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.

We show that two-dimensional JT gravity, the holographic dual of the IR fixed point of the SYK model, can be obtained from the consistent Kaluza-Klein reduction of a class of EMD theories in general D dimensions. For D = 4, 5, the EMD theories can be themselves embedded in supergravities. These exact embeddings provide the holographic duals in the framework of strings and M-theory. We find that a class of JT gravity solutions can be lifted to become time-dependent charged extremal black holes. They can be further lifted, for example, to describe the D1/D5-branes where the worldsheet is the Milne universe, rather than the typical Minkowski spacetime. †

By considering the realization of the emergent universe scenario in Eddington-inspired Born-Infeld (EiBI) theory, we study the stability of the Einstein static universe filled with perfect fluid in EiBI theory against both the homogeneous and inhomogeneous scalar perturbations in this work. We find that in both the spatially flat and closed cases, the emergent universe scenario is no longer viable, since the Einstein static universe cannot be stable against both the homogeneous and inhomogeneous scalar perturbations simultaneously. However, the emergent universe scenario survives in the spatially open case, while the Einstein static universe can be stable under some conditions.

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AdS black holes show richer transition behaviors in extended phase space by assuming the cosmological constant and its conjugate quantity to behave like thermodynamic pressure and thermodynamic volume. We study the extended thermodynamics of charged dilatonic AdS black holes in a class of Einstein-Maxwell-dilaton theories that can be embedded in gauged supergravities in various dimensions. We find that the transition behaviors of higher dimensional dilatonic AdS black holes are different from the four dimensional counterparts, and new transition behaviors emerge in higher dimensions. First, there exists a standard Van der Waals transition only in a five dimensional dilatonic AdS black hole with two equal charges. Second, there emerges a new phase transition branch in negative pressure region in six and seven dimensional dilatonic black holes with two equal charges. Third, there emerge transition behaviors in higher dimensional black hole with single charge cases, which are absent in four dimensions.