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The tidal interaction of a (rotating or nonrotating) black hole with nearbybodies produces changes in its mass, angular momentum, and surface area.Similarly, tidal forces acting on a Newtonian, viscous body do work on thebody, change its angular momentum, and part of the transferred gravitationalenergy is dissipated into heat. The equations that describe the rate of changeof the black-hole mass, angular momentum, and surface area as a result of thetidal interaction are compared with the equations that describe how the tidalforces do work, torque, and produce heat in the Newtonian body. The equationsare strikingly similar, and unexpectedly, the correspondence between theNewtonian-body and black-hole results is revealed to hold in near-quantitativedetail. The correspondence involves the combination k_2 \tau of ``Lovequantities'' that incorporate the details of the body's internal structure; k_2is the tidal Love number, and \tau is the viscosity-produced delay between theaction of the tidal forces and the body's reaction. The combination k_2 \tau isof order GM/c^3 for a black hole of mass M; it does not vanish, in spite of thefact that k_2 is known to vanish individually for a nonrotating black hole.

Tidal interaction of black holes and Newtonian viscous bodies