We prove smoothness and provide the asymptotic behavior at infinity of solutions of Dirac–Einstein equations on \(\mathbb {R}^3\), 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 \(-\frac{1}{2}\)-Killing spinors on the round sphere \(\mathbb {S}^3\).

中文翻译：

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狄拉克－爱因斯坦气泡的一些性质

我们证明了光滑度，并提供了\（\ mathbb {R} ^ 3 \）上Dirac–Einstein方程解的无穷大的渐近性，这出现在自旋3流形上的共形Dirac–Einstein方程的冒泡分析中。此外，我们对基态解进行分类，证明标量部分是由Aubin–Talenti函数给出的，而脊髓部分是\（-\ frac {1} {2} \）的保形图像-在圆球上杀死旋转子\（\ mathbb {S} ^ 3 \）。