Black Hole's Quantum N-Portrait (1112.3359v1)

Abstract: We establish a quantum measure of classicality in the form of the occupation number, $N$, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose-condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, $N$ is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by $N$. The black hole is a leaky bound-state in form of a cold Bose-condensate of $N$ weakly-interacting soft gravitons of wave-length $ \sqrt{N}$ times the Planck length and of quantum interaction strength 1/N. Such a bound-state exists for an arbitrary $N$. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose-condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature $T \, = \, 1/\sqrt{N}$. The Bekenstein entropy originates from the exponentially growing with $N$ number of quantum states. Finally, our quantum picture allows to understand classicalization of deep-UV gravitational scattering as $2 \rightarrow N$ transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects represent Bose-condensates of $N$ soft bosons of wavelength $\sqrt{N}$ and interaction strength 1/N. In short, the semi-classical black hole physics is 1/N-coupled large-$N$ quantum physics.

• The paper reframes black holes as quantum Bose-condensates defined by the occupation number N, offering a novel perspective on their entropy.
• It derives Hawking radiation through the quantum depletion of soft gravitons, aligning the temperature with traditional entropy calculations.
• The authors introduce gravitational self-completion via N-graviton states, drawing parallels with soliton behavior in other field theories.

Quantum N-Portrait of Black Holes: A Novel Perspective

The paper presented by Gia Dvali and Cesar Gomez offers a quantum mechanical perspective on black holes through the concept of the occupation number $N$, which quantifies the classicality of gravitating configurations. This approach recasts classical gravitational systems as quantum Bose-condensates, emphasizing that black holes maximize $N$, coinciding with their entropy. The authors propose that a black hole can be fundamentally described as a cold, leaky bound-state Bose-condensate of weakly interacting soft gravitons, characterized by a wave-length proportional to $\sqrt{N} \times L_P$. The interaction strength of these gravitons is diminutive, specifically $1/N$, which aligns with a wide-ranging gravitary interaction.

Key Contributions and Claims:

1. Reinterpretation of Black Holes: The paper posits that the semi-classical depiction of black holes can be reformulated entirely through the quantum parameter $N$. This stands in contrast to the traditional view that relies on classical geometry. The black hole is thus characterized without a reference to horizon or mass as primary parameters.
2. Hawking Radiation and Bekenstein Entropy via Quantum Effects: The emergent Hawking radiation is portrayed as the quantum depletion of the graviton condensate, leading to a thermal spectrum. This innovative quantum perspective yields a temperature $T = 1/\sqrt{N}$, and aligns with the traditional Bekenstein entropy result through a counting of exponentially numerous quantum states of these condensates.
3. Gravitational Self-Completion and Unitarity: The authors advance the notion of Einstein gravity being self-complete in a non-Wilsonian manner, where N increases with energy due to classicalization. Within this framework, high-energy scattering processes naturally evolve into N-graviton states, signaling a quantum picture of unitarization that sidesteps traditional UV-completion methods.
4. Comparison with Solitons and Implications for Other Theories: The paper notes the similarity between black holes and solitons (e.g., t'Hooft-Polyakov monopoles) as both represent Bose-condensates of $N$ soft bosons. This connection further extends to QCD baryons with large colors, underscoring a universal quantum N-portrait. However, due to differing energy self-sourcing dynamics, only black holes exhibit features like thermality.

Theoretical and Practical Implications:

The outlined quantum depiction of black holes offers notable implications for theoretical physics, particularly in providing a self-consistent framework that doesn't rely on classical geometric approximations. This understanding could reshape foundational approaches in quantum gravity and related fields, prompting a reassessment of how entropy and fundamental black hole properties are conceived.

In practical terms, insights from this model could inform experimental and observational methodologies. For example, enumerating interactions in graviton condensates might be extrapolated to develop new theoretical tools for probing high-energy physics phenomena.

Speculations for Future Developments:

In advancing this framework, exploration into its applicability in broader cosmic structures like de Sitter or anti-de Sitter spaces can be considered. Further investigation could delve into its compatibility or divergence with existing paradigms, such as holography or AdS/CFT correspondences, potentially uncovering novel structures in quantum field theories. Additionally, the ramifications of such a quantum mechanical model may offer paths to reconcile quantum mechanics with the continuously expanding scale of cosmology.

In conclusion, Dvali and Gomez's work presents a compelling reframing of black holes' quantum mechanics through the lens of large occupation number $N$, challenging prevailing interpretations and expanding the possibilities for interlinking quantum gravity with the broader tapestry of theoretical physics.