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PreprintarXiv licencearXiv

A new toric ALF gravitational instanton

  • Alfie Jones
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Abstract

We construct a new explicit toric ALF gravitational instanton. The instanton has Euler characteristic χ= 4 and Hirzebruch signature τ= 1. The topology at infinity is a lens space L(3,1). The solution depends on one parameter and is constructed from the Belinski--Zakharov four-soliton solution. We prove that the instanton is smooth and positive definite on and away from the axis. This is the first example of a non-Hermitian ALF (not AF) gravitational instanton.

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Cite

BibTeXRIS
BibTeX
@misc{jones2026toric,
  title = {{A new toric ALF gravitational instanton}},
  author = {Alfie Jones},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03221},
  eprint = {2611.03221},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03221},
}
RIS
TY  - UNPB
TI  - A new toric ALF gravitational instanton
AU  - Alfie Jones
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03221
UR  - https://arxiv.org/abs/2611.03221
AB  - We construct a new explicit toric ALF gravitational instanton. The instanton has Euler characteristic χ= 4 and Hirzebruch signature τ= 1. The topology at infinity is a lens space L(3,1). The solution depends on one parameter and is constructed from the Belinski--Zakharov four-soliton solution. We prove that the instanton is smooth and positive definite on and away from the axis. This is the first example of a non-Hermitian ALF (not AF) gravitational instanton.
ER  -