Listening to black mirrors with gravitational radiation

Abstract

The existence of curvature singularities and the information and firewall paradoxes are significant problems for the conventional black hole model. The black mirror provides a CPT-symmetric alternative to the classical description. We show that classical black holes can be distinguished from black mirrors by using gravitational waves. The principal challenge is to identify a unique, testable signature of the black mirror's reflective horizon that can be detected. The horizon singularity of the black mirror model necessitates that no energy flux is propagated beyond the horizon, which can be described effectively by imposing specific boundary conditions at the event horizon. We demonstrate that the quasi-normal mode spectrum of the black mirror is fundamentally different from that of classical black holes. We derive the reflectivity of the black mirror and find it is given precisely by the generalized Boltzmann factor. Moreover, we show that this is a universal behaviour: regardless of the specific details of the unknown quantum gravity interactions, the macroscopic reflectivity is dictated solely by the Hawking temperature $T_H$. This drastically alters the orbital dynamics of extreme-mass ratio inspirals. For low spins, the inspiral decelerates due to reduced absorption. For high spins and prograde orbits, the black mirror suppresses the superradiant amplification of classical black holes, acting instead as an absorber. This leads to an inspiral that proceeds faster than the classical prediction. Finally, we show that this model allows for the cosmic growth of supermassive black holes to high spins via accretion. A definitive detection of these signatures would provide compelling evidence distinguishing the reflective boundary of a black mirror from the perfectly absorbing horizon of a classical black hole.

Figures (3)

• Figure 1: A massive particle intersecting the horizon of the black mirror at a point $p$ is subsequently trapped in the horizon. An interaction at the horizon results in an outgoing signal, the thicker black segment, which propagates along the horizon. The points $i^+$, $i_-$, and $i_0$ represent future timelike, past timelike, and spacelike infinity, respectively, while $\mathscr{I}_-$ represents past null infinity.
• Figure 2: EMRI evolution in the low-spin regime ($a_* < a_c$). The evolution of the frequency parameter $x=M/r$ (solid line for BH, dashed line for BM) and the cumulative dephasing $\Delta \Phi$ (dotted line) are shown. The BM inspiral is slower than the BH inspiral due to reduced horizon absorption.
• Figure 3: Zoom view of the normalized gravitational waveform $h_{\text{norm}}$ in the low-spin regime near ISCO. Left panel: Classical black hole (BH). Right panel: Black mirror (BM). The BM waveform lags behind the BH waveform due to the accumulated dephasing shown in Fig. (\ref{['fig:BM_Evolution_Dephasing']}).