Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects (1406.5510v1)

Abstract: Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long-lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the "black hole hypothesis," once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we explore in some depth the mode structure of ultracompact stars, in particular constant-density stars and gravastars. We show that the existence of very long-lived modes -- localized near a second, stable null geodesic -- is a generic feature of gravitational perturbations of such configurations. Already at the linear level, such modes become unstable if the object rotates sufficiently fast to develop an ergoregion. Finally, we conjecture that the long-lived modes become unstable under fragmentation via a Dyson-Chandrasekhar-Fermi mechanism at the nonlinear level. Depending on the structure of the star, it is also possible that nonlinearities lead to the formation of small black holes close to the stable light ring. Our results suggest that the mere observation of a light ring is a strong evidence for the existence of black holes.

• The paper demonstrates that the presence of a light ring may serve as observational evidence for an event horizon.
• It reveals that ultracompact objects exhibit very long-lived modes that destabilize under rapid rotation, leading to ergoregion formation.
• It suggests that nonlinear evolution of these modes can trigger fragmentation and significant energy loss, affecting overall stability.

Analytical and Numerical Study of Ultracompact Objects

The paper examines the dynamics and properties of ultracompact objects, specifically focusing on the existence and implications of light rings as potential evidence for event horizons. These objects are analyzed in terms of their susceptibility to nonlinear instabilities and ergoregion phenomena.

Ultracompact Objects and Light Rings

Ultracompact objects possess a critical attribute—a light ring, which is a stable null geodesic potentially observable through electromagnetic or gravitational-wave signals. The authors argue that the presence of a light ring could imply that these objects are black holes, thus supporting the black hole hypothesis. If validated, this would offer a powerful tool for observational astrophysics, aiding in the identification of black holes.

Mode Structure and Stability

The research explores the perturbation modes of ultracompact objects, such as constant-density stars and gravastars. Through analytical and WKB approximations, the paper identifies very long-lived modes in these configurations. These modes become unstable under rapid rotation, leading to the generation of an ergoregion—a region where the dynamic properties are markedly altered, often resulting in instability for non-black hole configurations without horizons.

Nonlinear Instabilities and Observational Implications

A conjecture is made regarding the nonlinear evolution of these long-lived modes, suggesting a fragmentation scenario potentially leading to dynamic behavior akin to boiling. This fragmentation is posited to result in significant energy emission and mass loss, ultimately reducing the object's compactness and possibly altering its stability.

Future Directions

The analysis opens avenues for further research into nonlinear effects and instabilities in ultracompact objects. Understanding the nonlinear dynamics and potential dissipation mechanisms could reveal insights into gravitational-wave emissions and their effects on the structure and fate of such objects. Future observational efforts can leverage these findings to probe the nature of compact dark objects, like supermassive black holes, in our universe.

Conclusion

The paper serves as a substantial step towards understanding the complex dynamics associated with ultracompact objects and their potential classification as black holes based on the presence of observable light rings. It influences gravitational physics and motivates future work in high-energy astrophysics to confirm these theoretical predictions and their implications through observational techniques.