# Inequivalence of first- and second-order formulations in D=2 gravity models

@article{Deser1996InequivalenceOF, title={Inequivalence of first- and second-order formulations in D=2 gravity models}, author={Stanley Deser}, journal={Foundations of Physics}, year={1996}, volume={26}, pages={617-621} }

The usual equivalence between the Palalini and metric (or affinity and vielbein) formulations of Einstein theory fails in two spacetime dimensions for its “Kaluza-Klein” reduced (as well as for its standard) version. Among the differences is the necessary vanishing of the cosmological constant in the first-order forms. The purely affine Eddington formulation of Einstein theory also fails here.

## 12 Citations

(Non-)Uniqueness of Einstein–Palatini Gravity

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We analyse the most general connection allowed by Einstein-Hilbert theory in Palatini formalism. We also consider a matter lagrangian independent of the affine connection. We show that any solution…

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The solutions of two-dimensional gravityfollowing from a non-linear Lagrangian ℒ =f(R)□g are classified, and their symmetry andsingularity properties are described. Then a conformaltransformation is…

Universality of the Einstein equations for Ricci squared Lagrangians

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It has been shown recently that, in the first-order (Palatini) formalism, there is universality of the Einstein equations and the Komar energy-momentum complex, in the sense that for a generic…

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Recently Kiriushcheva and Kuzmin1 claimed to have shown that the Einstein–Hilbert Lagrangian density cannot be written in any coordinate gauge as an exact differential in a two-dimensional spacetime.…

VARIATIONAL STRUCTURES AND COSMOLOGICAL DYNAMICS IN HIGHER ORDER GRAVITY

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In the first part of this thesis we analyse the variational structure of arbitrary nonlinear Langrangian theories of gravity. After a critique on the traditional Palatini variation we exploit the…

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- Mathematics
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We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature…

Would two dimensions be world enough for spacetime?

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Comments on “ The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential ”

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Recently Kiriushcheva and Kuzmin [1] claimed to have shown that the Einstein-Hilbert Lagrangian density cannot be written in any coordinate gauge as an exact differential in a 2-dimensional…

Geometric Structures Modeled on Affine Hypersurfaces and Generalizations of the Einstein–Weyl and Affine Sphere Equations

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Affine hypersurface structures (AH structures) simultaneously generalize Weyl structures and abstract geometric structures induced on a nondegenerate co-oriented hypersurface in flat affine space.…

Constructing Quantum Mechanics from a Clifford substructure of the relativistic point particle

- Physics, Mathematics
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We show that the quantized free relativistic point particle can be understood as a string in a Clifford space which generates the space-time coordinates through its inner product. The generating…

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