A study on a five-dimensional scenario of a ghost-free nonlinear massive gravity proposed by de Rham, Gabadadze, and Tolley (dRGT) will be presented in this article. In particular, we will show how to construct a five-dimensional massive graviton term using the Cayley-Hamilton theorem. | VNU Journal of Science: Mathematics – Physics, Vol. 33, No. 1 (2017) 69-75 On a Five-dimensional Scenario of Massive Gravity Tuan Quoc Do* Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Hanoi, Vietnam Received 25 January 2017 Revised 01 March 2017; Accepted 20 March 2017 Abstract: A study on a five-dimensional scenario of a ghost-free nonlinear massive gravity proposed by de Rham, Gabadadze, and Tolley (dRGT) will be presented in this article. In particular, we will show how to construct a five-dimensional massive graviton term using the Cayley-Hamilton theorem. Then some cosmological solutions such as the Friedmann-LemaitreRobertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS spacetimes will be solved for the five-dimensional dRGT theory thanks to the constant-like behavior of massive graviton terms under an assumption that the reference metric is compatible with the physical one. Keywords: Massive gravity, higher dimensions, Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS spacetimes. 1. Introduction Recently, an important nonlinear extension of the Fierz-Pauli massive gravity [1] has been proposed by de Rham, Gabadadze, and Tolley (dRGT) [2], which has been confirmed to be free of the so-called Boulware-Deser (BD) ghost, a negative energy mode arising from nonlinear terms [3], by several approaches [4]. It turns out that a number of cosmological implications of dRGT theory have been investigated extensively. For example, the dRGT theory has been expected to provide an alternative solution to the cosmological constant problem. Besides the Friedmann-LemaitreRobertson-Walker (FLRW) metric, some anisotropic metrics such as the Bianchi type I metric along with some black holes such as the Schwarzschild, Kerr, and charged black holes have also been shown to exist in the context of dRGT theory [5, 6]. Since the dRGT theory has been proved to be free of the BD ghost for arbitrary reference .
