Revisiting Stability in New General Relativity

Abstract

We study the degrees of freedom in New General Relativity -- flat and metric compatible family of theories -- around the Minkowski background in a gauge invariant manner. First, we confirm the decoupling case, in which the theory reduces to linearized gravity plus a massless KR field. We then show that, unless they vanish, the vector modes of this theory will be unstable. In addition, we find two new branches of the theories, which are instability-free and propagate linearly two tensor modes and in one of the cases also a massless scalar field. This shows that while the generic theory is ill-behaved, there are three possible realizations of instability-free cases, in contradiction to the previous literature, which states that there is only one healthy theory in addition to general relativity.

16 pages. Minor changes. It matches the version published in PRD

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Cited by in corpus (7)

• Weak Gravity Limit in Newer General Relativity
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• On black holes in new general relativity
• Geometric formulation of $k$-essence and late-time acceleration
• Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions
• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions