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We find a vacuum stationary twisted solution in four-dimensional Einstein gravity. Its frame dragging angular velocities are antisymmetric with respect to the equatorial plane. It possesses a symmetry of joint inversion of time and parity with respect to the equatorial plane. Its Arnowitt-Deser-Misner (ADM) mass and angular momentum are zero. It is curved but regular all over the manifold. Its Komar mass and Komar angular momentum are also zero. Its infinite red-shift surface coincides with its event horizon, since the event horizon does not rotate. Furthermore we extend this solution to the massive case, and find some similar properties. This solution is a stationary axisymmetric solution, but not Kerr. It explicitly proves that pure Einstein gravity permits different rotational mode other than Kerr. Our results demonstrate that the Einstein theory may have much more rich structures than what we ever imagine.

An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of gauge/gravity duality, a singular reference metric corresponds to momentum dissipations, which describes the electric and heat conductivity for normal conductors. We demonstrate in detail that the massive gravity with singular reference metric is ghost-free., Comment: 6pages, no figure

We obtain the Misner-Sharp mass in the massive gravity for a four dimensional spacetime with a two dimensional maximally symmetric subspace via the inverse unified first law method. Significantly, the stress energy is conserved in this case with a widely used reference metric. Based on this property we confirm the derived Misner-Sharp mass by the conserved charge method. We find that the existence of the Misner-sharp mass in this case does not lead to extra constraint for the massive gravity, which is notable in modified gravities. In addition, as a special case, we also investigate the Misner-Sharp mass in the static spacetime. Especially, we take the FRW universe into account for investigating the thermodynamics of the massive gravity. The result shows that the massive gravity can be in thermodynamic equilibrium, which fills in the gap in the previous studies of thermodynamics in the massive gravity., Comment: 11 pages, no figure, version published in PRD

Gravity/fluid correspondence becomes an important tool to investigate the strongly correlated fluids. We carefully investigate the holographic fluids at the finite cutoff surface by considering different boundary conditions in the scenario of gravity/fluid correspondence. We find that the sonic velocity of the boundary fluids at the finite cutoff surface is critical to clarify the superficial similarity between bulk viscosity and perturbation of the pressure for the holographic fluid, where we set a special boundary condition at the finite cutoff surface to explicitly express this superficial similarity. Moreover, we further take the sonic velocity into account to investigate a case with more general boundary condition. In this more general case, two parameters in the first order stress tensor of holographic fluid cannot be fixed, one can still extract the information of transport coefficients by considering the sonic velocity seriously., Comment: 13 pages; version accepted by Chinese Physics C

In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the \sch~solution through thermodynamic laws by the aid of the Misner-Sharp mass in an adiabatic system. In this paper we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner-Sharp mass is the mass for an adiabatic system, we reproduce the Boulware-Deser-Cai solution in Guass-Bonnet gravity. Using this gravi-thermodynamics thought, we obtain a NEW class of solution in $F(R)$ gravity in an $n$-dimensional (n$\geq$3) spacetime which permits three-type $(n-2)$-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton-Barrow solution in $F(R)$ gravity., Comment: 9pages

We study the Misner-Sharp mass for the $f(R)$ gravity in an $n$-dimensional (n$\geq$3) spacetime which permits three-type $(n-2)$-dimensional maximally symmetric subspace. We obtain the Misner-Sharp mass via two approaches. One is the inverse unified first law method, and the other is the conserved charge method by using a generalized Kodama vector. In the first approach, we assume the unified first still holds in the $n$-dimensional $f(R)$ gravity, which requires a quasi-local mass form (We define it as the generalized Misner-Sharp mass). In the second approach, the conserved charge corresponding to the generalized local Kodama vector is the generalized Misner-Sharp mass. The two approaches are equivalent, which are bridged by a constraint. This constraint determines the existence of a well-defined Misner-Sharp mass. As an important special case, we present the explicit form for the static space, and we calculate the Misner-Sharp mass for Clifton-Barrow solution as an example., Comment: 8 pages

We discuss a Higgs inflation model in the warped DGP braneworld background. It generates reasonable primordial perturbations. At the same time with enhanced non-minimal coupling it overcomes the severe problem in the Higgs inflation in 4 dimension, which says that the effective field theory become invalid at an energy scale far below the energy scale for inflation exit. Furthermore we present the constraints for the parameters confront to PLANCK and related observations. PLANCK low-l data almost fixes the inflation energy scale in this Higgs inflation model with specific brane parameters., Comment: 10 pages, 3 figures

In the three-dimensional pure Einstein gravity, the geometries of the vacuum space-times are always trivial, and gravitational waves (gravitons) are strictly forbidden. For the first time, we find a vacuum circularly symmetric black hole with nontrivial geometries in $f(R)$ gravity theory, in which a true singularity appears. In this frame with nontrivial geometry, a perturbative gravitational wave does exist. Beyond the perturbative level, we make a constructive proof of the existence of a gravitational wave in $f(R)$ gravity, where the Birkhoff-like theorem becomes invalid. We find two classes of exact solutions of circularly symmetric pure gravitational wave radiation and absorption., Comment: 6 pages, minor corrections, to match the published version

In this paper, the perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, and the main equation is obtained. As the application of this main equation, the Reissner-Nordstorm-AdS solution and Clifton-Barrow solution in $f(R)$ gravity have been taken for the examples. We find that both the electric charge and $f(R)$ gravity can affect the perihelion precession and deflection of light, while the cosmological constant can only effect the perihelion precession. Moreover, we clarify a subtlety in the deflection of light in the solar system that the possible sun's electric charge is usually used to interpret the gap between the experiment data and theoretical result. However, after also considering the effect from the sun's same electric charge on the perihelion precession of Mercury, we can find that it is not the truth., Comment: 13 pages, no figure, published version