### Abstract

It is shown that the C-metric (with parameters chosen to lie in suitable intervals) admits a conformal completion such that the space of generators of null infinity, ℐ, is a 2-sphere. This structure of ℐ is both necessary and sufficient for the analysis of gravitational radiation in exact general relativity. Bondi news (as well as the electromagnetic radiation field, in the charget case) is examined and found to be non-zero. Thus the issue of existence of exact solutions to the Einstein (and Einstein-Maxwell) equations admitting radiation (in the sense of Bondi, Sachs, and Penrose) is resolved. In addition, the analysis clarifies the sense in which the vacuum C-metric represents the gravitational field of two accelerating black-holes.

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

Pages (from-to) | 581-599 |

Number of pages | 19 |

Journal | Communications In Mathematical Physics |

Volume | 79 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1981 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications In Mathematical Physics*,

*79*(4), 581-599. https://doi.org/10.1007/BF01209313

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*Communications In Mathematical Physics*, vol. 79, no. 4, pp. 581-599. https://doi.org/10.1007/BF01209313

**On the existence of solutions to Einstein's equation with non-zero Bondi news.** / Ashtekar, Abhay; Dray, Tevian.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the existence of solutions to Einstein's equation with non-zero Bondi news

AU - Ashtekar, Abhay

AU - Dray, Tevian

PY - 1981/12/1

Y1 - 1981/12/1

N2 - It is shown that the C-metric (with parameters chosen to lie in suitable intervals) admits a conformal completion such that the space of generators of null infinity, ℐ, is a 2-sphere. This structure of ℐ is both necessary and sufficient for the analysis of gravitational radiation in exact general relativity. Bondi news (as well as the electromagnetic radiation field, in the charget case) is examined and found to be non-zero. Thus the issue of existence of exact solutions to the Einstein (and Einstein-Maxwell) equations admitting radiation (in the sense of Bondi, Sachs, and Penrose) is resolved. In addition, the analysis clarifies the sense in which the vacuum C-metric represents the gravitational field of two accelerating black-holes.

AB - It is shown that the C-metric (with parameters chosen to lie in suitable intervals) admits a conformal completion such that the space of generators of null infinity, ℐ, is a 2-sphere. This structure of ℐ is both necessary and sufficient for the analysis of gravitational radiation in exact general relativity. Bondi news (as well as the electromagnetic radiation field, in the charget case) is examined and found to be non-zero. Thus the issue of existence of exact solutions to the Einstein (and Einstein-Maxwell) equations admitting radiation (in the sense of Bondi, Sachs, and Penrose) is resolved. In addition, the analysis clarifies the sense in which the vacuum C-metric represents the gravitational field of two accelerating black-holes.

UR - http://www.scopus.com/inward/record.url?scp=33646617708&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646617708&partnerID=8YFLogxK

U2 - 10.1007/BF01209313

DO - 10.1007/BF01209313

M3 - Article

AN - SCOPUS:33646617708

VL - 79

SP - 581

EP - 599

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 4

ER -