Plebanski-like action for general relativity and anti-self-dual gravity

Celada, Mariano; González, Diego López; Montesinos, Merced

doi:10.1103/physrevd.93.104058

Cited by 6 publications

(19 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equations (5), (7), (8), and (9) are the Plebanski equations of motion for general relativity, which have been obtained from the set of equations (2a)-(2c) with a = 1 and b = 0. In other words, for these values of the parameters a and b, the action (1) describes general relativity with a nonvanishing cosmological constant given by Λ = −b.…”

Section: General Relativitymentioning

confidence: 99%

“…In order to describe general relativity with few variables and still have a BF -type action after integrating out some fields in the action, a slight modification of Plebanski's action was proposed in Ref. [8], showing that it led to the action principle introduced in Ref. [9] to describe general relativity as a BF theory with a potential term depending only on the B field.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Polynomial BF -type action for general relativity and anti-self-dual gravity

2018

Self Cite

View full text Add to dashboard Cite

We report a gravitational BF -type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the B field, only employs an additional Lagrange multiplier. The action depends on two parameters and remarkably is polynomial in the B field. For a particular choice of the involved parameters the action provides an alternative description of (complex) general relativity with a nonvanishing cosmological constant, whereas another choice corresponds to antiself-dual gravity. Generic values of the parameters produce "close neighbors" of general relativity, although there is a peculiar choice of the parameters that leads to a Hamiltonian theory with two scalar constraints. Given the nontrivial form of the resulting scalar constraint for these models, we consider a more general setting where the scalar constraint is replaced with an arbitrary analytic function of some fundamental variables and show that the Poisson algebra involving this constraint together with the Gauss and vector constraints of the Ashtekar formalism closes, thus generating an infinite family of gravitational models that propagate the same number of degrees of freedom as general relativity.

show abstract

Section: General Relativitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polynomial BF -type action for general relativity and anti-self-dual gravity

2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…It has already been described in [33] and cannot be obtained from the Plebanski action (see however [34] for a derivation from a more complicated Lagrangian):…”

Section: A4 Intermediate Actions Of the Type S[a B]mentioning

confidence: 99%

Pure connection formulation, twistors, and the chase for a twistor action for general relativity

Herfray

2017

Journal of Mathematical Physics

View full text Add to dashboard Cite

This paper establishes the relation between traditional results from (euclidean) twistor theory and chiral formulations of General Relativity (GR), especially the pure connection formulation. Starting from a SU (2)-connection only we show how to construct natural complex data on twistor space, mainly an almost Hermitian structure and a connection on some complex line bundle. Only when this almost Hermitian structure is integrable is the connection related to an anti-self-dual-Einstein metric and makes contact with the usual results. This leads to a new proof of the non-linear-graviton theorem. Finally we discuss what new strategies this 'connection approach' to twistors suggests for constructing a twistor action for gravity. In appendix we also review all known chiral Lagrangians for GR.

show abstract

“…For that reason, the solutions of BF theory using the equation δS/δω = 0 are searched for. In general, the equations of motion of constrained BF theory including matter give a relation between the curvature F I J (ω) and the frame fields Σ I J = e I ∧ e J (the Plebanski 2-form), in matrix notation, that is F = χΣ + ξ Σ, where the bar indicates anti-frame field, and χ, ξ are symmetric matrices of scalar fields [4]. Therefore, the problem turns to finding χ and ξ.…”

Section: Introductionmentioning

confidence: 99%

Spin Current in BF Theory

Almatwi

2021

Physics

View full text Add to dashboard Cite

In this paper, a current that is called spin current and corresponds to the variation of the matter action in BF theory with respect to the spin connection A which takes values in Lie algebra so(3,C), in self-dual formalism is introduced. For keeping the 2-form Bi constraint (covariant derivation) DBi=0 satisfied, it is suggested adding a new term to the BF Lagrangian using a new field ψi, which can be used for calculating the spin current. The equations of motion are derived and the solutions are dicussed. It is shown that the solutions of the equations do not require a specific metric on the 4-manifold M, and one just needs to know the symmetry of the system and the information about the spin current. Finally, the solutions for spherically and cylindrically symmetric systems are found.

show abstract

Plebanski-like action for general relativity and anti-self-dual gravity

Cited by 6 publications

References 22 publications

Polynomial BF -type action for general relativity and anti-self-dual gravity

Polynomial BF -type action for general relativity and anti-self-dual gravity

Pure connection formulation, twistors, and the chase for a twistor action for general relativity

Spin Current in BF Theory

Contact Info

Product

Resources

About