Cauchy constraints and particle content of fourth-order gravity in \(n\) dimensions. (English) Zbl 1033.83025
The full class of purely metrical gravitational theories in \(n\geq 3\) dimensions which follows from a Lagrangian composed of linear and quadratic curvature ters is analyzed. The type of the field equations is discussed in a suitable gauge. The principal symbol and the particle content of the linearized field equations are investigated. The space+time decomposition and the ADM formalism are used to derive the constraints and evolution equations for the variational derivative tensor.
However, the paper contains several errors for the case \(n=3\). Example 1: In the Corollary to Theorem 2.1., the phrase “iff \(n=4\)” has to be replaced by “iff \(n=3\) or \(n=4\)”, to get a valid statement.
Example 2: Theorem 3.8. is not valid for the case \(n=3\) due to the fact that in 3 dimensions, the Riemann tensor is a linear combination of products of the Ricci tensor with the metric. This leads to more restrictions to the particle content of the corresponding theory in 3 dimensions.
These inaccuracies do not prevent this paper to be a quite useful one, as for physical applications, the case \(n=3\) is excluded anyhow.
However, the paper contains several errors for the case \(n=3\). Example 1: In the Corollary to Theorem 2.1., the phrase “iff \(n=4\)” has to be replaced by “iff \(n=3\) or \(n=4\)”, to get a valid statement.
Example 2: Theorem 3.8. is not valid for the case \(n=3\) due to the fact that in 3 dimensions, the Riemann tensor is a linear combination of products of the Ricci tensor with the metric. This leads to more restrictions to the particle content of the corresponding theory in 3 dimensions.
These inaccuracies do not prevent this paper to be a quite useful one, as for physical applications, the case \(n=3\) is excluded anyhow.
Reviewer: Hans-Jürgen Schmidt (Potsdam)
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
Keywords:
purely metrical gravitational theories; Lagrangian; gauge; principal symbol; linearized field equations; variational derivative; Riemann tensor; Ricci tensorReferences:
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