Narrow Results

In this paper, we investigate the behavior of linearized gravitational excitation in the Born–Infeld gravity in AdS₃ space. We obtain the linearized equation of motion and show that this higher-order gravity propagate two gravitons, massless and massive, on the AdS₃ background. In contrast to the R² models, such as TMG or NMG, Born–Infeld gravity does not have a critical point for any regular choice of parameters. So the logarithmic solution is not a solution of this model, due to this one cannot find a logarithmic conformal field theory as a dual model for Born–Infeld gravity.

In this paper, a modified Born–Infeld gravitation theory with an $f(R)$ function being added to the determinant action is analyzed from a cosmological viewpoint. The corresponding accelerating dynamics are studied in a simplified conformal approach without matter. Three different structures for the auxiliary metric function are analyzed, with the aim to establish a deeper understanding of the role of this function in cosmology. After performing the analysis, it is seen that by modifying the auxiliary metric function, a Big Rip singularity or either a Little Rip dark energy model may arise.

The Born-Infeld gravity is a modified gravity motivated by the quantum gravity, which has the ability to get rid of the big bang and other singularities. We consider the Palatini formalism of the Born-Infeld gravity and investigate the FRW cosmology by using an effective potential. It is shown that the big bang singularity does not always emerge but the scale factor can be bounced. Based on this result, we also study the black hole formation for spherical dust collapse, and find that the dust ball does not always collapse into a singularity.

We study the propagation of a null fluid under the modified dynamics provided by the Palatini formulation of the Born-Infeld theory of gravity. Working in a Cartesian coordinate system, we obtain exact analytical solutions for the metric tensor, which describes the gravitational wave produced by the null fluid. The result is compared with the prediction of general relativity.

In recent years, many kinds of modified gravity theories are suggested to get over problems in the general relativity. We consider a kind of modified gravity theories “Born- Infeld gravity in the Palatini formalism” and apply this theory to the black hole formation by considering the spherically symmetric collapse of the dust ball. We find the condition for the mass that the black hole horizon is formed.