Boson and Dirac stars in $D\geq 4$ dimensions

We present a comparative study of spherically symmetric, localized, particle-like solutions for spin $s=0,1/2$ and $1$ gravitating fields in a $D$-dimensional, asymptotically flat spacetime. These fields are massive, possessing a harmonic time dependence and no self-interaction. Special attention is paid to the mathematical similarities and physical differences between the bosonic and fermonic cases. We find that the generic pattern of solutions is similar for any value of the spin $s$, depending only on the dimensionality of spacetime, the cases $D=4,5$ being special.