Abstract
We investigate how the complexity=anything observables proposed by [1, 2] can be used to investigate the interior geometry of AdS black holes. In particular, we illustrate how the flexibility of the complexity=anything approach allows us to systematically probe the geometric properties of black hole singularities. We contrast our results for the AdS Schwarzschild and AdS Reissner-Nordström geometries, i.e., for uncharged and charged black holes, respectively. In the latter case, the holographic complexity observables can only probe the interior up to the inner horizon.
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Acknowledgments
We are happy to thank Alex Belin, Aidan Herderschee, Ted Jacobson, Finn Larsen, Gabor Sarosi and Antony Speranza for fruitful discussions and useful comments. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. RCM is supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada, and by funding from the BMO Financial Group. RCM and SMR are supported by the Simons Foundation through the “It from Qubit” collaboration. SMR is also supported by MEXT-JSPS Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe”, No. 21H05187 and by JSPS KAKENHI Research Activity Start-up Grant Number JP22K20370.
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Jørstad, E., Myers, R.C. & Ruan, SM. Complexity=anything: singularity probes. J. High Energ. Phys. 2023, 223 (2023). https://doi.org/10.1007/JHEP07(2023)223
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DOI: https://doi.org/10.1007/JHEP07(2023)223