Translation invariant time-dependent solutions to massive gravity II

J. Mourad; D. A. Steer

doi:10.1088/1475-7516/2014/06/058

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arXiv · 1405.1862

Translation invariant time-dependent solutions to massive gravity II

J. Mourad·D. A. Steer

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Abstract

This paper is a sequel to arXiv:1310.6560 [hep-th] and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a $β_3$ term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the $β_1$ case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the $β_1$ case where time evolution is always well defined. We conclude that the $β_3$ mass term can be pathological and should be treated with care.

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J. Mourad, D. A. Steer. 2014-05-08. Translation invariant time-dependent solutions to massive gravity II. https://doi.org/10.1088/1475-7516%2F2014%2F06%2F058

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