Cosmic Censorship Conjecture and Quantum Mechanics George E

Cosmic Censorship Conjecture and Quantum Mechanics George E. A. Matsas IFT/ Unesp

Singularities Geodesically incomplete spacetimes or containing “bad behaved” physical observables are said to be singular Under a wide variety of physical circumstances the Einstein equations develop singularities

Cosmic Censorship Conjecture unpredictable Naked singularities are so imoral that there may exist cosmic censors to dress them all (but the big bang) with event horizons. Weak Cosmic Censorship Conjecture If one starts out with an initially non-singular asymptotically flat situation, any singularities which subsequently develop due to gravitational collapse will be hidden from the view of an observer at infinity by the event horizon of a black hole (Penrose, Nuovo Cimento 1969)

Naked singularities from matter collapse?

time Naked singularity SPECIAL initial conditions (Choptuik, PRL 1993)

time GENERIC initial conditions

Naked singularities from black holes?

Black Holes and Naked Singularities Uniqueness theorems: Mass M, electric charge Q, and angular momentum J characterize all “physical” stationary black holes. Question: Is it possible to overspin or overcharge a black hole stripping bare a black hole to reveal its singularity?

Throwing a classical particle into an extreme black hole For related work with further developments see “Overcharging a black hole and cosmic censorship”. (Hubeny, PRD 99) Gravitational Potential particle (Wald, Ann. Phys. 74)

Gravitational Potential Overspinning a nearly extreme charged black hole via a quantum tunneling process particle (G. E. A. M. & A. R. R. da Silva, Phys. Rev. Lett 2007) [comments also in Nature, 450, 147 (2007)]

Basic framework: Semiclassical gravity Reissner-Nordstrom line element Quantized free massless scalar field

Canonical Quantization • Commutation relations: • Scalar field operator: • Inner product: • Commutation relations: • Boulware vacuum: • States: [Castineiras & G. E. A. M, PRD (2000)]

Throwing in a quantum particle Schwinger effect Asymptotic observer

Particle generation mechanism Asymptotic observer [Crispino, da Silva & G. E. A. M, PRD (2009)]

Particle production rate

Tunneling probability M = 100 Mp Q=M–e l = 413

The backreaction issue (Hod, PRL 2008) (in preparation) (Richartz & Saa, PRD 2008) (Hod, PLB 2008)

Generalized second law

Quantum Gravity final veredictum

Final Remarks • It may be that quantum mechanics gives rise to naked singularities • In this case quantum gravity should be very important to unveil the physical structure of the naked singularities recovering the predictability of physics • A final veredictum about whether or not quantum mechanics is able to generate naked singularities will mostly depend on backreaction effects which can be partially unveiled by semi-classical gravity but will require a full quantum gravity theory for a “final” answer.