We analyze the ghost issue in the recently proposed models of nonlinear massive gravity in the Arnowitt-Deser-Misner formalism. We show that, in the entire two-parameter family of actions, the ...Hamiltonian constraint is maintained at the complete nonlinear level and we argue for the existence of a nontrivial secondary constraint. This implies the absence of the pathological Boulware-Deser ghost to all orders. To our knowledge, this is the first demonstration of the existence of a consistent theory of massive gravity at the complete nonlinear level, in four dimensions.
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Generically, non-linear bimetric theories of gravity suffer from the same Boulware-Deser ghost instability as non-linear theories of massive gravity. However, recently proposed theories of ...massive gravity have been shown to be ghost-free. These theories are formulated with respect to a flat, non-dynamical reference metric. In this work we show that it is possible to give dynamics to the reference metric in such a way that the consistency of the theory is maintained. The result is a non-linear bimetric theory of a massless spin-2 field interacting with a massive spin-2 field that is free of the Boulware-Deser ghost. To our knowledge, this is the first construction of such a ghost-free bimetric theory.
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The ghost-free bimetric theory describes interactions of gravity with another spin-2 field in terms of two Lorentzian metrics. However, if the two metrics do not admit compatible notions of ...space and time, the formulation of the initial value problem becomes problematic. Furthermore, the interaction potential is given in terms of the square root of a matrix which is in general nonunique and possibly nonreal. In this paper we show that both these issues are evaded by requiring reality and general covariance of the equations. First we prove that the reality of the square root matrix leads to a classification of the allowed metrics in terms of the intersections of their null cones. Then, the requirement of general covariance further restricts the allowed metrics to geometries that admit compatible notions of space and time. It also selects a unique definition of the square root matrix. The restrictions are compatible with the equations of motion. These results ensure that the ghost-free bimetric theory can be defined unambiguously and that the two metrics always admit compatible 3+1 decompositions, at least locally. In particular, these considerations rule out certain solutions of massive gravity with locally Closed Causal Curves, which have been used to argue that the theory is acausal.
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In massive gravity and in bimetric theories of gravity, two constraints are needed to eliminate the two phase-space degrees of freedom of the Boulware-Deser ghost. For recently proposed ...non-linear theories, a Hamiltonian constraint has been shown to exist and an associated secondary constraint was argued to arise as well. In this paper we explicitly demonstrate the existence of the secondary constraint. Thus the Boulware-Deser ghost is completely absent from these non-linear massive gravity theories and from the corresponding bimetric theories. Equivalently, this proves the existence of classically ghost-free theories of massive spin-2 fields, in both fixed and dynamical gravitational backgrounds.
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We perform a canonical analysis of the bimetric theory in the metric formulation, computing the constraints and their algebra explicitly. In particular, we compute a secondary constraint, ...that has been argued to exist earlier, and show that it has the correct form to eliminate the ghost. We also identify a set of four first class constraints that generate the algebra of general covariance. The covariance algebra naturally determines a spacetime metric for the theory. However, in bimetric theory, this metric is not unique but depends on how the first class constraints are identified.
In this work we present a systematic construction of the potentially ghost-free non-linear massive gravity actions. The most general action can be regarded as a 2-parameter deformation of a minimal ...massive action. Further extensions vanish in 4 dimensions. The general mass term is constructed in terms of a “deformed” determinant from which this property can clearly be seen. In addition, our formulation identifies nondynamical terms that appear in previous constructions and which do not contribute to the equations of motion. We elaborate on the formal structure of these theories as well as some of their implications.
In the present study, magnesium based composites with three different volume percentages of nano-sized Al2O3 particulates reinforcement were fabricated using blend-press-sinter methodology avoiding ...ball milling. Microstructural characterization of the materials revealed reasonably uniform distribution of nano-size Al2O3 reinforcement and presence of minimal porosity. Mechanical properties characterization revealed that the presence of nano-Al2O3 particulates as reinforcement lead to a simultaneous increase in hardness, elastic modulus, 0.2% yield strength, UTS and ductility of pure magnesium. The results revealed that the 0.2% yield strength, UTS and ductility combination of the magnesium nano-composites containing 0.66 and 1.11 vol% of alumina remained higher when compared to high strength magnesium alloy AZ91 reinforced with much higher amount of micrometer size SiC particulates. An attempt is made in the present study to correlate the effect of presence of nano-Al2O3 as reinforcement and its increasing amount with the microstructural and mechanical properties of magnesium.
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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.
In this paper we investigate a particular ghost-free bimetric theory that exhibits the partially massless (PM) symmetry at quadratic order. At this order the global SO(1,4) symmetry of the theory is ...enhanced to SO(1,5). We show that this global symmetry becomes inconsistent at cubic order, in agreement with a previous calculation. Furthermore, we find that the PM symmetry of this theory cannot be extended beyond cubic order in the PM field. More importantly, it is shown that the PM symmetry cannot be extended to quartic order in any theory with one massless and one massive spin-2 fields.
Thus far, all known ghost-free interactions of multiple spin-2 fields have involved at most pairwise couplings of the fields, which are direct generalizations of bimetric interactions. We present a ...class of spin-2 theories with genuine multifield interactions and explicitly demonstrate the absence of ghost instabilities. The construction involves integrating out a nondynamical field in a theory of spin-2 fields with only pairwise ghost-free interactions. The new multivierbein interactions generated are not always expressible in terms of the associated metrics.
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