Searcharxiv⌕ Search

arXiv subjects

Chao-Guang Huang

Publications and source records attributed to Chao-Guang Huang.

At least 19 recordsLinked to original sources
arXiv2025

Hamiltonian Analysis of 3-dimensional Spacetime in Bondi-like Coordinates

The Hamiltonian analysis for a 3-dimensional connection dynamics of $\frak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01}, L_{02}, L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the system is clearly presented. A null coframe with 3 independent variables and 9 connection coefficients are treated as basic configuration variables. All constraints and their consistency conditions, the solutions of Lagrange multipliers as well as the equations of motion are presented. There is no physical degree of freedom in the system. The Bañados-Teitelboim-Zanelli (BTZ) spacetime is discussed as an example to check the analysis. Unlike the ADM formalism, where only non-degenerate geometries on slices are dealt with and the Ashtekar formalism, where non-degenerate geometries on slices are mainly concerned though the degenerate geometries may be studied as well, in the present formalism the geometries on the slices are always degenerate though the geometries for the spacetime are not degenerate.

gr-qc↗
arXiv2025

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 $(e^I_μ)$ and connection $(ω^{IJ}_μ)$ 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 $π^μ_{IJ}$. The consistency conditions of the primary constraints $π^0_{IJ}=0$ 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 $π^0_{IJ}=0$ 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.

gr-qc↗
arXiv2023

The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity

By applying the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, the metric for the external gravitational field of a spatially compact stationary source is provided in $F(X,Y,Z)$ gravity, a generic fourth-order theory of gravity, where $X:=R$ is Ricci scalar, $Y:=R_{μν}R^{μν}$ is Ricci square, and $Z:=R_{μνρσ}R^{μνρσ}$ is Riemann square. A new type of gauge condition is proposed so that the linearized gravitational field equations of $F(X,Y,Z)$ gravity are greatly simplified, and then, the stationary metric in the region exterior to the source is derived. In the process of applying the result, integrations are performed only over the domain occupied by the source. The multipole expansion of the metric potential in $F(X,Y,Z)$ gravity for a spatially compact stationary source is also presented. In the expansion, the corrections of $F(X,Y,Z)$ gravity to General Relativity are Yukawa-like ones, dependent on two characteristic lengths. Two additional sets of mass-type source multipole moments appear in the corrections and the salient feature characterizing them is that the integrations in their expressions are always modulated by a common radial factor related to the source distribution.

gr-qc↗
arXiv2020

Analytical analysis on the orbits of Taiji spacecrafts to infinite order of the orbital eccentricity

The dual configuration of the original one is proposed for the orbit design of Taiji spacecrafts. In terms of these two configurations of Taiji, an algorithm is devised to expand the unperturbed Keplerian orbits of spacecrafts to infinite order of $e$, the orbital eccentricity, in the heliocentric coordinate system. Further, based on the algorithm, all the kinematic indicators of Taiji triangles, say three arm-lengths and their corresponding rates of change, and three vertex angles, in both configurations are also be expanded to infinite order of $e$, and it is proved that both configurations of Taiji possess the same symmetry: At every order, three components of every kinematic indicator of Taiji triangle are identical to each other up to a phase shift of $2π/3$, which is independent on the tilt angle of Taiji plane relative to the ecliptic plane. Finally, the above algorithm is slightly modified, and with it, by adjusting the tilt angle around $π/3$ to any order of $e$, the orbits of Taiji spacecrafts in each configuration can be optimized.

gr-qc↗
arXiv2019

Analytical analysis on the orbits of Taiji spacecrafts

The unperturbed Keplerian orbits of Taiji spacecrafts are expanded to $e^3$ order in the heliocentric coordinate system, where $e$ is their orbital eccentricity. The three arm-lengths of Taiji triangle and their rates of change are also expanded to $e^3$ order, while the three vertex angles are expanded to $e^2$ order. These kinematic indicators of Taiji triangle are, further, minimized, respectively, by adjusting the tilt angle of Taiji plane relative to the ecliptic plane around $\pmπ/3$, and thus, their corresponding optimized expressions are presented. Then, under the case that the nominal trailing angle of Taiji constellation following the Earth is set to be $χ(\approx\pmπ/9)$ from the viewpoint of the Sun, the influence of the Earth perturbation on three spacecrafts is calculated according to the equations of motion in the problem of three bodies, and the perturbative solutions of the leading order and the next leading order are derived. With the perturbative solutions, the leading-order corrections to the above kinematic indicators of Taiji triangle and the expression of the above trailing angle to the order of $e^3$ are provided.

gr-qc↗
arXiv2018

Multipole analysis in the radiation field for linearized $f(R)$ gravity with irreducible Cartesian tensors

The $1/r$-expansion in the distance to the source is applied to the linearized $f(R)$ gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized $f(R)$ gravity. All of these results have two parts which are associated with the tensor part and the scalar part in the multipole expansion of linearized $f(R)$ gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom, and places an important role in distinguishing GR and $f(R)$ gravity.

gr-qc↗
arXiv2018

Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors

The field equations of $f(R)$ gravity are rewritten in the form of obvious wave equations with the stress-energy pseudotensor of the matter fields and the gravitational field as its source under the de Donder condition. The method of multipole analysis in terms of irreducible Cartesian tensors is applied to the linearized $f(R)$ gravity, and its multipole expansion is presented explicitly. In this expansion, the tensor part is symmetric and trace-free and is the same as that in General Relativity, and the scalar part predicts the appearance of monopole and dipole radiation in $f(R)$ gravity, as shown in literature. As a by-product, the multipole expansion for the massive Klein-Gordon field with an external source in terms of irreducible Cartesian tensors and its corresponding stationary results are provided.

gr-qc↗
arXiv2017

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.

gr-qc↗
arXiv2016

Motion of photons in a background of gravitational wave

The photon motion in a Michelson interferometer is re-analyzed in both geometrical optics and wave optics. The classical paths of the photons in the background of gravitational wave are derived from Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of gravitational wave are presented in flat-space approximation. Both methods show that the response of an interferometer depends on the frequency of a gravitational wave, however it is almost independent of the frequency of the mirror's vibrations. It implies that the vibrating mirror cannot mimic a gravitational wave very well.

gr-qc↗
arXiv2016

Is GW151226 a really signal of gravitational wave?

Recently, the LIGO Scientific Collaboration and Virgo Collaboration published the second observation on gravitational wave GW151226 [Phys. Rev. Lett. 116, 241103 (2016)] from the binary black hole coalescence with initial masses about 14 M$_\odot$ and 8 M$_\odot$. They claimed that the peak gravitational strain was reached at about 450 Hz, the inverse of which has been longer than the average time a photon staying in the Fabry-Perot cavities in two arms. In this case, the phase-difference of a photon in the two arms due to the propagation of gravitational wave does not always increase as the photon stays in the cavities. It might even be cancelled to zero in extreme cases. When the propagation effect is taken into account, we find that the claimed signal GW151226 would almost disappear.

gr-qc↗
arXiv2016

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$_\odot$.

gr-qc↗
arXiv2016

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.

gr-qc↗
arXiv2015

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.

gr-qc↗
arXiv2015

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.

gr-qc↗
arXiv2014

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.

hep-th↗
arXiv2014

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.

gr-qc↗
arXiv2013

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 Poincaré 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.

gr-qc↗