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Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions · Around

2010

Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions

Yale, Alexandre, Padmanabhan, T.

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The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order.

The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor.
The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language.
While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$.

Built on

C. Lanczos, Z. Phys. A73
1971
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T. Eguchi, P. B. Gilkey and A. J. Hanson, Phys. Rep. 66
1980
Earlier work this paper cites.
R. C. Myers, Phys. Rev. D. 36
1987
Earlier work this paper cites.
M. Nakahara, Geometry, Topology and Physics
Original
1990
Earlier work this paper cites.
S. Deser and R. Jackiw, Int. J. Mod. Phys. B10
1996
Earlier work this paper cites.

Similar

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A. Bidal (2008) [arXiv:0802.0634]
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Efstratios Tsantilis, Roland A. Puntigam, Friedrich W. Hehl, A quadratic curvature Lagrangian of Pawłowski and Rcaczka: a finger exercise with MathTensor
Cited in the paper.
This curious result was first pointed out to one of us (T.P) by Dawood Kothawala and Kinjal Banerjee
Cited in the paper.

Then

D. Kothawala and T. Padmanabhan, Phys. Rev. D 79
Original
2009
Later among the works it cites.
T. Padmanabhan, Rep. Prog. Phys. 73
Original
2010
Closest in time.
T.Padmanabhan, (2010) Gravitation: Foundations and Frontiers
2010
Closest in time.
T. Padmanabhan and Aseem Paranjape, Phys. Rev. D75
Original
2010
Closest in time.
S. Kolekar and T. Padmanabhan Phys.Rev., D 82
Original
2010
Closest in time.

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