[Paper Review] Dynamics and Thermodynamics of Blackholes and Naked Singularities

L. Fatibene, M. Francaviglia+2 more|ArXiv.org|Dec 15, 2005

Geophysics and Sensor Technology4 citations

TL;DR

This paper presents the proceedings of an international workshop on black hole dynamics and thermodynamics, focusing on gravitational collapse, cosmic censorship, and the thermodynamic properties of black holes and naked singularities. Key contributions include geometric frameworks for entropy, Hamiltonian thermodynamics, critical phenomena in collapse, and analyses of singularities and higher-dimensional black holes.

ABSTRACT

Proceedings of the international Workshop on ``Dynamics and Thermodynamics of Blackholes and Naked Singularities``, that took place at the Department of Mathematics of the Politecnico of Milano from 13 to 15 May 2004.

Motivation & Objective

• To explore the thermodynamic behavior of black holes and naked singularities in the context of general relativity and extended theories.
• To investigate the validity and implications of the cosmic censorship hypothesis through analytical and numerical studies of gravitational collapse.
• To develop geometric and Hamiltonian frameworks for defining entropy and thermodynamic quantities in relativistic spacetimes.
• To examine the stability and physical properties of black holes and singularities in higher-dimensional and string-theoretic settings.
• To analyze critical phenomena and global structure in spherically symmetric collapse, particularly in the Choptuik spacetime.

Proposed method

• Application of geometric and symplectic techniques to define entropy in general relativity using the covariant phase space formalism.
• Use of Hamiltonian methods to derive thermodynamic laws for black holes from first principles, particularly in stationary spacetimes.
• Employment of nonlinear ODE techniques to study the dynamics of spherically symmetric gravitational collapse and the formation of singularities.
• Numerical and analytical investigation of the Einstein-Vlasov system to model self-gravitating collisionless matter in collapse.
• Analysis of critical behavior in the Choptuik spacetime using global structure and scaling laws.
• Study of stability and extendibility of spacetimes with naked singularities and black holes via linear and nonlinear perturbation methods.

Experimental results

Research questions

• RQ1 How can entropy be consistently defined in general relativity using geometric and covariant phase space methods?
• RQ2 To what extent do Hamiltonian formulations reproduce standard black hole thermodynamics, especially for stationary solutions?
• RQ3 What determines the critical behavior in gravitational collapse, and how does the global structure of spacetime affect cosmic censorship?
• RQ4 How do higher-dimensional and string-theoretic models modify the thermodynamic and dynamical properties of black holes and singularities?
• RQ5 What are the physical and mathematical conditions under which naked singularities can be stable or extendible, and how do they differ from black holes?

Key findings

• A geometric framework for entropy in general relativity was developed using the covariant phase space formalism, providing a consistent derivation of Bekenstein-Hawking entropy.
• Hamiltonian methods confirmed the first law of black hole thermodynamics for stationary spacetimes, linking energy, mass, and entropy through symplectic structures.
• Critical phenomena in the Choptuik spacetime were analyzed, revealing universal scaling behavior near the threshold of black hole formation.
• The stability of naked singularities in static spacetimes was investigated, showing that certain configurations remain unstable under linear perturbations.
• Numerical and analytical results on the Einstein-Vlasov system demonstrated the formation of black holes from self-gravitating collisionless matter under specific initial conditions.
• In higher-dimensional spacetimes, black holes with large extra dimensions were shown to exhibit modified thermodynamic and horizon properties compared to four-dimensional counterparts.