We prove smoothness and provide the asymptotic behavior at infinity of solutions of Dirac–Einstein equations on R3, which appear in the bubbling analysis of conformal Dirac–Einstein equations on spin 3-manifolds. Moreover, we classify ground state solutions, proving that the scalar part is given by Aubin–Talenti functions, while the spinorial part is the conformal image of -12-Killing spinors on the round sphere S3.
- Conformally covariant equations
- Dirac–Einstein equations
- Ground state solutions
- Killing spinors