利用旋转黑洞的隐藏对称性：守恒定律和数值检验
Exploiting the hidden symmetry of spinning black holes: conservation laws and numerical tests
摘要：
克尔黑洞是静止的和轴对称的，这导致了能量能量守恒和方位角动量沿着其附近的自由测试粒子的轨道，但也守恒定律的连续体物质场的演化。然而，克尔时空拥有一个额外的“隐藏对称性”，它以一个意想不到的守恒量沿着测地线表现出来，称为卡特常数。我们调查使用这种隐藏的对称性，以获得守恒定律和其他身份，可用于测试天体物理模拟旋转黑洞附近的物质场的演化的可能性。推导出这样的身份后，我们建立了一个简单的数字玩具模型，我们展示了他们如何可以检测到违反演化方程的数值模拟。即使我们得到的表达式之一是以守恒定律的形式，我们最终推荐了一个等效的，但更简单的表达式，不是以守恒定律的形式用于实际应用。
英文摘要：
The Kerr black hole is stationary and axisymmetric, which leads to conservation of energy and azimuthal angular momentum along the orbits of free test particles in its vicinity, but also to conservation laws for the evolution of continuum matter fields. However, the Kerr space-time possesses an additional "hidden symmetry" which exhibits itself in an unexpected conserved quantity along geodesics known as the Carter constant. We investigate the possibility of using this hidden symmetry to obtain conservation laws and other identities which could be used to test astrophysical simulations of the evolution of matter fields near spinning black holes. After deriving such identities, we set up a simple numerical toy model on which we demonstrate how they can detect the violations of evolution equations in a numerical simulation. Even though one of the expressions we derive is in the form of a conservation law, we end up recommending an equivalent but simpler expression that is not in the form of a conservation law for practical implementation.
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