Regular Article - Theoretical Physics
A class of higher-dimensional solutions of Einstein’s vacuum equation
Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco, 50740-560, Brazil
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Accepted: 12 December 2018
Published online: 7 January 2019
A new class of higher-dimensional exact solutions of Einstein’s vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to higher-dimensional generalizations of Kasner spacetime with a cosmological constant. On the other hand, the metrics attained when such matrix is non-diagonal have more intricate algebraic structures. In the same vein, we integrate Einstein’s equation for homogeneous spacetimes, but not necessarily isotropic, in the presence of a perfect fluid and attain exact solutions in terms of the exponential of a symmetric matrix. Such solutions have not been presented in the literature yet.
© The Author(s), 2019