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Black Holes


Event Horizon: Interfacing the Classical and the Quantum

Tech Area / Field

  • PHY-PFA/Particles, Fields and Accelerator Physics/Physics

3 Approved without Funding

Registration date

Leading Institute
VNIIEF, Russia, N. Novgorod reg., Sarov

Supporting institutes

  • Joint Institute of Nuclear Research, Russia, Moscow reg., Dubna


  • University College London / Department of Mathematics, UK, London\nUniversity of Missouri, USA, MO, Columbia

Project summary

The formation of a black hole resembles a phase transition in condensed matter physics. The energy content of a collapsing star differs significantly from that of the resulting black hole. This transition entails a drastic symmetry change. The present study proceeds from the assumption that forming the black hole horizon is a transition between the classical and quantum regimes of evolution. The idea that the formation of a black hole is a phase transition and that the laws of classical general relativity cease to be valid as the collapsing object approaches the Schwarzschild radius was previously developed by Laughlin with coauthors in their pioneer studies. However, they pondered on the nature of the phase transition somewhat different from that developed in this Project. One task of the Project is to clarify the pros and cons of both views of forming a black hole as a phase transition. When the essentials of classical theory are compared with those of quantum theory, it transpires that spontaneous creations and annihilations of particle-antiparticle pairs are possible in the quantum world, but impossible in the classical world. In flat spacetime, we must change the overall sign of the spacetime signature in the classical description of field propagation for it to be treated as the quantum description of field propagation. This leads us to consider the event horizon of a Schwarzschild black hole as a sharply defined boundary which demarcates the classical and the quantum. However, the classical-quantum transition problem for spinning black holes is distinct in nature from that in the presence of spherical symmetry. Here, it seems to be impossible to discriminate between classical and quantum pictures by making direct reference to the concept of event horizon. A major problem of this Project is to establish a general criterion for discriminating classical and quantum regimes of evolution on geometrical manifolds with event horizons. To cope with this task, several particular problems on motion of particles and their spin precession in weak and strong gravitational fields are to be studied thoroughly.

The feasibility of the classical regime of evolution is another way of stating that the system enjoys the property of supersymmetry. To describe a self-gravitating object at the last stage of its classical evolution, just before its shrinking down to below the horizon, we propose to invoke the Foldy–Wouthuysen representation of the Dirac equation in curved spacetimes, and the Gozzi classical path integral technique. In both descriptions, maintaining the dynamics in the classical regime is controlled by supersymmetry. The main concern of the Project is to justify these approaches in full measure and refine pertinent techniques. If we would succeed in integrating the Foldy–Wouthuysen dynamics for a gravitationally collapsing wave packet (say, in the Schwarzschild background), or, alternatively, in calculating the Gozzi path integral for a collapsing perfect fluid, we would establish a point where a self-destruction of this classical machinery occurs. The supersymmetry structure undergoes a breakdown at this point. This might help to illuminate the general mechanism of supersymmetry breaking.

The Project objective is to study the mechanism of the formation of a black hole as a phase transition, clarify the nature of this phase transition, and give a fully developed description of the key features of the event horizon, the boundary which demarcates the classical and the quantum regimes of evolution of gravitationally collapsing systems.


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