Universal embeddings for spherical spacetimes and radiating stars

We examine the Karmarkar embedding condition for spherically symmetric spacetimes in higher dimensions. By analyzing the Riemann curvature tensor, we show that the core algebraic relation derived in the four-dimensional scenario can be extended to higher dimensions. The embedding into higher dimensional Euclidean space depends solely on the four-dimensional Riemannian curvature. We apply our embedding results to generate models of a radiating star in higher dimensions. This class of solutions satisfies the embedding constraints, admits a linear equation of state and can be matched to the exterior Vaidya spacetime. Remarkably all these properties arise in the same model by utilizing the Lie point symmetries of differential equations.