Abstract
A 2-2-hole is an explicit realization of a horizonless object that can still very closely resemble a BH. An ordinary relativistic gas can serve as the matter source for the 2-2-hole solution of quadratic gravity, and this leads to a calculable area-law entropy. Here we show that it also leads to an estimate of the damping of a gravitational wave as it travels to the center of the 2-2-hole and back out again. We identify two frequency dependent effects that greatly diminish the damping. Spinning 2-2-hole solutions are not known, but we are still able to consider some spin dependent effects. The frequency and spin dependence of the damping helps to determine the possible echo resonance signal from the rotating remnants of merger events. It also controls the fate of the ergoregion instability.
Highlights
A 2-2-hole [1] is an example of an extremely compact horizonless object that deviates from a black hole (BH) only within some Planck-like distance from the would-be horizon. 2-2-holes exist as a class of solutions to the field equations of quadratic gravity whose only mass scale is the Planck mass
The collisional frequency in the gas is typically less than the wave frequency and this drastically reduces the damping for those wave frequencies
When spin is introduced the damping is largest for low |ω − ω0|
Summary
A 2-2-hole [1] is an example of an extremely compact horizonless object that deviates from a black hole (BH) only within some Planck-like distance from the would-be horizon. 2-2-holes exist as a class of solutions to the field equations of quadratic gravity whose only mass scale is the Planck mass. The gravitational field equations in this high curvature region would need to be obtained from the quadratic gravity action This region contains the matter, the relativistic gas, of interest here for its possible damping effect. In this case the 2-2-hole solutions are not known and so we lack the precise thermodynamical description, we expect the qualitative features to be similar. We study the spin dependent damping in the context of the truncated Kerr BH model, which is a popular model for rotating objects of extreme compactness It shares with the truncated Schwarzchild model a non-diverging potential, a property we expect for the rotating 2-2-hole. The role that damping can have on the ergoregion instability of extremely compact objects has been studied previously in [11, 12]
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