The “Studies on dynamical and thermodynamical properties and the intrinsic relation between them in gravity” led by Rong-Gen Cai was awarded the National Natural Science Award (the Second Class) in 2011. This project mainly achieved the following results.

(1) Some exact asymptotically anti-de Sitter black hole solutions of gravitational field equations have been presented, including the topological Gauss-Bonnet black hole solution, the latter is sometimes called the Boulware-Deser-Cai black hole solution in the literature. These black hole solutions have been considered as the starting point for the various following studies. A topological de Sitter spacetime solution has been found, and the conjecture on the upper bound of the mass in de Sitter spacetime has been checked.

(2) Dynamical properties of the charged anti-de Sitter black hole have been first studied. For the small anti-de Sitter black hole, it has been found that the quasinormal frequency does not change with the black hole temperature, which has clarified the clash on this topic. The study on the evolution of a scalar field coupled to curvature in topological black hole spacetimes has been first carried out and it has been shown that topology can imprint in the perturbation behaviors. The connection between the black hole thermodynamics in (anti)-de-Sitter spacetime and the conformal field theory has been constructed through the Cardy-Verlinde formula. The study of the thermodynamic and holographic properties has been generalized to dynamical spacetimes. In the realistic inhomogeneous cosmology, it has been shown that thermodynamics and holography can be useful to select physical models to describe our universe.

(3) The intrinsic connection between dynamics and thermodynamics of gravity has been disclosed. The thermodynamics on the cosmological apparent horizon has been established. From the first law of thermodynamics, the Friedmann equation which governs the dynamics of the universe has been derived successfully. The Hawking radiation on the cosmological apparent horizon was first discovered. The disclosed intrinsic relations between dynamics and thermodynamics in gravity provide a new way to understand the fundamental property of gravity.

This project published more than 260 papers in refereed international journals such as Phys. Rev. Lett, Nucl. Phys. B, Phys. Lett. B, Phys. Rev. D, JHEP and JCAP etc. And these works have received more than 8300 SCI citations.