期刊
CLASSICAL AND QUANTUM GRAVITY
卷 38, 期 7, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1361-6382/abdf28
关键词
modified gravity; ghost-free bimetric theory; geometric mean; 3+1 decomposition
The article introduces the use of geometric mean to parametrize metrics in the Hassan-Rosen ghost-free bimetric theory and solves the initial-value problem. The parametrization based on geometric mean metric ensures the reality of the square root in the ghost-free bimetric interaction potential. It also mentions the standard n + 1 decomposition derived in a frame adapted to the geometric mean.
We use the geometric mean to parametrize metrics in the Hassan-Rosen ghost-free bimetric theory and pose the initial-value problem. The geometric mean of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended to quadratic forms having the Lorentzian signature, say metrics g and f. In such a case, the null cone of the geometric mean metric h is in the middle of the null cones of g and f appearing as a geometric average of a bimetric spacetime. The parametrization based on h ensures the reality of the square root in the ghost-free bimetric interaction potential. Subsequently, we derive the standard n + 1 decomposition in a frame adapted to the geometric mean and state the initial-value problem, that is, the evolution equations, the constraints, and the preservation of the constraints equation.
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