed by f ( r , T ) -gravity. • We study Yamabe and hyperbolic Ricci solitons in relativistic TFS. • Characterize solitons via specific classes of vector fields. • Identify conditions for cosmic acceleration via cosmological constant. • An example is presented to recognize our results. • Explore solitonic geometry and applications in f ( r , T ) -gravity.