Mass inflation without Cauchy horizons (2402.14913v1)

Abstract: Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are generically present for dynamical geometries endowed with slowly-evolving inner trapping horizons, even in the absence of Cauchy horizons. This provides a more general definition of mass inflation based on quasi-local concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with non-extremal inner horizons, including the Kerr geometry in general relativity, and non-extremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived endpoint of gravitational collapse.

• The paper establishes a generalized definition of mass inflation in dynamic spacetimes that lack conventional Cauchy horizons.
• It employs analytical models and perturbative simulations to reveal a finite yet significant exponential energy buildup near inner trapping horizons.
• These findings challenge traditional black hole models and offer insights with potential implications for quantum gravity and gravitational wave research.

Analysis of "Mass Inflation without Cauchy Horizons"

The paper authored by Carballo-Rubio, Di Filippo, Liberati, and Visser addresses a nuanced topic in the domain of black hole physics, specifically concerning the mass inflation instability in the absence of Cauchy horizons. Traditionally, mass inflation—a critical instability indicative of exponential energy accumulation—has been associated with Cauchy horizons in stationary black hole geometries. The authors extend this understanding by demonstrating that such phenomena can occur in dynamical spacetimes equipped with slowly evolving inner trapping horizons, even when Cauchy horizons are absent.

The principal contribution of the paper is the establishment of a generalized definition of mass inflation, adaptable to dynamic, quasi-local conditions. The paper makes the strong assertion that finite yet significant exponential buildups of energy are prevalent in such scenarios. This extended perspective is particularly vital for understanding black holes with non-extremal inner horizons, providing insights into both classical theories of general relativity and regular black holes described within alternative theoretical frameworks.

Key Findings and Methodology

The authors employ two models to substantiate their claims: one involving intersecting null shells and a second comprising a null shell and a radiation stream. These models illustrate the presence of an exponential mass buildup without relying on the conventional divergence linked with stationary Cauchy horizons. Analytically, the paper derives conditions under which the exponential nature of mass inflation can manifest, introducing adiabatic conditions that characterize the slow temporal evolution required for this behavior. The surface gravity of the inner horizon plays a crucial role in this dynamic, providing a metric for the exponential growth rate until other physical mechanisms intervene.

The numerical investigation extends the analytical framework using perturbative methods akin to the Ori model, reinforcing the robustness of the theoretical predictions. The results of these simulations corroborate the analytical findings, showcasing a large but finite exponential energy increase that eventually leads to a breakdown of the adiabatic conditions.

Implications

The conclusions drawn have considerable implications for our understanding of black hole inner horizons. The assertion that inner horizons in dynamically evolving spacetimes can undergo mass inflation suggests that they may not persist as static entities. This challenges the conventional depiction of black holes, particularly the quasi-stationary description used in astrophysical contexts.

From a theoretical standpoint, these insights could influence ongoing discussions in quantum gravity, especially concerning the fate of singularities and potential regularization mechanisms. Furthermore, the results may have practical implications for gravitational wave astronomy and the electromagnetic spectrum, where dynamic transitions in black hole spacetimes might manifest observable signatures.

Future Directions

The research opens avenues for further investigation into the end states of gravitational collapse and the precise nature of horizon stability. It invites further exploration of non-spherical geometries, particularly rotating black holes, which are anticipated to exhibit similar mass inflation characteristics despite the apparent complexity added by angular momentum dynamics.

In summary, this paper contributes a significant re-evaluation of mass inflation within the context of dynamical black hole spacetimes. It shifts the lens from internals dominated by seemingly permanent features like Cauchy horizons to a field where inner horizon dynamics can instigate notable and impactful events, potentially altering the landscape of black hole physics substantially.