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VOL. 85 | 2020 Harmonic maps and the Einstein equation
Sumio Yamada

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

In 1917, very shortly after Einstein had announced his master equation on the general relativity and Schwarzschild had discovered the first explicit solution to the equation, H. Weyl characterized the Schwarzschild metric, by a harmonic function. Since then, the solutions to the Einstein equation with a certain set of symmetries are identified with elliptic variational problems, in particular the harmonic map equation. In collaboration with Marcus Khuri, Yukio Matsumoto and Gilbert Weinstein, we constructed a new set of stationary solutions to the 5-dimensional vacuum Einstein equation, which contains non-spherical event horizons. The higher dimensional spacetime exhibit a wider range of topological structures, compared to our 4-dimensional physical spacetime, and those stationary solutions are thus geometrically interesting.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510525

Subjects:
Primary: 83C05
Secondary: 35Q76, 53C43

Rights: Copyright © 2020 Mathematical Society of Japan

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