Critical gravity with a scalar field in four dimensions

TL;DR

This paper explores a four-dimensional critical gravity theory coupled with a scalar field, analyzing its solutions including dS, AdS, and Minkowski backgrounds, and examining properties of black holes and gravitons at the critical point.

Contribution

It introduces a scalar field into critical gravity in four dimensions and investigates its solutions and properties at the critical point, including the existence of Minkowski background.

Findings

Minkowski background appears only with scalar field inclusion.

At the critical point, the AD mass of Schwarzschild-de Sitter black holes vanishes.

The energy of the massless graviton is zero at the critical point.

Abstract

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.