General Relativity predicts that black holes (BHs) do not possess an internal structure and consequently cannot be excited. This leads to a specific prediction about the waveform of gravitational waves (GWs) which they emit during a binary BH inspiral and to the vanishing of their Love numbers. However, if astrophysical BHs 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 GWs 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 BHs and calculate the phase change of the GWs 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 values of the Love number as small as 10⁻⁴ for moderate values of the spin parameter. Our results indicate that, for extreme-mass-ratio inspirals with moderate spin parameter, the Love number could be detected by LISA with an accuracy which is higher by up to two orders of magnitude than what can be achieved via tidal deformation effects. Thus, our results indicate that resonant excitation of the central BH 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 BHs.

中文翻译：

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通过极端质量比吸气期间的共振激发发现洛夫数


广义相对论预测黑洞（BH）不具有内部结构，因此无法被激发。这导致了对它们在双星 BH 螺旋期间发出的引力波 (GW) 波形的具体预测，以及它们的洛夫数的消失。然而，如果天体物理黑洞确实拥有内部结构，它们的洛夫数将不再消失，并且它们可以在轨道能量转移的螺旋过程中被激发。这会影响轨道周期并导致在发射的引力波波形上产生可观察到的印记。如果双星伴星之一被共振激发，这种效应就会增强。我们讨论了假设的 BH 内部结构的共振激发条件，并计算了在中等和极端质量比螺旋期间由于这种共振激发而引起的 GW 波形的相位变化。然后，我们将相变与较大伴星的电四极洛夫数联系起来，该伴星被较小伴星共振激发。我们讨论了 LISA 测量 Love 数的统计误差，并表明，由于这种相变，即使对于中等值的 Love 数值小至 10 ⁻⁴ ，统计误差也很小。自旋参数。我们的结果表明，对于具有中等自旋参数的极端质量比螺旋，LISA 可以检测到洛夫数，其精度比通过潮汐变形效应所能达到的精度高出两个数量级。因此，我们的结果表明，在极端或中等质量比螺旋期间，中心 BH 的共振激发对于限制或检测 BH 的非消失潮汐 Love 数是最有希望的效果。