A Static Spherically Symmetric Solution of the Einstein-aether Theory

By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an inner Cauchy horizon and an outer black hole event horizon. But a remarkable difference from the Reissner-Nordstrom solution is that it is not asymptotically flat but approaches a two dimensional sphere. The resulting electric potential is regular in the whole spacetime except for the curvature singularity. On the other hand, the magnetic potential is divergent on both Cauchy horizon and the outer event horizon.Comment: 12 pages, 8 figures. To appear in PR

Cosmic evolution of scalar fields with multiple vacua: generalized DBI and quintessence

We find a method to rewrite the equations of motion of scalar fields, generalized DBI field and quintessence, in the autonomous form for\emph{arbitrary} scalar potentials. With the aid of this method, we explore the cosmic evolution of generalized DBI field and quintessence with the potential of multiple vacua. Then we find that the scalars are always frozen in the false or true vacuum in the end. Compared to the evolution of quintessence, the generalized DBI field has more times of oscillations around the vacuum of the potential. The reason for this point is that, with the increasing of speed $\dot{\phi}$, the friction term of generalized DBI field is greatly decreased. Thus the generalized DBI field acquires more times of oscillations.Comment: 8 pages, 9 figures, accepted by IJTP. A number of typos correcte

Quasinormal modes in Schwarschild black holes due to arbitrary spin fields

The Newman-Penrose formalism is used to deal with the massless scalar, neutrino, electromagnetic, gravitino and gravitational quasinormal modes (QNMs) in Schwarzschild black holes in a united form. The quasinormal mode frequencies evaluated by using the 3rd-order WKB potential approximation show that the boson perturbations and the fermion perturbations behave in a contrary way for the variation of the oscillation frequencies with spin, while this is no longer true for the damping's, which variate with $s$ in a same way both for boson and fermion perturbations.Comment: 11 pages, 3 figure

Singularities and the Finale of Black Hole Evaporation

In this essay we argue that once quantum gravitational effects change the classical geometry of a black hole and remove the curvature singularity, the black hole would not evaporate entirely but approach a remnant. In a modified Schwarzschild spacetime characterized by a finite Kretschmann scalar, a minimal mass of the black hole is naturally bounded by the existence of the horizon rather than introduced by hand. A thermodynamical analysis discloses that the temperature, heat capacity and the luminosity are vanishing naturally when the black hole mass approaches the minimal value. This phenomenon may be attributed to the existence of the minimal length in quantum gravity. It can also be understood heuristically by connecting the generalized uncertainty principle with the running of Newton's gravitational constant.Comment: 10 page

Quintessence and phantom emerging from the split-complex field and the split-quaternion field

Motivated by the mathematic theory of split-complex numbers (or hyperbolic numbers, also perplex numbers) and the split-quaternion numbers (or coquaternion numbers), we define the notion of split-complex scalar field and the split-quaternion scalar field. Then we explore the cosmic evolution of these scalar fields in the background of spatially flat Friedmann-Robertson-Walker Universe. We find that both the quintessence field and the phantom field could naturally emerge in these scalar fields. Introducing the metric of field space, these theories fall into a subclass of the multi-field theories which have been extensively studied in inflationary cosmology.Comment: 14 pages, 14 figure

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field $\phi$ played in Brans-Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with $\phi$; and almost all of the fundamental components of our universe can be unified into the dynamical equation for $\phi$. As a generalization of Brans-Dicke theory, we propose a new gravity theory with a complex scalar field $\phi$ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.Comment: 6 page