c-functions in the Born-Infeld extended New Massive Gravity

We derive and study the equations of motion of the Born-Infeld extension of New Massive Gravity for globally and asymptotically (anti-)de Sitter spaces, and show that the assumptions of the null-energy condition and holography (that bounds the c-function) lead to two simple c-functions one of which is equivalent to the c-function of Einstein's gravity. We also show that, at the fixed point, the c-function gives the central charge of the Virasoro algebra and the coefficient of the Weyl anomaly up to a constant.