Abstract
We analyze the most general case of third-order Chern-Simons-like theories of massive 3D gravity. Results show the conditions for finding the unitary regions on the parameter space. There exists $(n-1)$th order theories on the boundary of a unitary $n$th order model on parameter space under certain conditions, as the first example recently demonstrated from the bimetric generalization of exotic massive gravity. We investigated the mechanism that causes this type of transition for third-order models. Hamiltonian analysis of the theory also presents that ghost and no-ghost regions can be separated by Chern-Simons theories.
Highlights
General relativity (GR) can be considered as a consistent theory of nonlinearly interacting massless spin-2 particles, or gravitons, on four-dimensional space-time
If one abandons the parity-preserving condition on new massive gravity (NMG), the theory can be extended to general massive gravity (GMG) [5] that has Æ2 helicity states with different masses and gives both topological massive gravity (TMG) and NMG as a limit
Other than NMG and GMG, there is another fourth-order theory called exotic massive gravity (EMG) [6], which is a parity-odd theory with an intriguing feature called third-way consistency [7]
Summary
General relativity (GR) can be considered as a consistent theory of nonlinearly interacting massless spin-2 particles, or gravitons, on four-dimensional space-time. A degree of freedom is attainable by adding a gravitational Chern– Simons term to an Einstein–Hilbert action in 3D, which is called topological massive gravity (TMG) [2] This modification generates a massive bulk mode in the linearized theory, which emerges from the third-order derivative acting on the metric tensor. As seen in TMG, the number of degrees of freedom in the theory can be increased by adding higher-order derivate terms to an Einstein–Hilbert action. Another example, new massive gravity (NMG) [3], is a parity-preserving fourthorder model, and its linearization gives the Fierz–Pauli theory [4] with two massive graviton modes of helicity Æ2. After the study of the theory, we are expecting to observe 3 → 2 transitions at critical surfaces
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