Testing the cosmic censorship with an extremal black hole Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island   Testing the cosmic censorship with an extremal black hole Sijie Gao Beijing Normal University, China Ref. Sijie Gao and Yuan Zhang, Phys. Rev.D 87, 044028 (2013)

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island Black hole singularity （future null infinity） Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Kerr-Newman black hole (Stationary black hole) Three parameters: RN black hole Kerr black hole Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island Surface gravity (temperature): event horizon: Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island (RN black hole) extremal black hole Naked singularity Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island Cosmic censorship conjecture (Penrose 1969): Naked singularity does not exist. All singularities should be hidden in black holes. Gedanken experiments to test the cosmic censorship conjecture Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

In 1974, Wald [Ann.Phys. 83,548(1974)] proved that an extremal Kerr-Newman black hole cannot be overcharged or overspun. In his proof, linear approximation was used. In 1999, Hubeny [PRD, 59, 064013] showed that a nearly extremal RN black hole can be overcharged, leading to potential violation of the cosmic censorship. In 2009, Jacobson and Sotiriou (PRL 103, 141101) obtained similar Result for nearly extremal Kerr black hole. Both Hubeny and Jacobson’s results agree with Wald’s in the extremal limit even without linear approximation, i.e., no violation for extremal RN black hole ( ) or Kerr black hole ( ).

Results so far: So it seems that cosmic censorship is safe for extremal black holes. But the extremal Kerr-Newman black hole ( , ) with non-linear terms had not been checked.

Destroying an extremal Kerr-Newman black hole The metric is written as The particle’s four-velocity is The conserved energy and angular momentum are given by Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island At the horizon of an extremal Kerr-Newman black hole, it becomes Keeping terms linear to , Eq. (22) becomes which contradicts Eq.(21), meaning the particle cannot reach the horizon. Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island Define So with Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

The effective potential defined by is always negavive for ., so the particle can be released from infinity and fall all the way to the horizon.

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island We also show that, to violate the cosmic censorship, the allowed range of is of order . This fine tunning indicates that the back reaction and self-force effects should be considered. Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island Conclusions By considering high order terms, we show that the horizon of an extremal Kerr-Newman black hole can be destroyed by a test particle. The apparent violation of the cosmic censorship is generic. The fine-tuning on the particle’s parameters indicates that the back-reaction effect should be considered and may prevent violation of the cosmic censorship. Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island

Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island Thank you! Asia Pacific School on Gravitation and Cosmology 2013, Jeju Island