1203.3301 (Kyosuke Hirochi et al.)

Critical gravity with a scalar field in four dimensions    [PDF]

Kyosuke Hirochi, Shin'ichi Nojiri

We consider the critical gravity theory with a scalar field in four dimensions. We find that this theory has the solution corresponding to the de Sitter (dS), anti-de Sitter (AdS), and Minkowski background depending on whether the action includes the cosmological term or not. The Minkowski background is the solution which cannot be obtained in the model without a scalar field. At the critical point, we show that the Abbott-Deser (AD) mass of the Schwarzschild-de Sitter (SdS) black hole and the energy for the massless graviton vanish, whose situation is not changed from the model without a scalar field.

View original: http://arxiv.org/abs/1203.3301