On the structure of almost Ricci-Bourguignon solitons in Lorentzian para-Kenmotsu geometry

Abstract

This paper investigates almost Ricci-Bourguignon solitons on Lorentzian para-Kenmotsu (LP-Kenmotsu) manifolds. We show that when the soliton vector field coincides with the timelike vector field, the manifold admits an Einstein structure with constant scalar curvature, and the soliton is classified as shrinking or expanding depending on the soliton parameter. In the gradient case, the structure reduces either to an Einstein manifold or a gradient $u^\#$-Yamabe soliton. For manifolds of constant scalar curvature, we establish that the geometry is locally isometric to a Lorentzian hyperbolic space, while the Ricci-Bourguignon condition further yields a gradient conformal structure. These results provide a classification of almost Ricci-Bourguignon solitons in the LP-Kenmotsu setting and open avenues for exploring their role in Lorentzian paracontact geometry and spacetime models inspired by general relativity.