Li-Ming Cao

Topological Black Holes in Horava-Lifshitz Gravity

We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature 2k in Horcava-Lifshitz theory. Without loss of generality, one may take k=1, 0, and -1. The black hole solution is asymptotically anti-de Sitter with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Horcava-Lifshitz theory and Einsteins general relativity: the temperature behaviors of black holes with k=1, 0, and -1 in Horcava-Lifshitz theory are, respectively, dual to those of topological black holes with k=-1, 0, and 1 in Einsteins general relativity. The topological black holes in Horcava-Lifshitz theory are thermodynamically stable.

Hawking radiation of an apparent horizon in a FRW universe

Hawking radiation is an important quantum phenomenon of a black hole, which is closely related to the existence of an event horizon of a black hole. The cosmological event horizon of de Sitter space is also of Hawking radiation with a thermal spectrum. By use of the tunneling approach, we show that there is indeed a Hawking radiation with temperature, T = 1/2 pi(r) over tilde (A), for a locally defined apparent horizon of a Friedmann-Robertson-Walker universe with any spatial curvature, where (r) over tilde (A) is the apparent horizon radius. Thus we fill in the gap existing in the literature investigating the relation between the first law of thermodynamics and Friedmann equations; there the apparent horizon is assumed to have such a temperature without any proof. In addition, we stress the implication of the Hawking temperature associated with the apparent horizon.

Thermodynamics of Black Holes in Horava-Lifshitz Gravity

By using the canonical Hamiltonian method, we obtain the mass and entropy of the black holes with general dynamical coupling constant; in Horava-Lifshitz Gravity. Regardless of whether the horizon is sphere, plane or hyperboloid, we find these black holes are thermodynamically stable in some parameter space and unstable phase also exists in other parameter space. The relation between the entropy and horizon area of the black holes has an additional coefficient depending on the coupling constant;, compared to the lambda = 1 case. For lambda = 1, the well-known coefficient of one quarter is recovered in the infrared region

Friedmann equations from entropic force

In this paper, by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.

Generalized Vaidya spacetime in Lovelock gravity and thermodynamics on the apparent horizon

We present a kind of generalized Vaidya solutions in a generic Lovelock gravity. This solution generalizes the simple case in Gauss-Bonnet gravity reported recently by some authors. We study the thermodynamics of apparent horizon in this generalized Vaidya spacetime. Treating those terms except for the Einstein tensor as an effective energy-momentum tensor in the gravitational field equations, and using the unified first law in Einstein gravity theory, we obtain an entropy expression for the apparent horizon. We also obtain an energy expression of this spacetime, which coincides with the generalized Misner-Sharp energy proposed by Maeda and Nozawa in Lovelock gravity.

Notes on Entropy Force in General Spherically Symmetric Spacetimes

In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einsteins equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.

Generalized Misner-Sharp energy in f (R) gravity

We study generalized Misner-Sharp energy in f(R) gravity in a spherically symmetric space-time. We find that unlike the cases of Einstein gravity and Gauss-Bonnet gravity, the existence of the generalized Misner-Sharp energy depends on a constraint condition in the f(R) gravity. When the constraint condition is satisfied, one can define a generalized Misner-Sharp energy, but it cannot always be written in an explicit quasilocal form. However, such a form can be obtained in a Friedmann-Robertson-Walker universe and for static spherically symmetric solutions with constant scalar curvature. In the Friedmann-Robertson-Walker universe, the generalized Misner-Sharp energy is nothing but the total matter energy inside a sphere with radius r, which acts as the boundary of a finite region under consideration. The case of scalar-tensor gravity is also briefly discussed.

Black holes in gravity with conformal anomaly and logarithmic term in black hole entropy

We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.

Black holes without mass and entropy in Lovelock gravity

We present a class of new black hole solutions in D-dimensional Lovelock gravity theory. The solutions have a form of direct product M(m) x H(n), where D m + n, H(n) is a negative constant curvature space, and the solutions are characterized by two integration constants. When m 3 and 4, these solutions reduce to the exact black hole solutions recently found by Maeda and Dadhich in Gauss-Bonnet gravity theory. We study thermodynamics of these black hole solutions. Although these black holes have a nonvanishing Hawking temperature, surprisingly, the mass of these solutions always vanishes. While the entropy also vanishes when m is odd, it is a constant determined by an Euler characteristic of (m - 2)-dimensional cross section of black hole horizon when m is even. We argue that the constant in the entropy should be thrown away. Namely, when m is even, the entropy of these black holes also should vanish. We discuss the implications of these results.

Conformal symmetry for rotating D-branes

Abstract We apply the Kerr/CFT correspondence to the rotating black p-brane solutions. These solutions give the simplest examples from string theory point of view. Their near horizon geometries have structures of AdS, even though black p-brane solutions do not have AdS-like structures in the non-rotating case. The microscopic entropy which can be calculated via the Cardy formula exactly agrees with Bekenstein–Hawking entropy.