From black holes to white holes: a quantum gravitational, symmetric bounce (1707.07333v2)

Abstract: Recently a consistent non-perturbative quantization of the Schwarzschild interior resulting in a bounce from black hole to white hole geometry has been obtained by loop quantizing the Kantowski-Sachs vacuum spacetime. As in other spacetimes where the singularity is dominated by the Weyl part of the spacetime curvature, the structure of the singularity is highly anisotropic in the Kantowski-Sachs vacuum spacetime. As a result the bounce turns out to be in general asymmetric creating a large mass difference between the parent black hole and the child white hole. In this manuscript, we investigate under what circumstances a symmetric bounce scenario can be constructed in the above quantization. Using the setting of Dirac observables and geometric clocks we obtain a symmetric bounce condition which can be satisfied by a slight modification in the construction of loops over which holonomies are considered in the quantization procedure. These modifications can be viewed as quantization ambiguities, and are demonstrated in three different flavors which all lead to a non-singular black to white hole transition with identical masses. Our results show that quantization ambiguities can mitigate or even qualitatively change some key features of physics of singularity resolution. Further, these results are potentially helpful in motivating and constructing symmetric black to white hole transition scenarios.

From Black Holes to White Holes: A Quantum Gravitational, Symmetric Bounce

The paper under discussion presents a detailed analysis within the framework of loop quantum gravity (LQG) to explore the non-perturbative quantization of the Schwarzschild black hole's interior. The focal point of the paper is the investigation of the possibility of a symmetric bounce, facilitating a transition from a black hole to a white hole of identical mass, which contrasts with previous results suggesting a mass disparity.

Summary of Results

The analysis builds on the loop quantization of the Kantowski-Sachs vacuum spacetime, isometric to the Schwarzschild interior, where anisotropies prominently affect the dynamics near singularities. This quantization scheme aims to address the prevalent issue of asymmetric bounces that result in a significant mass difference between the original black hole and the emergent white hole.

The paper involves the construction of Dirac observables and internal geometric clocks which serve as the dynamical reference for tracking the evolution through quantum bounces. The authors introduce quantization ambiguities, modelled as modifications in the construction of loops for the holonomies in the gravitational sector, potentially leading to a symmetric bounce scenario.

Three viable prescriptions were explored, labeled as choices 1, 2, and 3, alongside a baseline asymmetric case from Corichi-Singh quantization. Each prescription involves the fine-tuning of parameters associated with loop areas, denoted by $\alpha$ and $\beta$, which are typically mass-dependent. The conditions for achieving a symmetric bounce are deduced from these parameter spaces.

Implications and Future Directions

Theoretical Implications: The paper implies that the choice of quantization parameters, often viewed as ambiguities, can significantly alter the qualitative physical predictions in the context of black hole singularities. The potential realization of a symmetric bounce offers a phenomenological picture consistent with some theoretical proposals on black hole evolution but underlines the crucial role of parameter choices underlying quantum gravitational effects.

Practical Implications: Though primarily theoretical, the paper's implications may eventually influence observational astrophysics, particularly in understanding the fate of information in black hole evaporation scenarios and the nature of singularities.

Speculative Future Directions: Future investigations could explore:

1. Generalizing these findings to other spacetime models with different degrees of anisotropy, such as Bianchi type cosmologies.
2. The consistency and robustness of symmetric bounces in full LQG beyond minisuperspaces.
3. Potential observational signatures that might arise in astrophysical phenomena if symmetric bounces occur in nature.

In summary, this paper enhances our understanding of black hole interiors through LQG, highlighting the significance of quantization parameters on the physics of singularity resolution and confirming that symmetric black-to-white hole transitions are not only mathematically feasible but also intrinsically linked to the underlying quantization ambiguities.