A five-parameter class of solutions to the vacuum Einstein equations

• Main Authors: Chen, Yu, Teo, Edward
• Format: Text
• Language: unknown
• Published: arXiv 2015
• Subjects: General Relativity and Quantum Cosmology gr-qc; FOS Physical sciences; South Pole; North Pole; Kerr; Alf; South pole
• Online Access: https://dx.doi.org/10.48550/arxiv.1504.01235; https://arxiv.org/abs/1504.01235

We present a new five-parameter class of Ricci-flat solutions in four dimensions with Euclidean signature. The solution is asymptotically locally flat (ALF), and contains a finite asymptotic NUT charge. When this charge is sent to infinity, the solution becomes asymptotically locally Euclidean (ALE), and one in fact obtains the Ricci-flat Plebanski-Demianski solution. The solution we have found can thus be regarded as an ALF generalisation of the latter solution. We also show that it can be interpreted as a system consisting of two touching Kerr-NUTs: the south pole of one Kerr-NUT touches the north pole of the other. The total NUT charge of such a system is then identified with the asymptotic NUT charge. Setting the asymptotic NUT charge to zero gives a four-parameter asymptotically flat (AF) solution, and contained within this subclass is the completely regular two-parameter AF instanton previously discovered by the present authors. Various other limits are also discussed, including that of the triple-collinearly-centered Gibbons-Hawking solution, and an ALF generalisation of the C-metric. : 33 pages, 4 figures, LaTeX