TY - JOUR

T1 - Gedanken experiments to destroy a BTZ black hole

AU - Ning, Bo

AU - Chen, Baoyi

AU - Lin, Feng Li

PY - 2019/8/23

Y1 - 2019/8/23

N2 - We consider Gedanken experiments to destroy an extremal or near-extremal Banados-Teitelboim-Zanelli (BTZ) black hole by throwing matter into the horizon. These black holes are vacuum solutions to (2+1)-dimensional gravity theories, and are asymptotically AdS3. Provided the null energy condition for the falling matter, we prove the following - (i) in a Mielke-Baekler model without ghost fields, when torsion is present, an extremal BTZ black hole can be overspun and becomes a naked conical singularity; (ii) in three-dimensional Einstein gravity and chiral gravity, which both live in the torsionless limits of the Mielke-Baekler model, an extremal BTZ black hole cannot be overspun; and (iii) in both Einstein gravity and chiral gravity, a near-extremal BTZ black hole cannot be overspun, leaving the weak cosmic censorship preserved. To obtain these results, we follow the analysis of Sorce and Wald on their Gedanken experiments to destroy a Kerr-Newman black hole, and calculate the second order variation of the black hole mechanics. Furthermore, Wald's type of Gedanken experiments provide an operational procedure of proving the third law of black hole dynamics. Through the AdS/CFT correspondence, our results on BTZ black holes also indicate that a third law of thermodynamics holds for the holographic conformal field theories dual to three-dimensional Einstein gravity and chiral gravity.

AB - We consider Gedanken experiments to destroy an extremal or near-extremal Banados-Teitelboim-Zanelli (BTZ) black hole by throwing matter into the horizon. These black holes are vacuum solutions to (2+1)-dimensional gravity theories, and are asymptotically AdS3. Provided the null energy condition for the falling matter, we prove the following - (i) in a Mielke-Baekler model without ghost fields, when torsion is present, an extremal BTZ black hole can be overspun and becomes a naked conical singularity; (ii) in three-dimensional Einstein gravity and chiral gravity, which both live in the torsionless limits of the Mielke-Baekler model, an extremal BTZ black hole cannot be overspun; and (iii) in both Einstein gravity and chiral gravity, a near-extremal BTZ black hole cannot be overspun, leaving the weak cosmic censorship preserved. To obtain these results, we follow the analysis of Sorce and Wald on their Gedanken experiments to destroy a Kerr-Newman black hole, and calculate the second order variation of the black hole mechanics. Furthermore, Wald's type of Gedanken experiments provide an operational procedure of proving the third law of black hole dynamics. Through the AdS/CFT correspondence, our results on BTZ black holes also indicate that a third law of thermodynamics holds for the holographic conformal field theories dual to three-dimensional Einstein gravity and chiral gravity.

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U2 - 10.1103/PhysRevD.100.044043

DO - 10.1103/PhysRevD.100.044043

M3 - Article

AN - SCOPUS:85072173181

VL - 100

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 044043

ER -