AI 中文总结
该研究计算了2+1维类黑洞与类白洞的动力学潮汐响应系数，发现类白洞TRC为对应类黑洞TRC的复共轭，且类黑洞在静态微扰下TLN呈对数演化、TDC消失。
AI 中文摘要
我们分别计算了由排水浴缸流和喷泉浴缸流产生的2+1维类黑洞与类白洞的动力学潮汐响应系数（TRC）。该参数空间由傅里叶模的频率、方位角数以及类黑洞或类白洞的旋转特性所表征。一般而言，TRC是这些参数的复值函数，其实部和虚部分别定义为潮汐洛夫数（TLN）和潮汐耗散系数（TDC）。类黑洞（ABH）的TRC呈现出若干有趣特征：在参数空间的某些点，包括微扰频率为零的静态情形，TLN表现出对数演化特性，而TDC则消失。与爱因斯坦引力不同，流体动力学允许类白洞（AWH）事件视界的物理存在。不随时间变化、无扭矩、正压、无粘性、轴对称的流体动力学方程可产生一对跨音速背景流解，对应ABH-AWH对的这对解具有相同的角动量和伯努利常数，但质量流率相反，二者均为守恒量。对于此类ABH-AWH对，AWH的TRC是ABH的TRC的复共轭。
英文摘要
We calculate the dynamical tidal response coefficients (TRCs) of 2+1D analogue black and white holes generated by draining and fountaining bathtub flows, respectively. The parameter space is characterized by the frequency and azimuthal number of the Fourier modes and the rotation of the analogue black or white hole. In general, the TRC is a complex-valued function of these parameters. Its real and imaginary parts are defined as the tidal Love number (TLN) and the tidal dissipation coefficient (TDC), respectively. The TRC of the analogue black hole (ABH) exhibits several interesting features. At certain points in the parameter space, including the static case of vanishing perturbation frequency, the TLN exhibits logarithmic running, while the TDC vanishes. Unlike in Einstein gravity, fluid dynamics allows for the physical existence of an analogue white hole (AWH) event horizon. Time-independent, torque-free, barotropic, inviscid, axisymmetric fluid dynamical equations can yield a pair of transonic background flow solutions. The solutions in the pair, corresponding to an ABH-AWH pair, share the same angular momentum and Bernoulli constant but have opposite mass flow rates, all of which are conserved quantities. For such an ABH-AWH pair, the TRC of the AWH is the complex conjugate of the TRC of the ABH.
