Chao-Guang Huang

On special relativity with cosmological constant

Based on the principle of relativity and the postulate of invariant speed and length, we propose the theory of special relativity with cosmological constant SRc, R, in which the cosmological constant is linked with the invariant length. Its relation with the doubly special relativity is briefly mentioned

Snyder's model—de Sitter special relativity duality and de Sitter gravity

Between Snyders quantized space-time model in de Sitter space of momenta and the dS special relativity on dS-spacetime of radius R with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with the Planck length lP, R (3/Λ)1/2 should be a fundamental constant. They lead to a dimensionless constant g ~ lPR−1 = (Gc−3Λ/3)1/2 ~ 10−61. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local dS-invariance characterized by g. A simple model of dS-gravity with a gauge-like action on umbilical manifolds may show these characteristics. It can pass the observation tests and support the duality.

On Beltrami model of de Sitter spacetime

Based on some important properties of dS space, we present a Beltrami model BA that may shed light on the observable puzzle of dS space and the paradox between the special relativity principle and cosmological principle. In BA, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order A. This has already been shown by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.

Mechanics and Newton-Cartan-like gravity on the Newton-Hooke space-time

We focus on the dynamical aspects on Newton-Hooke space-time NH+ mainly from the viewpoint of geometric contraction of the de Sitter spacetime with Beltrami metric. (The term spacetime is used to denote a space with non-degenerate metric, while the term space-time is used to denote a space with degenerate metric.) We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newtons gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrodinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time NH- contracted from anti-de Sitter spacetime.

Gravitational anomaly and Hawking radiation near a weakly isolated horizon

Based on the idea of the work by Wilczek and his collaborators, we consider the gravitational anomaly near a weakly isolated horizon. We find that there exists a universal choice of tortoise coordinate for any weakly isolated horizon. Under this coordinate, the leading behavior of a quite arbitrary scalar field near a horizon is a 2-dimensional chiral scalar field. This means we can extend the idea of Wilczek and his collaborators to more general cases and show the relation between gravitational anomaly and Hawking radiation is a universal property of a black hole horizon.

The principle of relativity, kinematics and algebraic relations

Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. These symmetries are connected to each other via combinations rather than via contractions and deformations.

NEWTON–HOOKE LIMIT OF BELTRAMI–DE SITTER SPACETIME, PRINCIPLE OF GALILEI–HOOKE'S RELATIVITY AND POSTULATE ON NEWTON–HOOKE UNIVERSAL TIME

Based on the Beltrami–de Sitter spacetime, we present the Newton–Hooke model under the Newton–Hooke contraction of the BdS spacetime with respect to the transformation group, algebra and geometry. It is shown that in Newton–Hooke space–time, there are inertial-type coordinate systems and inertial-type observers, which move along straight lines with uniform velocity. And they are invariant under the Newton–Hooke group. In order to determine uniquely the Newton–Hooke limit, we propose the Galilei–Hookes relativity principle as well as the postulate on Newton–Hooke universal time. All results are readily extended to the Newton–Hooke model as a contraction of Beltrami–anti-de Sitter spacetime with negative cosmological constant.

Yang's model as triply special relativity and the Snyder's model–de Sitter special relativity duality

We show that if Yangs quantized space-time model is completed at both classical and quantum level, it should contain both Snyders model, the de Sitter special relativity and their duality

Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity

We construct Kaluza-Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincare gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza-Klein-type models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsion-free limit will come back to general relativity with a corresponding cosmological term. We also generalize the results to the case with a variable cosmological term.

Geometries for Possible Kinematics

The physical and geometrical realizations of algebras for all possible Lorentzian and Euclidean kinematics with so(3) isotropy are presented in contraction approach and then re-classified. All geometries associated with these realizations are also obtained by the contraction method. Further relations among the geometries are revealed. Most geometries fall into pairs. There exists t ⇔ 1/(ν2t) correspondence in each pair. In the viewpoint of differential geometry, there are only 9 geometries, which have right signature and geometrical spatial isotropy. They are 3 relativistic geometries, 3 absolute-time geometries, and 3 absolute-space geometries.