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# Particle motion near high-spin black holes

## Abstract

General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Surprisingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. Furthermore, we review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particle's polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.

- Authors:

- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
- Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature and Society of Fellows

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF)

- OSTI Identifier:
- 1596657

- Grant/Contract Number:
- [SC0009988]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Classical and Quantum Gravity

- Additional Journal Information:
- [ Journal Volume: 37; Journal Issue: 1]; Journal ID: ISSN 0264-9381

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; black hole; Kerr geodesics; NHEK

### Citation Formats

```
Kapec, Daniel, and Lupsasca, Alexandru. Particle motion near high-spin black holes. United States: N. p., 2019.
Web. doi:10.1088/1361-6382/ab519e.
```

```
Kapec, Daniel, & Lupsasca, Alexandru. Particle motion near high-spin black holes. United States. doi:10.1088/1361-6382/ab519e.
```

```
Kapec, Daniel, and Lupsasca, Alexandru. Tue .
"Particle motion near high-spin black holes". United States. doi:10.1088/1361-6382/ab519e.
```

```
@article{osti_1596657,
```

title = {Particle motion near high-spin black holes},

author = {Kapec, Daniel and Lupsasca, Alexandru},

abstractNote = {General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Surprisingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. Furthermore, we review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particle's polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.},

doi = {10.1088/1361-6382/ab519e},

journal = {Classical and Quantum Gravity},

number = [1],

volume = [37],

place = {United States},

year = {2019},

month = {12}

}

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