Cai, RG
; Wang, SJ (reprint author), Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.
; Cai, RG
; Sasaki, M
; Wang, SJ (reprint author), Kyoto Univ, Yukawa Inst Theoret Phys, Ctr Gravitat Phys, Kyoto 6068502, Japan.
; Sasaki, M (reprint author), Kyoto Univ, Int Res Unit Adv Future Studies, Kyoto 6068502, Japan.
; Wang, SJ (reprint author), Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China.
文章类型:
Article
英文摘要:
According to the conjecture "complexity equals action," the complexity of a holographic state is equal to the action of a Wheeler-DeWitt (WDW) patch of black holes in anti-de Sitter space. In this paper we calculate the action growth of charged black holes with a single horizon, paying attention to the contribution from a spacelike singularity inside the horizon. We consider two kinds of such charged black holes: one is a charged dilaton black hole, and the other is a Born-Infeld black hole with beta(2)Q(2) < 1/4. In both cases, although an electric charge appears in the black hole solutions, the inner horizon is absent; instead a spacelike singularity appears inside the horizon. We find that the action growth of the WDWpatch of the charged black hole is finite and satisfies the Lloyd bound. As a check, we also calculate the action growth of a charged black hole with a phantom Maxwell field. In this case, although the contributions from the bulk integral and the spacelike singularity are individually divergent, these two divergences just cancel each other and a finite action growth is obtained. But in this case, the Lloyd bound is violated as expected.
National Natural Science Foundation of China [11375247, 11435006, 11447601]
; key project of CAS [QYZDJ-SSW-SYS006]
; MEXT KAKENHI [15H05888, 15K21733]
