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

2. 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

3. 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)

5. Naked singularities
from matter collapse? 5

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

7. !?
time
GENERIC initial conditions

8. Naked singularities
from black holes? 8

9. 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?

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

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

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

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

14. Throwing in a quantum particle
Schwinger effect
Asymptotic observer

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

16. Particle production rate

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

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

19. Generalized second law

21. Quantum Gravity final veredictum?

22. 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.