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1963
Earlier work this paper cites.
H. Lü and C.N. Pope, Critical gravity in four dimensions,
Original
1971
Earlier work this paper cites.
R.J. Riegert, Birkhoff’s theorem in conformal gravity,
1984
Earlier work this paper cites.
H.-J. Schmidt, Nontrivial solutions of the Bach equation exist,
1984
Earlier work this paper cites.
P.D. Mannheim and D. Kazanas, Solutions to the Kerr and Kerr-Newman problems in fourth order conformal Weyl gravity,
1991
Earlier work this paper cites.
P. Nurowski and J. F. Plebanski, Class. Quant. Grav. 18
2001
Earlier work this paper cites.
F. Bastianelli, G. Cuoghi and L. Nocetti, Consistency conditions and trace anomalies in six-dimensions,
2001
Earlier work this paper cites.

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2013

Not Conformally-Einstein Metrics in Conformal Gravity

Liu, Hai-Shan, Lu, H., Pope, C. N. et al.

Understand

The equations of motion of four-dimensional conformal gravity, whose Lagrangian is the square of the Weyl tensor, require that the Bach tensor $E_{\mu\nu}= (\nabla^\rho\nabla^\sigma + \ft12 R^{\rho\sigma})C_{\mu\rho\nu\sigma}$ vanishes.

Since $E_{\mu\nu}$ is zero for any Einstein metric, and any conformal scaling of such a metric, it follows that large classes of solutions in four-dimensional conformal gravity are simply given by metrics that are conformal to Einstein metrics (including Ricci-flat).
In fact it becomes more intriguing to find solutions that are {\it not} conformally Einstein.
We obtain five new such vacua, which are homogeneous and have asymptotic generalized Lifshitz anisotropic scaling symmetry.

Built on

V.R. Kaigorodov, Einstein spaces of maximum mobility
1963
Earlier work this paper cites.
H. Lü and C.N. Pope, Critical gravity in four dimensions,
Original
1971
Earlier work this paper cites.
R.J. Riegert, Birkhoff’s theorem in conformal gravity,
1984
Earlier work this paper cites.
H.-J. Schmidt, Nontrivial solutions of the Bach equation exist,
1984
Earlier work this paper cites.
P.D. Mannheim and D. Kazanas, Solutions to the Kerr and Kerr-Newman problems in fourth order conformal Weyl gravity,
1991
Earlier work this paper cites.
P. Nurowski and J. F. Plebanski, Class. Quant. Grav. 18
2001
Earlier work this paper cites.
F. Bastianelli, G. Cuoghi and L. Nocetti, Consistency conditions and trace anomalies in six-dimensions,
2001
Earlier work this paper cites.