标题： 通过极端质量比吸积期间的共振激发发现爱数 显示英文标题

标题： Discovering Love numbers through resonance excitation during extreme mass ratio inspirals

摘要： 广义相对论预测黑洞不具有内部结构，因此不能被激发。这导致了关于双黑洞旋近过程中发出的引力波波形的具体预测，以及它们的Love数消失。然而，如果天体物理黑洞确实具有内部结构，它们的Love数将不再消失，并且在旋近过程中可以通过轨道能量的传递被激发。这将影响轨道周期，并在发出的引力波波形上留下可观测的印记。如果双星中的一个成员被共振激发，这种效应会增强。我们讨论了假设的黑洞内部结构共振激发的条件，并计算了在中等质量和极端质量比旋近过程中由于这种共振激发引起的引力波波形相位变化。然后我们将相位变化与被其较小伴星共振激发的较大伴星的电四极Love数联系起来。我们讨论了通过LISA测量Love数的统计误差，并表明由于这种相位变化，即使Love数的值很小，统计误差也很小。我们的结果强烈表明，LISA可以以显著的精度检测Love数，远高于通过潮汐变形效应所能达到的精度。我们的结果进一步表明，在极端或中等质量比旋近过程中对中心黑洞的共振激发是限制或检测黑洞非消失潮汐Love数最有前景的效果。 显示英文摘要

摘要： General Relativity predicts that black holes do not possess an internal structure and consequently cannot be excited. This leads to a specific prediction about the waveform of gravitational waves, which they emit during a binary black hole inspiral and to the vanishing of their Love numbers. However, if astrophysical black holes do possess an internal structure, their Love numbers would no longer vanish, and they could be excited during an inspiral by the transfer of orbital energy. This would affect the orbital period and lead to an observable imprint on the emitted gravitational waves waveform. The effect is enhanced if one of the binary companions is resonantly excited. We discuss the conditions for resonant excitation of a hypothetical internal structure of black holes and calculate the phase change of the gravitational waves waveform that is induced due to such resonant excitation during intermediate- and extreme-mass-ratio inspirals. We then relate the phase change to the electric quadrupolar Love number of the larger companion, which is resonantly excited by its smaller companion. We discuss the statistical error on measuring the Love number by LISA and show that, because of this phase change, the statistical error is small even for small values of the Love number. Our results provide a strong indication that the Love number could be detected by LISA with remarkable accuracy, much higher than what can be achieved via tidal deformation effects. Our results further indicate that resonant excitation of the central black hole during an extreme- or intermediate-mass-ratio inspirals is the most promising effect for putting bounds on, or detecting, non-vanishing tidal Love numbers of black holes.