Kerr时空中四极试验体的广义Carter常数
Generalized Carter constant for quadrupolar test bodies in Kerr spacetime
AI总结：
本文证明在Kerr时空中，具有黑洞自旋诱导四极耦合的自旋试验体存在一个广义Carter常数，该常数在自旋二阶微扰下守恒；但对中子星等一般致密天体的四极耦合，证明此类守恒量不存在。
摘要：
我们证明了对通常Carter常数的一种形变的存在性，该形变在一个具有黑洞自旋诱导四极耦合的自旋试验体于固定Kerr背景中运动时守恒。该守恒在试验体自旋的二阶微扰范围内成立。这一运动常数是通过显式求解守恒约束方程得到的，利用了Kerr背景协变构建块之间的协变代数与微分关系。对于描述中子星等致密天体的一般自旋诱导四极耦合，我们得到了关于此类守恒量存在性的no-go结果。
英文摘要：
We establish the existence of a deformation of the usual Carter constant which is conserved along the motion in a fixed Kerr background of a spinning test body possessing the spin-induced quadrupole coupling of a black hole. The conservation holds perturbatively up to second order in the test body's spin. This constant of motion is obtained through the explicit resolution of the conservation constraint equations, employing covariant algebraic and differential relations amongst covariant building blocks of the Kerr background. For generic spin-induced quadrupole couplings, which describe compact objects such as neutron stars, we obtain a no-go result on the existence of such a conserved quantity.
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