Tidal-heating and viscous dissipation correspondence in black holes and viscous compact objects

The effect of energy absorption during the binary evolution of Exotic-compact-objects (ECOs) is extensively studied. We review the underlying mechanism that provides the energy dissipation in material objects—tidal friction. We show that unlike typical astrophysical objects, where absorption due to viscosity is negligible, in ECOs, absorption could potentially mimic the analogous effect of black-holes (BHs)—tidal heating. We stand for their differences and similarities in the context of energy dissipation during the inspiral. Inspired by the membrane paradigm and recent studies, we demonstrate how viscosity is a defining feature that quantifies how close is the ECO absorption to that of a classical BH absorption. We show that for ECOs, viscosity can induce significant modifications to the GW waveform, which in some favorable scenarios of supermassive binaries of equal mass and spin, enables the measurement of the ECO absorption in the future precision gravitational-wave (GW) observations. Finally, we discuss the implications on the ECO reflection coefficient and the relation to the universal viscosity to volume entropy bound.

Figure 1

The relative statistical error vs spin parameter for several values of ${\gamma }_{\mathrm{ECO}/\mathrm{UCO}}$ Eqs. (2.12), (3.10). We assume a binary of equal spin and nearly equal masses $M_1/M_2=1.01$ with luminosity distance $D_l=2\mathrm{Gpc}$. Points below the horizontal dashed line correspond to detection at better than $1\sigma$ confidence. The ${\gamma }_{\mathrm{UCO}}=(0.3,0.5,0.7,0.9)$ corresponds to ${\nu }_{\mathrm{UCO}}/{\nu }_{\mathrm{BH}}=(0.08,0.17,0.29,0.51)$.