We present a three-dimensional gravitational Born-Infeld theory which reduces to the recently found new massive gravity (NMG) at the quadratic level in the small curvature expansion and at the cubic order reproduces the deformation of NMG obtained from AdS/CFT. Our action provides a remarkable extension of NMG to all orders in the curvature and might define a consistent quantum gravity.

We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior. © 2011 American Physical Society

We find the propagator and calculate the tree level scattering amplitude between two covariantly conserved sources in an Anti-de Sitter background for the most general Ddimensional quadratic, four-derivative, gravity with a Pauli-Fierz mass. We also calculate the Newtonian potential for various limits of the theory in flat space. We show how the recently introduced three dimensional New Massive Gravity is uniquely singled out among higher derivative models as a (tree level) unitary model and that its Newtonian limit is equivalent to that of the usual massive gravity in flat space.

A new model of nonlinear electrodynamics is introduced and investigated. The theory carries one dimensionful parameter β as in Born-Infeld electrodynamics. It is shown that the dual symmetry and dilatation (scale) symmetry are broken in the proposed model. The electric field of a point-like charge is derived for this model, showing that it is non-singular at the origin. Using this electric field, the static electric energy of a point-like charge is calculated. In the presence of an external magnetic field, the theory shows a phenomenon known as vacuum birefringence. The refraction index of two polarizations, parallel and perpendicular to the external magnetic induction field, are calculated. The canonical and symmetrical Belinfante energy-momentum tensors are obtained. Using the causality and unitarity principles, the regions where the theory becomes causal and unitary are found.

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 nullenergy 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.