Validity of black hole complementarity in the BTZ black hole

Abstract

Based on the gedanken experiment for black hole complementarity in the Schwarzschild black hole, we calculate the energy required to duplicate information in the BTZ black hole under the assumption of absorbing boundary condition and its dual solution of the black string, respectively, in order to justify the validity of the no-cloning theorem in quantum mechanics. For the BTZ black hole, the required energy for the duplication of information can be made fairly small, whereas for the black string it exceeds the total mass of the black string, although they are related to each other under the dual transformation. So, the duplication of information might be possible in the BTZ black hole in contrast to the case of the black string, so that the no-cloning theorem could be violated for the former case. To save the duplication of information for the BTZ black hole, we perform an improved gedanken experiment by using the local thermodynamic quantities near the horizon rather than those defined at infinity, and show that the no-cloning theorem could be made valid even in the BTZ black hole. We also discuss how this local treatment for the no-cloning theorem can be applied to the black string as well as the Schwarzschild black hole innocuously.

14 pages, 1 figure, version to appear in PLB

References in corpus (6)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Evaporation of large black holes in AdS: coupling to the evaporon
• Hawking-Page phase transition in BTZ black hole revisited
• Fake Supersymmetry and Extremal Black Holes
• Hawking-Page Phase Transition of black Dp-branes and R-charged black holes with an IR Cutoff
• Black hole complementarity from AdS/CFT