### Abstract

It is well known through the work of Majumdar, Papapetrou, Har- tle, and Hawking that the coupled Einstein and Maxwell equations admit a static multiple blackhole solution representing a balanced equilibrium state of finitely many point charges. This is a result of the exact cancellation of gravita- tional attraction and electric repulsion under an explicit condition on the mass and charge ratio. The resulting system of particles, known as an extremely charged dust, gives rise to examples of spacetimes with naked singularities. In this paper, we consider the continuous limit of the Majumdar-Papapetrou- Hartle-Hawking solution modeling a space occupied by an extended distribu- tion of extremely charged dust. We show that for a given smooth distribution of matter of finite ADM mass there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

Original language | English (US) |
---|---|

Pages (from-to) | 567-589 |

Number of pages | 23 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 28 |

Issue number | 2 |

DOIs | |

State | Published - Oct 2010 |

### Fingerprint

### Keywords

- ADM mass
- Asymptotic flatness
- Electrically charged perfect fluid
- Elliptic methods
- The Einstein equations
- The Maxwell equations

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis

### Cite this

**Charged cosmological dust solutions of the coupled einstein and maxwell equations.** / Spruck, Joel; Yang, Yisong.

Research output: Contribution to journal › Article

*Discrete and Continuous Dynamical Systems*, vol. 28, no. 2, pp. 567-589. https://doi.org/10.3934/dcds.2010.28.567

}

TY - JOUR

T1 - Charged cosmological dust solutions of the coupled einstein and maxwell equations

AU - Spruck, Joel

AU - Yang, Yisong

PY - 2010/10

Y1 - 2010/10

N2 - It is well known through the work of Majumdar, Papapetrou, Har- tle, and Hawking that the coupled Einstein and Maxwell equations admit a static multiple blackhole solution representing a balanced equilibrium state of finitely many point charges. This is a result of the exact cancellation of gravita- tional attraction and electric repulsion under an explicit condition on the mass and charge ratio. The resulting system of particles, known as an extremely charged dust, gives rise to examples of spacetimes with naked singularities. In this paper, we consider the continuous limit of the Majumdar-Papapetrou- Hartle-Hawking solution modeling a space occupied by an extended distribu- tion of extremely charged dust. We show that for a given smooth distribution of matter of finite ADM mass there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

AB - It is well known through the work of Majumdar, Papapetrou, Har- tle, and Hawking that the coupled Einstein and Maxwell equations admit a static multiple blackhole solution representing a balanced equilibrium state of finitely many point charges. This is a result of the exact cancellation of gravita- tional attraction and electric repulsion under an explicit condition on the mass and charge ratio. The resulting system of particles, known as an extremely charged dust, gives rise to examples of spacetimes with naked singularities. In this paper, we consider the continuous limit of the Majumdar-Papapetrou- Hartle-Hawking solution modeling a space occupied by an extended distribu- tion of extremely charged dust. We show that for a given smooth distribution of matter of finite ADM mass there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

KW - ADM mass

KW - Asymptotic flatness

KW - Electrically charged perfect fluid

KW - Elliptic methods

KW - The Einstein equations

KW - The Maxwell equations

UR - http://www.scopus.com/inward/record.url?scp=79954578067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954578067&partnerID=8YFLogxK

U2 - 10.3934/dcds.2010.28.567

DO - 10.3934/dcds.2010.28.567

M3 - Article

VL - 28

SP - 567

EP - 589

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 2

ER -