Testing holographic conjectures of complexity with Born–Infeld black holes
Abstract In this paper, we use Born–Infeld black holes to test two recent holographic conjectures of complexity, the “Complexity = Action” (CA) duality and “Complexity = Volume 2.0” (CV) duality. The complexity of a boundary state is identified with the action of the Wheeler–deWitt patch in CA duali...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-12-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-017-5395-3 |
| _version_ | 1798044083549110272 |
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| author | Jun Tao Peng Wang Haitang Yang |
| author_facet | Jun Tao Peng Wang Haitang Yang |
| author_sort | Jun Tao |
| collection | DOAJ |
| description | Abstract In this paper, we use Born–Infeld black holes to test two recent holographic conjectures of complexity, the “Complexity = Action” (CA) duality and “Complexity = Volume 2.0” (CV) duality. The complexity of a boundary state is identified with the action of the Wheeler–deWitt patch in CA duality, while this complexity is identified with the spacetime volume of the WdW patch in CV duality. In particular, we check whether the Born–Infeld black holes violate the generalized Lloyd bound: $$\dot{\mathcal {C}}\le \frac{2}{\pi \hbar }\left[ \left( M-Q\Phi \right) -\left( M-Q\Phi \right) _{\text {gs}}\right] $$ C ˙ ≤ 2 π ħ M - Q Φ - M - Q Φ gs , where gs stands for the ground state for a given electrostatic potential. We find that the ground states are either some extremal black hole or regular spacetime with nonvanishing charges. For Born–Infeld black holes, we compute the action growth rate at the late-time limit and obtain the complexities in CA and CV dualities. Near extremality, the generalized Lloyd bound is violated in both dualities. Near the charged regular spacetime, this bound is satisfied in CV duality but violated in CA duality. When moving away from the ground state on a constant potential curve, the generalized Lloyd bound tends to be saturated from below in CA duality. |
| first_indexed | 2024-04-11T22:58:15Z |
| format | Article |
| id | doaj.art-2297374ff30c4e879a8c136d65bf51e7 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-04-11T22:58:15Z |
| publishDate | 2017-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-2297374ff30c4e879a8c136d65bf51e72022-12-22T03:58:18ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522017-12-01771211510.1140/epjc/s10052-017-5395-3Testing holographic conjectures of complexity with Born–Infeld black holesJun Tao0Peng Wang1Haitang Yang2Center for Theoretical Physics, College of Physical Science and Technology, Sichuan UniversityCenter for Theoretical Physics, College of Physical Science and Technology, Sichuan UniversityCenter for Theoretical Physics, College of Physical Science and Technology, Sichuan UniversityAbstract In this paper, we use Born–Infeld black holes to test two recent holographic conjectures of complexity, the “Complexity = Action” (CA) duality and “Complexity = Volume 2.0” (CV) duality. The complexity of a boundary state is identified with the action of the Wheeler–deWitt patch in CA duality, while this complexity is identified with the spacetime volume of the WdW patch in CV duality. In particular, we check whether the Born–Infeld black holes violate the generalized Lloyd bound: $$\dot{\mathcal {C}}\le \frac{2}{\pi \hbar }\left[ \left( M-Q\Phi \right) -\left( M-Q\Phi \right) _{\text {gs}}\right] $$ C ˙ ≤ 2 π ħ M - Q Φ - M - Q Φ gs , where gs stands for the ground state for a given electrostatic potential. We find that the ground states are either some extremal black hole or regular spacetime with nonvanishing charges. For Born–Infeld black holes, we compute the action growth rate at the late-time limit and obtain the complexities in CA and CV dualities. Near extremality, the generalized Lloyd bound is violated in both dualities. Near the charged regular spacetime, this bound is satisfied in CV duality but violated in CA duality. When moving away from the ground state on a constant potential curve, the generalized Lloyd bound tends to be saturated from below in CA duality.http://link.springer.com/article/10.1140/epjc/s10052-017-5395-3 |
| spellingShingle | Jun Tao Peng Wang Haitang Yang Testing holographic conjectures of complexity with Born–Infeld black holes European Physical Journal C: Particles and Fields |
| title | Testing holographic conjectures of complexity with Born–Infeld black holes |
| title_full | Testing holographic conjectures of complexity with Born–Infeld black holes |
| title_fullStr | Testing holographic conjectures of complexity with Born–Infeld black holes |
| title_full_unstemmed | Testing holographic conjectures of complexity with Born–Infeld black holes |
| title_short | Testing holographic conjectures of complexity with Born–Infeld black holes |
| title_sort | testing holographic conjectures of complexity with born infeld black holes |
| url | http://link.springer.com/article/10.1140/epjc/s10052-017-5395-3 |
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