The stochastic gravitational-wave background in the absence of horizons

TL;DR

The authors investigate whether horizonless ultracompact objects that mimic black holes can produce a detectable stochastic gravitational-wave background via ergoregion instability. By modeling a canonical perfectly reflecting surface and exploring interior regimes, they derive growth rates, energy emission, and the resulting GW background across LIGO and LISA bands. Their analysis shows that LIGO O1 already rules out the simplest BH mimicker models, with future runs and LISA providing even tighter constraints on the internal travel time t0 and the population fraction X of mimickers. This work delivers the strongest GW-based bounds to date on exotic compact objects and highlights how stochastic backgrounds can probe quantum-gravity-inspired BH alternatives across cosmic populations.

Abstract

Gravitational-wave astronomy has the potential to explore one of the deepest and most puzzling aspects of Einstein's theory: the existence of black holes. A plethora of ultracompact, horizonless objects have been proposed to arise in models inspired by quantum gravity. These objects may solve Hawking's information-loss paradox and the singularity problem associated with black holes, while mimicking almost all of their classical properties. They are, however, generically unstable on relatively short timescales. Here, we show that this "ergoregion instability" leads to a strong stochastic background of gravitational waves, at a level detectable by current and future gravitational-wave detectors. The absence of such background in the first observation run of Advanced LIGO already imposes the most stringent limits to date on black-hole alternatives, showing that certain models of "quantum-dressed" stellar black holes can be at most a small percentage of the total population. The future LISA mission will allow for similar constraints on supermassive black-hole mimickers.

Figures (4)

• Figure 1: Schematic potential for a non-spinning ultracompact object, as a function the tortoise radial coordinate (in practice, the coordinate time $t$ of a photon). For object radii $r_0\sim r_+$, the radiation travel time from the photosphere to the surface scales approximately as $t_0\sim t_H|\log\epsilon|$. The travel time from the surface to the interior is parametrized as $t_{\rm interior}$.
• Figure 2: Extragalactic stochastic background for the canonical model in the LIGO/Virgo (left panel), LISA and PTA bands (right panel). The blue band brackets our population models (from the most pessimistic to the most optimistic, as explained in the main text). The background depends very weakly on $\epsilon$ as long as $t_0\sim t_H| \log\epsilon | \ll 10^{10} t_H$, so here we show only the case $t_0\sim t_H | \log 10^{-40}|$. The black lines are the power-law integrated curves of Thrane:2013oya, computed using noise PSDs for LISA with one year of observation time Audley:2017drz, LIGO's first observing runs (O1), LIGO at design sensitivity as described in TheLIGOScientific:2016dpb, and an SKA-based pulsar timing array as described in Dvorkin:2017vvm. By definition, $\rho_{\rm stoch}> 2$ ($\rho_{\rm stoch}= 2$) when a power-law spectrum intersects (is tangent to) a power-law integrated curve.
• Figure 3: Same as in Fig. \ref{['fig:background']}, but for an agnostic model for the compact-object (dissipationless) interior, where the light travel time $t_0$ between the light ring and the surface is a free parameter.
• Figure 4: Instability timescale for $l=m=2$ gravitational perturbations as function of the BH spin $\chi$, for different values of $t_0$.