Some Results on Warped Product \(\eta \) -Ricci-Bourguignon Solitons

In this paper, we study \(\eta \) -Ricci-Bourguignon solitons structure on warped product manifolds. Moreover, we investigate that an \(\eta \) -Ricci-Bourguignon soliton warped product manifold whose potential vector field is conformal must be a quasi-Einstein manifold. As an application, we also study \(\eta \) -Ricci-Bourguignon solitons warped product standard static space-times and generalized Robertson-Walker space-times.