Gravitational wave signatures of the absence of an event horizon. II. Extreme mass ratio inspirals in the spacetime of a thin-shell gravastar

We study gravitational wave emission from the quasicircular, extreme mass ratio inspiral of compact objects of mass $m_0$ into massive objects of mass $M\gg m_0$ whose external metric is identical to the Schwarzschild metric, except for the absence of an event horizon. To be specific we consider one of the simplest realizations of such an object: a nonrotating thin-shell gravastar. The power radiated in gravitational waves during the inspiral shows distinctive peaks corresponding to the excitation of the polar oscillation modes of the gravastar. For ultracompact gravastars the frequency of these peaks depends mildly on the gravastar compactness. For masses $M\sim {10}^6{M}_{\odot }$ the peaks typically lie within the optimal sensitivity bandwidth of the Laser Interferometer Space Antenna, potentially providing a unique signature of the horizonless nature of the central object. For relatively modest values of the gravastar compactness the radiated power has even more peculiar features, carrying the signature of the microscopic properties of the physical surface replacing the event horizon.

Figure 1

Dominant ($l=2$) contribution to the energy flux for very high compactness and $v_s^2=0.1$ (but when $\mu \sim 0.5$ resonances are almost independent on $v_s^2$). From right to left the resonant peaks correspond to $\mu =0.49997,0.49998,0.49999,0.499995,0.499999$, respectively.

Figure 2

Left: The energy flux (summed up to $l=6$) of GWs emitted by a small mass orbiting a thin-shell gravastar with $v_s^2=0.1$ and different values of $\mu$ (plotted as a function of the particle orbital velocity $v$) is compared with the flux for a Schwarzschild BH. All peaks (with the exception of the last two peaks on the right) are due to the excitation of QNMs with $l=m$. Right: same for $v_s^2=0.1$ and selected values of $\mu \in [0.29,0.49]$. No QNMs are excited in this range.

Figure 3

Real part (left) and imaginary part (right) of gravastar QNMs with $l=2$ as a function of compactness for several fixed values of $v_s^2$ (as indicated in the legend). For clarity in illustrating the “selection rules” that determine QNM excitation during inspiral we only show the weakly damped part of the QNM spectrum (compare Fig. 2 and Fig. 6 in paper I). For $v_s^2>0.8$ the real part of the frequency is plotted down to the critical minimum compactness at which the imaginary part crosses zero within our numerical accuracy. The horizontal line at $2M{\omega }_R\simeq 0.2722$ corresponds to twice the orbital frequency of a particle in circular orbit at the ISCO: only QNMs below this line can be excited during a quasicircular inspiral.

Figure 4

Real part (left) and imaginary part (right) of gravastar QNMs with $l=3$ as a function of compactness for several fixed values of $v_s^2$ (as indicated in the legend). For clarity in illustrating the “selection rules” that determine QNM excitation during inspiral we only show the weakly damped part of the QNM spectrum. In the left panel, the horizontal lines at $2M{\omega }_R\simeq 0.1361$ ($2M{\omega }_R\simeq 0.4082$) correspond to the orbital frequency (or 3 times the orbital frequency) of a particle in circular orbit at the ISCO. Perturbations with $l=3$, $m=1$ can excite the QNMs below the first line, while perturbations with $l=m=3$ can excite QNMs below the second line.