By rescaling the Gauss-Bonnet (GB) coupling constant α → α/(D − 4) and considering the D → 4 limit, the GB gravity gives rise to nontrivial modification of general relativity in four dimensions. In this work, we investigate the realization of the emergent universe scenario in the 4D GB gravity. First, we obtain the Einstein static universe filled with a perfect fluid. Then, we show that both spatially closed and open universes can be stable against both homogeneous and inhomogeneous scalar perturbations simultaneously.

Abstract:We study Einstein-Born-Infeld gravity and construct the dyonic (A)dS planar black holes in general even dimensions, that carry both the electric charge and magnetic fluxes along the planar space. In four dimensions, the solution can be constructed with also spherical and hyperbolic topologies. We study the black hole thermodynamics and obtain the first law. We also classify the singularity structure.

We study thermodynamical properties of static dyonic AdS black holes in four-dimensional ω-deformed Kaluza-Klein gauged supergravity theory, and find that the differential first law requires a modification via introducing a new pair of thermodynamical conjugate variables (X, Y ). To ensure such a modification, we then apply the quasi-local ADT formalism developed in [20] to calculate the quasi-local conserved charge and identify that the new pair is precisely the one previously introduced to modify the differential form of the first law.

The Gödel universe is a direct product of a line and a three-dimensional spacetime we call G α . In this paper, we show that the Gödel metrics can arise as exact solutions in Einstein-Maxwell-Axion, Einstein-Proca-Axion, or Freedman-Schwarz gauged supergravity theories. The last option allows us to embed the Gödel universe in string theory. The ten-dimensional spacetime is a direct product of a line and the nine-dimensional one of an S 3 × S 3 bundle over G α , and it can be interpreted as some decoupling limit of the rotating D1/D5/D5 intersection. For some appropriate parameter choice, the nine-dimensional metric becomes an AdS 3 × S 3 bundle over squashed 3-sphere. We also study the properties of the Gödel black holes that are constructed from the double Wick rotations of the Gödel metrics.