Erratum: Zwei-Dreibein Gravity: A Two-Frame-Field Model of 3D Massive Gravity [Phys. Rev. Lett. 111, 111102 (2013)]

Bergshoeff, Eric; Haan, Sjoerd de; Hohm, Olaf; Merbis, Wout; Townsend, Paul

doi:10.1103/physrevlett.111.259902

Cited by 28 publications

(46 citation statements)

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“…This branch will carry less degrees of freedom. The Boulware-Deser mode in Zwei-Dreiben gravity, as discussed in [4], was killed in this way, as we will argue. However there exists other branches (in fact more generic) where this mode is present.…”

Section: Second Class Constraints: Ifmentioning

confidence: 93%

“…For example, the proportional ansatz [4] ℓ a = αe a yields solutions with rank=4, while the family of solutions (20) and (21) have the maximum rank=6. The maximum rank is 6 because the action (1) has 6 gauge symmetries and twelve constraints.…”

Section: Second Class Constraints: Ifmentioning

confidence: 99%

“…The action is built using vielbeins 1-forms and their corresponding 2-forms curvatures. A three dimensional version of this formulation, which can shed light on the four dimensional one, has recently been considered in [4]. The action is…”

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confidence: 99%

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The Boulware-Deser mode in 3D first-order massive gravity

2013

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Massive gravity in three dimensions accepts several different formulations. Recently, the 3-dimensional bigravity dRGT model in first order form, Zwei-Dreibein gravity, was considered by Bergshoeff et al. and it was argued that the Boulware-Deser mode is killed by extra constraints. We revisit this assertion and conclude that there are sectors on the space of initial conditions, or subsets of the most general such model, where this mode is absent. But, generically, the theory does carry 3 degrees of freedom and thus the Boulware-Deser mode is still active. Our results also sheds light on the equivalence between metric and vierbein formulations of dRGT model.The search for a well-defined, unitary, stable, massive version of general relativity has seen huge interest in recent years (for a review see [17] A particularly simple and nice formulation of dRGT gravity was put forward in [18] (see also [11,12] for a discussion on the equivalence between metric and vielbein formulations). The action is built using vielbeins 1-forms and their corresponding 2-forms curvatures. A three dimensional version of this formulation, which can shed light on the four dimensional one, has recently been considered in [4]. The action iswhereê a andl a are two independent dreibeins. Here and henceforth wedge product are implicit. The connections are denoted byŵ a andπ a with curvatureŝAll hatted quantities are spacetime forms. The corresponding spatial forms will be denoted by the same letter without the hat. Latin indexes are raised and lowered with Minkowski metric η ab and η ab . For simplicity we do not incorporate cosmological constants at each sector. k 1 and k 2 are free parameters. It was argued in [4] that (1) does not carry a BoulwareDeser mode, in agreement with the 4-dimensional claims (mostly based on the metric formulation, see however [1,12,18]). The goal of this Letter is to critically analyze this issue. Our conclusion will be that the BoulwareDeser mode is generically still active in the formulation (1) even though there are indeed subcases where it is absent.The simplicity of working in three dimensions is seen by the fact that the action (1) is already in Hamiltonian form. One only needs to perform a 2+1 decomposition of forms,êand likewise forŵ a µ dx µ ,π a µ dx µ . The action in the 2+1 decomposition becomeswhere one can read the symplectic structure in a straightforward way. Here 'dot' stands for time derivative andNote that we still use form notation on the 2-dimensional spatial manifold. The spatial fields {e a i , w b j } and {ℓ a i , π b j } form 12 canonical pairs, while the temporal components e a 0 , ℓ a 0 , w a 0 , π a 0 are 12 Lagrange multipliers. This property is characteristic of generally covariant systems and, as we shall remark below, has important consequences on the consistency algorithm. Let us do a first counting of degrees of freedom based on the number of canonical variables and constraints (we shall argue below that there are no secondary constraints in the most generic case). There are 24 ca...

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Section: Second Class Constraints: Ifmentioning

confidence: 93%

Section: Second Class Constraints: Ifmentioning

confidence: 99%

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The Boulware-Deser mode in 3D first-order massive gravity

2013

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“…It is closely related to a problem that the asymptotic Ad S 3 black hole solution have negative mass value whenever the bulk graviton modes have posi-tive energy, so-called "bulk vs. boundary clash". In order to circumvent this inconsistency there were some suggestions like the Boulware-Deser ghost [26], "Zwei Dreibein Gravity (ZDG)" as a viable alternative to NMG [27,28]. Recently the new "minimal massive gravity (MMG)" theory has been suggested to resolve this inconsistency and to represent an alternative to TMG [29].…”

Section: Introductionmentioning

confidence: 99%

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

Nam

Park

2018

Eur. Phys. J. C

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We apply the Wald formalism to obtain masses and angular momenta of black holes in three dimensional gravity theories using the first order formalism. Wald formalism suggests that the entropy of a black hole can be defined by an integration of a conserved charge on the bifurcation horizon, and mass and angular momentum of a black hole as an integration of some charge variation form at spatial infinity. The action of three dimensional gravity theories can be represented by a form including some auxiliary fields. As well-known examples we have calculated masses and angular momenta of some black holes in topologically massive gravity and new massive gravity theories using the first order formalism. We have also calculated mass and angular momentum of BTZ black hole and new type black hole in minimal massive gravity theory with the action represented by the first order formalism. We have also calculated the entropy and central charges of new type black hole. According to Ad S/C FT correspondence we suggest that the left and right moving temperatures should be equal to the Hawking temperature in the case of new type black hole in minimal massive gravity.

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“…A model of the Zwei-Dreibein gravity has been proposed in a very recent paper [6]. The presence or absence of the Boulware-Deser mode in the model has been reanalyzed in [7]; the Hamiltonian analysis shows in general the existence of sectors, and, in each sector, the system has different number of degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Dynamical sectors of a relativistic two particle model

et al. 2014

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We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.

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Erratum: Zwei-Dreibein Gravity: A Two-Frame-Field Model of 3D Massive Gravity [Phys. Rev. Lett. 111, 111102 (2013)]

Cited by 28 publications

References 1 publication

The Boulware-Deser mode in 3D first-order massive gravity

The Boulware-Deser mode in 3D first-order massive gravity

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

Dynamical sectors of a relativistic two particle model

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