Nonlocal Massive Gravity from Einstein Gravity

Abstract

We present a top-down construction of a three-dimensional non-local theory of massive gravity. This "Non-Local Massive Gravity" (NLMG) is obtained as the gravitational theory induced by Einstein gravity on a brane inserted in Anti-de Sitter space modified by an overall minus sign. The theory involves an infinite series of increasingly complicated higher-derivative corrections to the Einstein-Hilbert action, with the quadratic term coinciding with New Massive Gravity. We obtain an analytic formula for the quadratic action of NLMG and show that its linearized spectrum consists of an infinite tower of positive-energy massive spin-2 modes. We compute the Newtonian potential and show that the introduction of the infinite series of terms makes it behave as $\sim 1/r$ at short distances, as opposed to the logarithmic behavior encountered when the series is truncated at any finite order. We use this and input from brane-world holography to argue that the theory may contain asymptotically flat black hole solutions.