Comments on (super)luminality

C. De Rham, Gregory Gabadadze, A. J. Tolley

    Research output: Contribution to journalArticle

    Abstract

    Recently, in an interesting work arXiv:1106.3972 a solution of the equations of motion of massive gravity was discussed, and it was shown that one of the fluctuations on that solution is superluminal. It was also stated that this rules out massive gravity. Here we find that the solution itself is rather unphysical. For this we show that there is another mode on the same background which grows and overcomes the background in an arbitrarily short period of time, that can be excited by a negligible cost in energy. This solution is triggered by the parameter governing the superluminality. Furthermore, we also show that the solution, if viewed as a perfect fluid, has no rest frame, or that the Lorentz transformation that is needed to boost to the rest frame is superluminal itself. The stress-tensor of this fluid has complex eigenvalues, and could not be obtained from any physically sensible matter. Moreover, for the same setup we find another background solution, fluctuations of which are all stable and subluminal. Based on these results, we conclude that the superluminality found in arXiv:1106.3972 is an artifact of using an inappropriate background, nevertheless, this solution represents an instructive example for understanding massive gravity. For instance, on this background the Boulware-Deser ghost is absent, even though this may naively appear not to be the case.
    Original languageUndefined
    Article number1107.0710
    JournalarXiv
    StatePublished - Jul 4 2011

    Keywords

    • hep-th

    Cite this

    De Rham, C., Gabadadze, G., & Tolley, A. J. (2011). Comments on (super)luminality. arXiv, [1107.0710].

    Comments on (super)luminality. / De Rham, C.; Gabadadze, Gregory; Tolley, A. J.

    In: arXiv, 04.07.2011.

    Research output: Contribution to journalArticle

    De Rham, C, Gabadadze, G & Tolley, AJ 2011, 'Comments on (super)luminality', arXiv.
    De Rham C, Gabadadze G, Tolley AJ. Comments on (super)luminality. arXiv. 2011 Jul 4. 1107.0710.
    De Rham, C. ; Gabadadze, Gregory ; Tolley, A. J. / Comments on (super)luminality. In: arXiv. 2011.
    @article{e6858e50abd841aeb332ad3fa1b32428,
    title = "Comments on (super)luminality",
    abstract = "Recently, in an interesting work arXiv:1106.3972 a solution of the equations of motion of massive gravity was discussed, and it was shown that one of the fluctuations on that solution is superluminal. It was also stated that this rules out massive gravity. Here we find that the solution itself is rather unphysical. For this we show that there is another mode on the same background which grows and overcomes the background in an arbitrarily short period of time, that can be excited by a negligible cost in energy. This solution is triggered by the parameter governing the superluminality. Furthermore, we also show that the solution, if viewed as a perfect fluid, has no rest frame, or that the Lorentz transformation that is needed to boost to the rest frame is superluminal itself. The stress-tensor of this fluid has complex eigenvalues, and could not be obtained from any physically sensible matter. Moreover, for the same setup we find another background solution, fluctuations of which are all stable and subluminal. Based on these results, we conclude that the superluminality found in arXiv:1106.3972 is an artifact of using an inappropriate background, nevertheless, this solution represents an instructive example for understanding massive gravity. For instance, on this background the Boulware-Deser ghost is absent, even though this may naively appear not to be the case.",
    keywords = "hep-th",
    author = "{De Rham}, C. and Gregory Gabadadze and Tolley, {A. J.}",
    note = "12 pages. v2: improved and expanded version: certain statements corrected, appendix added; the conclusion unchanged",
    year = "2011",
    month = "7",
    day = "4",
    language = "Undefined",
    journal = "arXiv",

    }

    TY - JOUR

    T1 - Comments on (super)luminality

    AU - De Rham, C.

    AU - Gabadadze, Gregory

    AU - Tolley, A. J.

    N1 - 12 pages. v2: improved and expanded version: certain statements corrected, appendix added; the conclusion unchanged

    PY - 2011/7/4

    Y1 - 2011/7/4

    N2 - Recently, in an interesting work arXiv:1106.3972 a solution of the equations of motion of massive gravity was discussed, and it was shown that one of the fluctuations on that solution is superluminal. It was also stated that this rules out massive gravity. Here we find that the solution itself is rather unphysical. For this we show that there is another mode on the same background which grows and overcomes the background in an arbitrarily short period of time, that can be excited by a negligible cost in energy. This solution is triggered by the parameter governing the superluminality. Furthermore, we also show that the solution, if viewed as a perfect fluid, has no rest frame, or that the Lorentz transformation that is needed to boost to the rest frame is superluminal itself. The stress-tensor of this fluid has complex eigenvalues, and could not be obtained from any physically sensible matter. Moreover, for the same setup we find another background solution, fluctuations of which are all stable and subluminal. Based on these results, we conclude that the superluminality found in arXiv:1106.3972 is an artifact of using an inappropriate background, nevertheless, this solution represents an instructive example for understanding massive gravity. For instance, on this background the Boulware-Deser ghost is absent, even though this may naively appear not to be the case.

    AB - Recently, in an interesting work arXiv:1106.3972 a solution of the equations of motion of massive gravity was discussed, and it was shown that one of the fluctuations on that solution is superluminal. It was also stated that this rules out massive gravity. Here we find that the solution itself is rather unphysical. For this we show that there is another mode on the same background which grows and overcomes the background in an arbitrarily short period of time, that can be excited by a negligible cost in energy. This solution is triggered by the parameter governing the superluminality. Furthermore, we also show that the solution, if viewed as a perfect fluid, has no rest frame, or that the Lorentz transformation that is needed to boost to the rest frame is superluminal itself. The stress-tensor of this fluid has complex eigenvalues, and could not be obtained from any physically sensible matter. Moreover, for the same setup we find another background solution, fluctuations of which are all stable and subluminal. Based on these results, we conclude that the superluminality found in arXiv:1106.3972 is an artifact of using an inappropriate background, nevertheless, this solution represents an instructive example for understanding massive gravity. For instance, on this background the Boulware-Deser ghost is absent, even though this may naively appear not to be the case.

    KW - hep-th

    M3 - Article

    JO - arXiv

    JF - arXiv

    M1 - 1107.0710

    ER -