Love numbers sound like they really posses some sentimental value, no doubt they are holding humongous sentiments but not in a manner you are currently thinking of. Love numbers denoted as h, k, and l are dimensionless that measure the rigidity of a planetary body and susceptibility of its shape to change in response to a tidal potential. The first two h and k were first introduced in 1909 by Augustus Edward Hough Love, he characterizes them as the overall response of the earth to the tides. Tides as we observe are the effect of gravitational fields that raises and drops the sea level, for us it is basically a combined effect lead by the sun and the moon. We know that every action has an equal and opposite reaction. So Love introduced these parameters in order to generalize this condition. Later in 1920, Shida introduced 'l' as the third factor governing the situation, this claimed to deduce the complete description of the picture.
Tidal deformation of Ganymede
Now if we are talking about Black holes then we have to keep in mind that there is no real composition of a Black hole. We know that it is Singularity hidden with a Horizon (Event Horizon). Just like a pearl in a shell, the only difference is that we know the spherical volume of the pearl. But a recent study shows that we can actually build a reminiscent condition in order to apply it to the Black holes.
The vertical axis represents the value of tidal deformability, which is the deformation on each planetary objects caused by tides. The horizontal axis represents the Mass and Radius ratio of an object. This study clears the tidal deformation on various stars and clears that Black holes have zero deformability. The Love number of these stars is a continuous function of the compactness, positive-valued and vanishing as M/R → 1/2. An analysis of available gravitational wave data allowing for nonzero tidal deformability in the binary black hole merger events would likely provide interesting upper limits for the black hole tidal deformability
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