Spin connection formulations of real Lorentzian general relativity

Mitsou, Ermis

doi:10.1088/1361-6382/ab00b1

Cited by 8 publications

(21 citation statements)

References 58 publications

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“…In addition, another interesting technical thing of BF theories is that they can be seen as intermediate formulations of GR, that further allow for the integration of the Lagrange multipliers and even the B field, to finally get a pure connection formulation of GR [46]. These are very special actions for GR whose applications have not been fully explored yet (see recent advances in [57]). In contrast with the BF, that are first order formulations, this pure connection is a second order formulation, as the metric one, and that spoils the simplicity of the formula for surface charge.…”

Section: Bf Actionmentioning

confidence: 99%

Surface charges toolkit for gravity

Frodden¹,

Hidalgo

2020

Int. J. Mod. Phys. D

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These notes provide a detailed catalog of surface charge formulas for different classes of gravity theories. The present catalog reviews and extends the existing literature on the topic. Part of the focus is on reviewing the method to compute quasi-local surface charges for gauge theories in order to clarify conceptual issues and their range of applicability. Many surface charge formulas for gravity theories are expressed in metric, tetrads-connection, Chern-Simons connection, and even BF variables. For most of them the language of differential forms is exploited and contrasted with the more popular metric components language. The gravity theory is coupled with matter fields as scalar, Maxwell, Skyrme, Yang-Mills, and spinors. Furthermore, three examples with ready-to-download notebook codes, show the method in full action. Several new results are highlighted through the notes.

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Section: Bf Actionmentioning

confidence: 99%

Surface charges toolkit for gravity

Frodden¹,

Hidalgo

2020

Int. J. Mod. Phys. D

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“…We now specialise to the case of Lorentz group G = SO (1,3). The condition (1.5) implies that f is not polynomial in X, except for the topological case f (X) = Tr [zX].…”

Section: Vacuum Solution and Linearized Theorymentioning

confidence: 99%

“…Rather, the case of GR is the restriction from four to two independent parameters M 2 /C and β, i.e. including the overall normalization, [1,35,36]…”

Section: Vacuum Solution and Linearized Theorymentioning

confidence: 99%

“…These are the theories for which (5.2) does not fully determine M , thus turning part of the equations (5.2) into phase space constraints. There are several possibilities for partially determining M , because the tensor M abcd is reducible under the local SO (1,3) symmetry. As we will see, the case of GR corresponds to a completely undetermined M .…”

Section: Extra Primary Constraintsmentioning

confidence: 99%

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Pure Lorentz spin connection theories and uniqueness of General Relativity

Krasnov,

Mitsou

2021

Preprint

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General Relativity can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type f (F ∧ F ), where F is the curvature 2-form of the spin connection. A theory from this class with a generic f is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. General Relativity in this formalism avoids extra degrees of freedom because the function f is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories of the type f (F ∧F ) that lead to six extra primary constraints. However, only in the case of GR the dynamics is such that these six primary constraints get supplemented by six secondary constraints, which gives the end result of two propagating degrees of freedom. This is how uniqueness of GR manifests itself in this "pure spin connection" formalism. The other theories we discover are shown to give examples of irregular dynamical systems. At the linear level around (anti-)de Sitter space they have two degrees of freedom, as General Relativity, with the extra ones manifesting themselves only non-linearly.

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“…As for the parameters, M := (8πG) −1/2 is the reduced Planck mass, Λ is the cosmological constant and β −1 is the Immirzi parameter. 1 In (1.1) we make a slight abuse of notation by considering functions of 1 The trace of a matrix square root still has the cyclic property if these matrices are invertible [1], which is the case in (1.1) for real β, so one can also express the function entering the trace as √ z 2 X.…”

Section: Introductionmentioning

confidence: 99%

Pure Lorentz spin connection theories and uniqueness of general relativity

Krasnov¹,

Mitsou²

2021

Class. Quantum Grav.

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General relativity (GR) can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type f(F F), where F is the curvature two-form of the spin connection. A theory from this class with a generic f is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. GR in this formalism avoids extra degrees of freedom because the function f is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories of the type f(F F) that lead to six extra primary constraints. However, only in the case of GR the dynamics is such that these six primary constraints get supplemented by six secondary constraints, which gives the end result of two propagating degrees of freedom. This is how uniqueness of GR manifests itself in this 'pure spin connection' formalism. The other theories we discover are shown to give examples of irregular dynamical systems. At the linear level around (anti-)de Sitter space they have two degrees of freedom, as GR, with the extra ones manifesting themselves only non-linearly.

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Spin connection formulations of real Lorentzian general relativity

Cited by 8 publications

References 58 publications

Surface charges toolkit for gravity

Surface charges toolkit for gravity

Pure Lorentz spin connection theories and uniqueness of General Relativity

Pure Lorentz spin connection theories and uniqueness of general relativity

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