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Poincar\'e invariance and asymptotic flatness in Shape Dynamics · Around

2012

Poincar\'e invariance and asymptotic flatness in Shape Dynamics

Gomes, Henrique

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Shape Dynamics is a theory of gravity that waives refoliation invariance in favor of spatial Weyl invariance.

It is a canonical theory, constructed from a Hamiltonian, 3+1 perspective.
One of the main deficits of Shape Dynamics is that its Hamiltonian is only implicitly constructed as a functional of the phase space variables.
In this paper, I write down the equations of motion for Shape Dynamics to show that over a curve in phase space representing a Minkowski spacetime, Shape Dynamics possesses Poincar\'e symmetry for appropriate boundary conditions.

Built on

J. W. York, Jr., “Role of conformal three geometry in the dynamics of gravitation,” Phys. Rev. Lett. 28
1972
Earlier work this paper cites.
T. Regge and C. Teitelboim “Role of Surface Integrals in the Hamiltonian Formulation of General relativity” Ann. of Phys. 88
1974
Earlier work this paper cites.
A. J. Hanson, T. Regge, and C. Teitelboim, “Constrained Hamiltonian Systems”. Academia Nazionale dei Lincei, Roma, 1976
1976
Earlier work this paper cites.

Similar

R. Beig and N. Ó Murchadha “The Poincaré Group as the Symmetry Group of Canonical General Relativity” Ann. of Phys. 174
1987
Cited alongside, same era.
M. Henneaux and C. Teitelboim, “Quantization of gauge systems” Princeton University Press, 1992
1992
Cited alongside, same era.
H. Gomes and T. Koslowski, “Frequently asked questions about Shape Dynamics” [arXiv:1211.5878 [gr-qc]]
Original
Cited in the paper.
H. Gomes, T. Koslowski, F. Mercati and S. Gryb, “The gravity/CFT correspondence” [arXiv:1209.4858 [gr-qc]]
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H. Gomes and T. Koslowski, “Symmetry Doubling in General relativity” [arXiv:1206.4823 [gr-qc]]
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Cited in the paper.
F. Mercati and S. Gryb, “2+1 gravity on the conformal sphere” [arXiv:1209.4858 [gr-qc]]
Original
Cited in the paper.
S. Carlip “Effective Conformal Descriptions of Black Hole Entropy” [arXiv:1107.2678 [gr-qc]]
Original
Cited in the paper.
E. Gourgoulhon “3+1 Formalism for general relativity” Lecture Notes in Physics 846, Springer
Cited in the paper.
H. Gomes, T. Koslowski “Coupling Shape Dynamics to Matter Gives Spacetime” arXiv:1110.3837 [gr-qc]
Original
Cited in the paper.
H. Gomes, “The Coupling of Shape Dynamics to Matter,” arXiv:1112.0374 [gr-qc]
Original
Cited in the paper.
J. Isenberg, “The waveless approximation to theories of gravity” [arXiv:0702113 [gr-qc]]
Cited in the paper.
M. Atiyah, I. Singer “The Index of Elliptic Operators: V” Annals of Math. Vol 93, No 1
Original
Cited in the paper.

Then

H. Gomes, S. Gryb and T. Koslowski, “Einstein gravity as a 3D conformally invariant theory,” Class. Quant. Grav. 28
Original
2011
Later among the works it cites.
H. Gomes and T. Koslowski, “The Link between General Relativity and Shape Dynamics,” Class. Quant. Grav. 29
Original
2012
Closest in time.

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