On three dimensional bigravity

TL;DR

The paper investigates a three-dimensional $f$-$g$ gravity with interaction $U_m(g,f)$ and two independent cosmological constants, showing the theory admits $AdS_3$ and $AdS_3$ wave vacua and, at a critical coupling, a Log gravity phase. It derives AdS wave solutions via a $g_{\mu\nu}$-$f_{\mu\nu}$ ansatz, analyzes linear fluctuations around the vacuum to reveal an $NMG$-like massive mode plus a decoupled massless mode, and constructs a class of exact static BTZ-like black hole solutions whose asymptotics are AdS and whose isometries depend on parameter choices. The results connect to Pauli-Fierz and NMG structures in the linearized regime and suggest a holographic interpretation with a central charge $c_m=\frac{3\ell_{eff}}{2G}(1+\sigma\sqrt{\gamma})$, offering concrete 3D bigravity realizations and potential extensions to parity-violating or warped geometries.

Abstract

In this paper we explore some features of f-g theory in three dimensions. We show that the theory has (A)dS and (A)dS wave solutions. In particular at a critical value of the coupling constant we see that the model admits Log gravity solution as well, reminiscing TMG and NMG. We have also studied a class of exact static spherically symmetric black hole solution in the model.