# BPS Kerr-AdS time machines

## Abstract

It was recently observed that Kerr-AdS metrics with negative mass can describe smooth spacetimes that have a region within which naked closed time-like curves can arise, bounded by a velocity of light surface. Such spacetimes are sometimes known as time machines. In this paper we study the BPS limit of these metrics, and find that the mass and angular momenta become discretised. The completeness of the spacetime also requires that the asymptotic time coordinate be periodic, with precisely the same period as that which arises naturally for the global AdS, viewed as a hyperboliod in one extra dimension, in which the time machine spacetime is immersed. For the case of equal angular momenta in odd dimensions, we construct the Killing spinors explicitly, and show they are consistent with the global structure. Thus in examples where the solutions can be embedded in gauged supergravity, they will be supersymmetric. As a result, we also compare the global structure of the BPS AdS3 time machine with the BTZ black hole, and show that the global structure allows two different supersymmetric limits.

- Authors:

- Beijing Normal Univ., Beijing (China). Dept. of Physics; Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
- Beijing Normal Univ., Beijing (China). Dept. of Physics
- Tianjin Univ., Tianjin (China). Dept. of Physics
- Beijing Normal Univ., Beijing (China). Dept. of Physics; Texas A & M Univ., College Station, TX (United States). George P. & Cynthia Woods Mitchell Inst. for Fundamental Physics and Astronomy; Cambridge Univ., Cambridge (United Kingdom). Centre for Mathematical Sciences

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1501477

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

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Classical Theories of Gravity; Supersymmetry and Duality

### Citation Formats

```
Cvetič, M., Geng, Wei -Jian, Lü, H., and Pope, C. N. BPS Kerr-AdS time machines. United States: N. p., 2018.
Web. doi:10.1007/jhep07(2018)088.
```

```
Cvetič, M., Geng, Wei -Jian, Lü, H., & Pope, C. N. BPS Kerr-AdS time machines. United States. doi:10.1007/jhep07(2018)088.
```

```
Cvetič, M., Geng, Wei -Jian, Lü, H., and Pope, C. N. Thu .
"BPS Kerr-AdS time machines". United States. doi:10.1007/jhep07(2018)088. https://www.osti.gov/servlets/purl/1501477.
```

```
@article{osti_1501477,
```

title = {BPS Kerr-AdS time machines},

author = {Cvetič, M. and Geng, Wei -Jian and Lü, H. and Pope, C. N.},

abstractNote = {It was recently observed that Kerr-AdS metrics with negative mass can describe smooth spacetimes that have a region within which naked closed time-like curves can arise, bounded by a velocity of light surface. Such spacetimes are sometimes known as time machines. In this paper we study the BPS limit of these metrics, and find that the mass and angular momenta become discretised. The completeness of the spacetime also requires that the asymptotic time coordinate be periodic, with precisely the same period as that which arises naturally for the global AdS, viewed as a hyperboliod in one extra dimension, in which the time machine spacetime is immersed. For the case of equal angular momenta in odd dimensions, we construct the Killing spinors explicitly, and show they are consistent with the global structure. Thus in examples where the solutions can be embedded in gauged supergravity, they will be supersymmetric. As a result, we also compare the global structure of the BPS AdS3 time machine with the BTZ black hole, and show that the global structure allows two different supersymmetric limits.},

doi = {10.1007/jhep07(2018)088},

journal = {Journal of High Energy Physics (Online)},

number = 7,

volume = 2018,

place = {United States},

year = {2018},

month = {7}

}

Works referenced in this record:

##
Kaluza-Klein consistency, Killing vectors and Kähler spaces

journal, September 2000

- Hoxha, P.; Martinez-Acosta, R. R.; Pope, C. N.
- Classical and Quantum Gravity, Vol. 17, Issue 20

##
The general Kerr–de Sitter metrics in all dimensions

journal, January 2005

- Gibbons, G. W.; Lü, H.; Page, Don N.
- Journal of Geometry and Physics, Vol. 53, Issue 1

##
New Einstein-Sasaki Spaces in Five and Higher Dimensions

journal, August 2005

- Cvetič, M.; Lü, H.; Page, Don N.
- Physical Review Letters, Vol. 95, Issue 7

##
Black hole in three-dimensional spacetime

journal, September 1992

- Bañados, Máximo; Teitelboim, Claudio; Zanelli, Jorge
- Physical Review Letters, Vol. 69, Issue 13

##
Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

journal, September 1963

- Kerr, Roy P.
- Physical Review Letters, Vol. 11, Issue 5

##
The first law of thermodynamics for Kerr–anti-de Sitter black holes

journal, May 2005

- Gibbons, G. W.; Perry, M. J.; Pope, C. N.
- Classical and Quantum Gravity, Vol. 22, Issue 9

##
General (Anti-)de Sitter black holes in five dimensions

journal, February 2001

- Klemm, Dietmar; Sabra, Wafic A.
- Journal of High Energy Physics, Vol. 2001, Issue 02

##
Supersymmetry of the (2+1)-dimensional black holes

journal, January 1994

- Coussaert, Olivier; Henneaux, Marc
- Physical Review Letters, Vol. 72, Issue 2

##
New Einstein-Sasaki and Einstein spaces from Kerr-de Sitter

journal, July 2009

- Cvetic, M.; Lü, H.; Page, Don N.
- Journal of High Energy Physics, Vol. 2009, Issue 07

##
Rotation and the AdS-CFT correspondence

journal, February 1999

- Hawking, S. W.; Hunter, C. J.; Taylor-Robinson, M. M.
- Physical Review D, Vol. 59, Issue 6

##
D-branes and spinning black holes

journal, January 1997

- Breckenridge, J. C.; Myers, R. C.; Peet, A. W.
- Physics Letters B, Vol. 391, Issue 1-2

##
Banados and SUSY: on supersymmetry and minimal surfaces of locally AdS _{3} geometries

journal, April 2017

- Ó Colgáin, E.; Yavartanoo, H.
- Classical and Quantum Gravity, Vol. 34, Issue 9

##
Rotating Black Holes in Higher Dimensions with a Cosmological Constant

journal, October 2004

- Gibbons, G. W.; Lü, H.; Page, Don N.
- Physical Review Letters, Vol. 93, Issue 17

##
Sasaki-Einstein Metrics on S^2\times S^3

journal, January 2004

- Gauntlett, Jerome P.; Martelli, Dario; Sparks, James
- Advances in Theoretical and Mathematical Physics, Vol. 8, Issue 4

##
Spinning deformations of the D1–D5 system and a geometric resolution of closed timelike curves

journal, August 2003

- Herdeiro, Carlos A. R.
- Nuclear Physics B, Vol. 665

##
Supersymmetric Kerr–anti-de Sitter solutions

journal, July 2005

- Cvetič, Mirjam; Gao, Peng; Simón, Joan
- Physical Review D, Vol. 72, Issue 2

##
Black holes in higher dimensional space-times

journal, December 1986

- Myers, R. C.; Perry, M. J.
- Annals of Physics, Vol. 172, Issue 2

##
An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation

journal, July 1949

- Gödel, Kurt
- Reviews of Modern Physics, Vol. 21, Issue 3

##
Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations

journal, December 1968

- Carter, Brandon
- Communications in Mathematical Physics, Vol. 10, Issue 4

##
Special properties of five-dimensional BPS rotating black holes

journal, August 2000

- Herdeiro, C. A. R.
- Nuclear Physics B, Vol. 582, Issue 1-3

##
Supersymmetric rotating black hole spacetime tested by geodesics

journal, April 2014

- Diemer, Valeria; Kunz, Jutta
- Physical Review D, Vol. 89, Issue 8

##
Black holes of *D* = 5 supergravity

journal, January 1999

- Gauntlett, Jerome P.; Myers, Robert C.; Townsend, Paul K.
- Classical and Quantum Gravity, Vol. 16, Issue 1

##
Supersymmetric rotating black holes and causality violation

journal, October 1999

- Gibbons, G. W.; Herdeiro, C. A. R.
- Classical and Quantum Gravity, Vol. 16, Issue 11

##
Quantum Time Crystals

journal, October 2012

- Wilczek, Frank
- Physical Review Letters, Vol. 109, Issue 16

##
Charged rotating black holes in 5d Einstein–Maxwell–(A)dS gravity

journal, March 2001

- Klemm, D.; Sabra, W. A.
- Physics Letters B, Vol. 503, Issue 1-2