# Generalized Couch-Torrence symmetry for rotating extremal black holes in maximal supergravity

## Abstract

The extremal Reissner-Nordström black hole admits a conformal inversion symmetry, in which the metric is mapped into itself under an inversion of the radial coordinate combined with a conformal rescaling. In the rotating generalization, Couch and Torrence showed that the Kerr-Newman metric no longer exhibits a conformal inversion symmetry, but the radial equation arising in the separation of the massless Klein-Gordon equation admits a mode-dependent inversion symmetry, where the radius of inversion depends upon the energy and azimuthal angular momentum of the mode.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Pennsylvania, Philadelphia, PA (United States); Texas A & M Univ., College Station, TX (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)

- OSTI Identifier:
- 1671155

- Alternate Identifier(s):
- OSTI ID: 1684629

- Grant/Contract Number:
- SC0013528; FG02-13ER42020; SC0010813

- Resource Type:
- Published Article

- Journal Name:
- Physical Review. D.

- Additional Journal Information:
- Journal Name: Physical Review. D. Journal Volume: 102 Journal Issue: 8; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Classical black holes; supergravity; supersymmetry; conformal symmetry

## Citation Formats

```
Cvetič, M., Pope, C. N., and Saha, A. Generalized Couch-Torrence symmetry for rotating extremal black holes in maximal supergravity. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.102.086007.
```

```
Cvetič, M., Pope, C. N., & Saha, A. Generalized Couch-Torrence symmetry for rotating extremal black holes in maximal supergravity. United States. https://doi.org/10.1103/PhysRevD.102.086007
```

```
Cvetič, M., Pope, C. N., and Saha, A. Thu .
"Generalized Couch-Torrence symmetry for rotating extremal black holes in maximal supergravity". United States. https://doi.org/10.1103/PhysRevD.102.086007.
```

```
@article{osti_1671155,
```

title = {Generalized Couch-Torrence symmetry for rotating extremal black holes in maximal supergravity},

author = {Cvetič, M. and Pope, C. N. and Saha, A.},

abstractNote = {The extremal Reissner-Nordström black hole admits a conformal inversion symmetry, in which the metric is mapped into itself under an inversion of the radial coordinate combined with a conformal rescaling. In the rotating generalization, Couch and Torrence showed that the Kerr-Newman metric no longer exhibits a conformal inversion symmetry, but the radial equation arising in the separation of the massless Klein-Gordon equation admits a mode-dependent inversion symmetry, where the radius of inversion depends upon the energy and azimuthal angular momentum of the mode.},

doi = {10.1103/PhysRevD.102.086007},

journal = {Physical Review. D.},

number = 8,

volume = 102,

place = {United States},

year = {2020},

month = {10}

}

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