Principle of Relativity, 24 possible kinematical algebras and new geometries with Poincar\'e symmetry

From the principle of relativity with two universal invariant parameters $c$ and $l$, 24 possible kinematical (including geometrical and static) algebras can be obtained. Each algebra is of 10 dimensional, generating the symmetry of a 4 dimensional homogeneous space-time or a pure space. In addition to the ordinary Poincar\'e algebra, there is another Poincar\'e algebra among the 24 algebras. New 4d geometries with the new Poincar\'e symmetry are presented. The motion of free particles on one of the new space-times is discussed.Comment: 11 pages, talk on the 9th Asia-Pacific International Conference on Gravitation and Astrophysics, Jun. 29-Jul. 2, Wuhan, Chin

Reformulation of Boundary BF Theory Approach to Statistical Explanation of the Entropy of Isolated Horizons

It is shown in this paper that the symplectic form for the system consisting of $D$-dimensional bulk Palatini gravity and SO$(1,1)$ BF theory on an isolated horizon as a boundary just contains the bulk term. An alternative quantization procedure for the boundary BF theory is presented. The area entropy is determined by the degree of freedom of the bulk spin network states which satisfy a suitable boundary condition. The gauge-fixing condition in the approach and the advantages of the approach are also discussed.Comment: 17 pages, no figure

The Entropy of Higher Dimensional Nonrotating Isolated Horizons from Loop Quantum Gravity

In this paper, we extend the calculation of the entropy of the nonrotating isolated horizons in 4 dimensional spacetime to that in a higher dimensional spacetime. We show that the boundary degrees of freedom on an isolated horizon can be described effectively by a punctured $SO(1,1)$ BF theory. Then the entropy of the nonrotating isolated horizon can be calculated out by counting the microstates. It satisfies the Bekenstein-Hawking law

The entropy of isolated horizons in non-minimally coupling scalar field theory from BF theory

In this paper, the entropy of isolated horizons in non-minimally coupling scalar field theory and in the scalar-tensor theory of gravitation is calculated by counting the degree of freedom of quantum states in loop quantum gravity. Instead of boundary Chern-Simons theory, the boundary BF theory is used. The advantages of the new approaches are that no spherical symmetry is needed, and that the final result matches exactly with the Wald entropy formula.Comment: 10 page

BF theory explanation of the entropy for rotating isolated horizons

In this paper, the isolated horizons with rotation are considered. It is shown that the symplectic form is the same as that in the nonrotating case. As a result, the boundary degrees of freedom can be also described by an SO$(1,1)$ BF theory. The entropy satisfies the Bekenstein-Hawking area law with the same Barbero-Immirzi parameter.Comment: 8 pages, no figure

The Conformal Field Theory on the Horizon of BTZ Black Hole

In three dimensional spacetime with negative cosmology constant, the general relativity can be written as two copies of SO$(2,1)$ Chern-Simons theory. On a manifold with boundary the Chern-Simons theory induces a conformal field theory--WZW theory on the boundary. In this paper, it is show that with suitable boundary condition for BTZ black hole, the WZW theory can reduce to a massless scalar field on the horizon.Comment: 7 page

Hamiltonian Analysis of 4-dimensional Spacetime in Bondi-like Coordinates

We discuss the Hamiltonian formulation of gravity in 4-dimensional spacetime under Bondi-like coordinates{v, r, x^a, a=2, 3}. In Bondi-like coordinates, the 3-dimensional hypersurface is a null hypersurface and the evolution direction is the advanced time v. The internal symmetry group SO(1,3) of the 4-dimensional spacetime is decomposed into SO(1,1), SO(2), and T^\pm(2), whose Lie algebra so(1,3) is decomposed into so(1,1), so(2), t^\pm(2) correspondingly. The SO(1,1) symmetry is very obvious in this kind of decomposition, which is very useful in so(1,1) BF theory. General relativity can be reformulated as the 4-dimensional coframe (e^I_\mu) and connection ({\omega}^{IJ}_\mu) dynamics of gravity based on this kind of decomposition in the Bondi-like coordinate system. The coframe consists of 2 null 1-forms e^-, e^+ and 2 spacelike 1-forms e^2, e^3. The Palatini action is used. The Hamiltonian analysis is conducted by the Dirac's methods. The consistency analysis of constraints has been done completely. There are 2 scalar constraints and one 2-dimensional vector constraint. The torsion-free conditions are acquired from the consistency conditions of the primary constraints about {\pi}^\mu_{IJ}. The consistency conditions of the primary constraints {\pi}^0_{IJ}=0 can be reformulated as Gauss constraints. The conditions of the Lagrange multipliers have been acquired. The Poisson brackets among the constraints have been calculated. There are 46 constraints including 6 first class constraints {\pi}^0_{IJ}=0 and 40 second class constraints. The local physical degrees of freedom is 2. The integrability conditions of Lagrange multipliers n_0, l_0, and e^A_0 are Ricci identities. The equations of motion of the canonical variables have also been shown

Possible Supersymmetric Kinematics

The contraction method in different limits to obtain 22 different realizations of kinematical algebras is applied to study the supersymmetric extension of \AdS\ algebra and its contractions. It is shown that $\frak{p}_2$ $\frak{h}_-$, $\frak{p}'$, $\frak{c}_2$ and $\frak{g}'$ algebras, in addition to $\frak{d}_-$, $\frak{p}$, $\frak{n}_-$, $\frak{g}$ and $\frak{c}$ algebras, have supersymmetric extension, while $\frak{n}_{-2}$, $\frak{g}_2$ and $\frak{g}'_2$ algebras have no supersymmetric extension. The connections among the superalgebras are established

Propagation effect of gravitational wave on detector response

The response of a detector to gravitational wave is a function of frequency. When the time a photon moving around in the Fabry-Perot cavities is the same order of the period of a gravitational wave, the phase-difference due to the gravitational wave should be an integral along the path. We present a formula description for detector response to gravitational wave with varied frequencies. The LIGO data for GW150914 and GW 151226 are reexamined in this framework. For GW150924, the traveling time of a photon in the LIGO detector is just a bit larger than a half period of the highest frequency of gravitational wave and the similar result is obtained with LIGO and Virgo collaborations. However, we are not always so luck. In the case of GW151226, the time of a photon traveling in the detector is larger than the period of the highest frequency of gravitational wave and the announced signal cannot match well the template with the initial black hole masses 14.2M$_\odot$ and 7.5M$_\odot$

Weak field approximation in a model of de Sitter gravity: Schwarzschild-de Sitter solutions

The weak field approximation in a model of de Sitter gravity is investigated in the static and spherically symmetric case, under the assumption that the vacuum spacetime without perturbations from matter fields is a torsion-free de Sitter spacetime. It is shown on one hand that any solution should be singular at the center of the matter field, if the exterior is described by a Schwarzschild-de Sitter spacetime and is smoothly connected to the interior. On the other, all the regular solutions are obtained, which might be used to explain the galactic rotation curves without involving dark matter.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1301.579