Black Holes as Critical Point of Quantum Phase Transition

Abstract: We reformulate the quantum black hole portrait in the language of modern condensed matter physics. We show that black holes can be understood as a graviton Bose-Einstein condensate at the critical point of a quantum phase transition, identical to what has been observed in systems of cold atoms. The Bogoliubov modes that become degenerate and nearly gapless at this point are the holographic quantum degrees of freedom responsible for the black hole entropy and the information storage. They have no (semi)classical counterparts and become inaccessible in this limit. These findings indicate a deep connection between the seemingly remote systems and suggest a new quantum foundation of holography. They also open an intriguing possibility of simulating black hole information processing in table-top labs.

• The paper demonstrates that black holes can be modeled as graviton BECs at the critical point of quantum phase transitions.
• The authors detail numerical scaling laws, such as L = √N L_P and coupling α = 1/N, to connect BEC behavior with black hole properties.
• The study implies that Hawking radiation results from quantum depletion, opening pathways for laboratory simulations of gravitational phenomena.

Understanding Black Holes as Critical Points in Quantum Phase Transitions

The paper by Gia Dvali and Cesar Gomez proposes a compelling theoretical framework that connects the physics of black holes to quantum phase transitions observed in systems like Bose-Einstein condensates (BECs) of cold atoms. The central thesis of their work is that black holes can be interpreted as graviton BECs at the critical point of a quantum phase transition. This perspective provides novel insights into the quantum aspects of black holes, particularly with regards to holographic principles and information storage capacities.

The authors suggest that, just like in quantum systems, black holes can be viewed as critical graviton condensates. In this framework, black holes are self-sustained entities where the graviton interactions lead to a state of maximal occupation or "maximal packing." A key aspect of this theory is the role of Bogoliubov modes, which become nearly gapless at the critical point. These modes, otherwise absent in classical interpretations, are posited as the quantum degrees of freedom responsible for black hole entropy and information processing.

Acknowledging the long-standing problem of fully reconciling quantum mechanics and gravitational phenomena, this work not only bridges conceptual gaps between seemingly distinct physical systems but also provides a possible pathway for laboratory simulations of black hole analogs. The authors emphasize that while peculiarities inherent to black holes aren't entirely replicated in lab BECs, understanding these parallels might significantly widen the scope for experimental pursuits.

Numerical Results and Key Assertions

Several numerical relationships underpin this theory. For instance, at maximal packing, the system's size $L$ scales with the occupation number $N$ as $L = \sqrt{N}L_P$ with an interaction coupling proportional to $\alpha = 1/N$. The authors further assert that Hawking radiation can be reinterpreted as quantum depletion of the graviton BEC. Here, the effective temperature of black hole radiation correlates with quantum depletion, showing thermal behavior up to corrections of order $1/N$.

Moreover, the relationship between the Bekenstein entropy and the quantum degeneracy of BEC states at the critical point is striking. The entropy of black holes, traditionally expressed as $S \sim (L/L_P)^2$, finds an analogue in the degeneracy inherent to BECs at phase transitions. This is posited to be a consequence of the nearly gapless modes emerging from subtle quantum interactions.

Broader Implications and Future Directions

The implications of this research stretch beyond theoretical pursuits, potentially impacting practical and experimental aspects of quantum gravity. By translating black hole dynamics into a more accessible framework of quantum phase transitions, the authors hint at the possibility of simulating these cosmic phenomena in controlled settings. Such advances could foster a greater understanding surrounding quantum gravitational effects and holography.

Further, this work proposes that the inherent quantum mechanics of maximally packed systems offer a natural explanation for holographic principles. The equivalence of large-N BECs with critical points in these systems lays a foundation for the emergence of conformal field theories, reflecting the nearly gapless nature of quantum excitations.

Conclusion

In summary, Dvali and Gomez offer a quantum-centric perspective on black holes, innovatively characterized through the lens of condensate phases. By likening black holes to critical BECs, the study enlightens our understanding of black hole entropy, information retention, and Hawking radiation. It challenges traditional notions by exposing the quantum essence underlying classical black hole descriptions. Additionally, extending this quantum framework might unlock new avenues in simulating gravitational phenomena, enriching our exploration of quantum gravity in both theoretical and experimental domains.