Unusual square roots in the ghost-free theory of massive gravity

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Regular Article - Theoretical Physics
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Abstract

A crucial building block of the ghost free massive gravity is the square root function of a matrix. This is a problematic entity from the viewpoint of existence and uniqueness properties. We accurately describe the freedom of choosing a square root of a (non-degenerate) matrix. It has discrete and (in special cases) continuous parts. When continuous freedom is present, the usual perturbation theory in terms of matrices can be critically ill defined for some choices of the square root. We consider the new formulation of massive and bimetric gravity which deals directly with eigenvalues (in disguise of elementary symmetric polynomials) instead of matrices. It allows for a meaningful discussion of perturbation theory in such cases, even though certain non-analytic features arise.

Keywords

Classical Theories of Gravity Space-Time Symmetries Spacetime Singularities 

Notes

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Faculty of PhysicsSt. Petersburg State UniversitySaint PetersburgRussia
  2. 2.St. Petersburg National Research University of Information Technologies, Mechanics and OpticsSaint PetersburgRussia

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