Extending the Barnes-Rivers operators to D = 3 topological gravity

Nunes, Fábio Carvalho; Pires, Gentil O.

doi:10.1016/0370-2693(93)91160-o

Cited by 16 publications

(13 citation statements)

References 8 publications

(8 reference statements)

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“…The treatment here follows [43]. In our conventions, a negative residue of the saturated propagator T µν ∆ µνρσ T * ρσ implies the presence of a ghost.…”

Section: A Appendix: Further Review Of the Ghost Problemmentioning

confidence: 99%

Ghost-free massive gravity with a general reference metric

Hassan

Rosen

Schmidt-May

2012

J. High Energ. Phys.

426

527

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Theories of massive gravity inevitably include an auxiliary reference metric. Generically, they also contain an inconsistency known as the Boulware-Deser ghost. Recently, a family of non-linear massive gravity actions, formulated with a flat reference metric, were proposed and shown to be ghost free at the complete non-linear level. In this paper we consider these non-linear massive gravity actions but now formulated with a general reference metric. We extend the proof of the absence of the Boulware-Deser ghost to this case. The analysis is carried out in the ADM formalism at the complete non-linear level. We show that in these models there always exists a Hamiltonian constraint which, with an associated secondary constraint, eliminates the ghost. This result considerably extends the range of known consistent non-linear massive gravity theories. In addition, these theories can also be used to describe a massive spin-2 field in an arbitrary, fixed gravitational background. We also discuss the positivity of the Hamiltonian.

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“…The treatment here follows [43]. In our conventions, a negative residue of the saturated propagator T µν ∆ µνρσ T * ρσ implies the presence of a ghost.…”

Section: A Appendix: Further Review Of the Ghost Problemmentioning

confidence: 99%

Ghost-free massive gravity with a general reference metric

Hassan

Rosen

Schmidt-May

2012

J. High Energ. Phys.

426

527

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“…Tree-level unitarity The general and clear way to address the unitarity problem in Lagrangian formalism can be summarized as follows (for more details, see [23][24][25][26][27]): (1) we calculate the propagator expanding the action to the second order in the graviton fluctuation, (2) we calculate the amplitude with general external energy tensor sources, and (3) we evaluate the residue at the poles. A general theory is well defined if "tachyons" and "ghosts" are absent, in which case the corresponding propagator has only first poles at k 2 − M 2 = 0 with real masses (no tachyons) and with positive residues (no ghosts).…”

Section: Appendix A: Theoretical Frameworkmentioning

confidence: 99%

Can static regular black holes form from gravitational collapse?

et al. 2015

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Starting from the Oppenheimer-Snyder model, we know how in classical general relativity the gravitational collapse of matter forms a black hole with a central spacetime singularity. It is widely believed that the singularity must be removed by quantum-gravity effects. Some static quantum-inspired singularity-free black hole solutions have been proposed in the literature, but when one considers simple examples of gravitational collapse the classical singularity is replaced by a bounce, after which the collapsing matter expands for ever. We may expect three possible explanations: (i) the static regular black hole solutions are not physical, in the sense that they cannot be realized in Nature, (ii) the final product of the collapse is not unique, but it depends on the initial conditions, or (iii) boundary effects play an important role and our simple models miss important physics. In the latter case, after proper adjustment, the bouncing solution would approach the static one. We argue that the "correct answer" may be related to the appearance of a ghost state in de Sitter spacetimes with super Planckian mass. Our black holes have indeed a de Sitter core and the ghost would make these configurations unstable. Therefore we believe that these black hole static solutions represent the transient phase of a gravitational collapse but never survive as asymptotic states.

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“…3) Ghost problem: It is well known [31,44,45] that a propagator for h µν with the tensor structure of ordinary massless gravity in 4-dimensions, is ghost free only for zero graviton masses. Thus the non-zero masses and the −2/3 factor in the s solution makes the tachyonic spin 0 mode also a ghost [28].…”

Section: Equation Of Motion and Solutionsmentioning

confidence: 99%

Brane induced gravity, its ghost and the cosmological constant problem

Hassan¹,

Hofmann²,

Strauss³

2011

J. Cosmol. Astropart. Phys.

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"Brane Induced Gravity" is regarded as a promising framework for addressing the cosmological constant problem, but it also suffers from a ghost instability for parameter values that make it phenomenologically viable. We carry out a detailed analysis of codimension > 2 models employing gauge invariant variables in a flat background approximation. It is argued that using instead a curved background sourced by the brane would not resolve the ghost issue, unless a very specific condition is satisfied (if satisfiable at all). As for other properties of the model, from an explicit analysis of the 4-dimensional graviton propagator we extract a mass, a decay width and a momentum dependent modification of the gravitational coupling for the spin 2 mode. In the flat space approximation, the mass of the problematic spin 0 ghost is instrumental in filtering out a brane cosmological constant. The mass replaces a background curvature that would have had the same function. The optical theorem is used to demonstrate the suppression of graviton leakage into the uncompactified bulk. Then, we derive the 4-dimensional effective action for gravity and show that general covariance is spontaneously broken by the bulk-brane setup. This provides a natural realization of the gravitational Higgs mechanism. We also show that the addition of extrinsic curvature dependent terms has no bearing on linearized brane gravity.

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Extending the Barnes-Rivers operators to D = 3 topological gravity

Cited by 16 publications

References 8 publications

Ghost-free massive gravity with a general reference metric

Ghost-free massive gravity with a general reference metric

Can static regular black holes form from gravitational collapse?

Brane induced gravity, its ghost and the cosmological constant problem

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