Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866916304258072576 |
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| author | Ahn, Yongjun Jahnke, Viktor Jeong, Hyun-Sik Kim, Keun-Young |
| author_facet | Ahn, Yongjun Jahnke, Viktor Jeong, Hyun-Sik Kim, Keun-Young |
| contents | We study the scrambling properties of $(d+1)$-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius $\ell$, which is dual to a $d-$dimensional conformal field theory (CFT) in hyperbolic space with temperature $T = 1/(2 π\ell)$. We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity $v_B(T)$ nicely interpolates between the Rindler-AdS result $v_B(T=\frac{1}{2π\ell})=\frac{1}{d-1}$ and the planar result $v_B(T \gg \frac{1}{\ell})=\sqrt{\frac{d}{2(d-1)}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_08030 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping Ahn, Yongjun Jahnke, Viktor Jeong, Hyun-Sik Kim, Keun-Young High Energy Physics - Theory We study the scrambling properties of $(d+1)$-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius $\ell$, which is dual to a $d-$dimensional conformal field theory (CFT) in hyperbolic space with temperature $T = 1/(2 π\ell)$. We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity $v_B(T)$ nicely interpolates between the Rindler-AdS result $v_B(T=\frac{1}{2π\ell})=\frac{1}{d-1}$ and the planar result $v_B(T \gg \frac{1}{\ell})=\sqrt{\frac{d}{2(d-1)}}$. |
| title | Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/1907.08030 |