The authors discuss the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity. This is achieved by reduction to a second-order theory using an appropriate Legendre transformation. The starting point of the discussion is a Lagrangian which depends quadratically on the Ricci tensor of the metric. The authors explore the two possible second-order pictures known as the "Helmholtz-Jordan frame" and the "Einstein frame". The authors show that the theory based on the quadratic Lagrangian admits a unique and linearly stable ground state solution. They also demonstrate that the equations of motion are consistent by showing that the results presented can be obtained independently in either frame. The full field equations and the energy-momentum tensor for the spin-2 field in the Einstein frame are presented. The authors also discuss a specific solution to the corresponding field equations. The authors point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. From this they argue that the ghost-like nature of the nonlinear spin-2 field may not be as "harmful" to classical stability issues as is usually expected.
Nonlinear massive spin-two field generated by higher derivative gravity
MAGNANO, Guido;
2003-01-01
Abstract
The authors discuss the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity. This is achieved by reduction to a second-order theory using an appropriate Legendre transformation. The starting point of the discussion is a Lagrangian which depends quadratically on the Ricci tensor of the metric. The authors explore the two possible second-order pictures known as the "Helmholtz-Jordan frame" and the "Einstein frame". The authors show that the theory based on the quadratic Lagrangian admits a unique and linearly stable ground state solution. They also demonstrate that the equations of motion are consistent by showing that the results presented can be obtained independently in either frame. The full field equations and the energy-momentum tensor for the spin-2 field in the Einstein frame are presented. The authors also discuss a specific solution to the corresponding field equations. The authors point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. From this they argue that the ghost-like nature of the nonlinear spin-2 field may not be as "harmful" to classical stability issues as is usually expected.
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