arXiv subjects

W. F. Kao

Publications and source records attributed to W. F. Kao.

At least 37 records · Page 2Linked to original sources

arXiv2006

Modified Newtonian Dynamics and Induced gravity

Modified Newtonian dynamics, a successful alternative to the cosmic dark matter model, proposes that gravitational field deviates from the Newtonian law when the field strength $g$ is weaker than a critical value $g_0$. We will show that the dynamics of MOND can be derived from an induced gravity model. New dynamics is shown to be compatible with the spatial deformation of scalar fields coupled to the system. Approximate solutions are shown explicitly for a simple toy model.

gr-qc↗

arXiv2006

Anisotropic higher derivative gravity and inflationary universe

Stability analysis of the Kantowski-Sachs type universe in pure higher derivative gravity theory is studied in details. The non-redundant generalized Friedmann equation of the system is derived by introducing a reduced one dimensional generalized KS type action. This method greatly reduces the labor in deriving field equations of any complicate models. Existence and stability of inflationary solution in the presence of higher derivative terms are also studied in details. Implications to the choice of physical theories are discussed in details in this paper.

hep-th↗

arXiv2006

Modified Newtonian Dynamics as an extra dimensional effect

Modified Newtonian dynamics can be considered as an effect derived from a squeezable extra dimension space. The third law of Newtonian dynamics can be managed to remain valid in the 5-space. The critical acceleration parameter $a_0$ appears naturally as the bulk acceleration that has to do with the expanding universe in this setup. A simple toy model is presented in this Letter to show that consistent theory can be built with the help of the extra dimensional space.

astro-ph↗

arXiv2005

Modified Newtonian Dynamics In Dimensionless Form

Modified Newtonian dynamics proposed that gravitational field needs modifications when the field strength $g$ is weaker than a critical value $g_0$. This has been shown to be a good candidate as an alternative to cosmic dark matter. There is another way to look at this theory as a length scale dependent theory. One will show that modification of the Newtonian field strength depends on the mass distribution and the coordinate scale of the system. It is useful to separate the effective gravitation field $g(r)$ into a small scale (or short-distance)$g_s$ field and a large scale (or a long-distance) $g_l$ field that should be helpful for a better understanding of the underlying physics. The effective potential is also derived.

astro-ph↗

arXiv2003

Rotational Perturbations of High Density Matter in the Brane Cosmology

We consider the evolution of small rotational perturbations, with azimuthal symmetry, of the brane-world cosmological models. The equations describing the temporal, radial, and angular dependence of the perturbations are derived by taking into account the effects of both scalar and tensor parts of the dark energy term on the brane. The time decay of the initial rotation is investigated for several types of equation of state of the ultra-high density cosmological matter. For an expanding Universe, rotation always decays in the case of the perfect dragging, for which the angular velocity of the matter on the brane equals the rotation metric tensor. For non-perfect dragging, the behavior of the rotation is strongly equation of state dependent. For some classes of dense matter, like the stiff causal or the Chaplygin gas, the angular velocity of the matter on the brane is an increasing function of time. For other types of the ultra-dense matter, like the Hagedorn fluid, rotation is smoothed out by the expansion of the Universe. Therefore the study of dynamics of rotational perturbations of brane world models, as well as in general relativity, could provide some insights on the physical properties and equation of state of the cosmological fluid filling the very early Universe.

hep-th↗

arXiv2003

Parameterization of the Equation of State and the expansion history of the very recent universe

Motivated by a nice result shown by E. Linder, a detailed discussion on the choice of the expansion parameters of the Maclaurin series for the equation of states of a perfect fluid is presented in this paper. We show that their nice recent result is in fact a linear approximation to the full Maclaurin series as a power series of the parameter $y=z/(1+z)$. The power series for the energy density function, the Hubble parameter and related physical quantities of interest are also shown in this paper. The method presented here will have significant application in the precision distance-redshift observations aiming to map out the recent expansion history of the universe. In addition, a complete analysis of all known advantageous parameterizations for the equation of states to high redshift is also presented.

gr-qc↗

arXiv2003

A note on 4-dimensional traversable wormholes and energy conditions in higher dimensions

We show explicitly that traversable wormholes requiring exotic matter in 4-dimensions nevertheless have acceptable stress-tensors obeying reasonable energy conditions in higher dimensions if the wormholes are regarded as being embedded in higher dimensional space-times satisfying Einstein's field equations. From the 4-dimensional perspective, the existence of higher dimensions may thus facilitate wormhole and time-machine constructions through access to "exotic matter".

gr-qc↗

arXiv2002

On Analytic Properties of the Photon Polarization Function in a Background Magnetic Field

We examine the analytic properties of the photon polarization function in a background magnetic field, using the technique of inverse Mellin transform. The photon polarization function is first expressed as a power series of the photon energy $ω$ with $ω< 2m_e$. Based upon this energy expansion and the branch cut of the photon polarization function in the complex $ω$ plane, we compute the absorptive part of the polarization function with the inverse Mellin transform. Our results are valid for arbitrary photon energies and magnetic-field strengths. The applications of our approach are briefly discussed.

hep-ph↗

arXiv2002

Universal Formula for the Expectation Value of the Radial Operator under the Aharonov-Bohm Flux and the Coulomb Field

A useful and universal formula for the expectation value of the radial operator in the presence of the Aharonov-Bohm flux and the Coulomb Field is established. We find that the expectation value $< r^λ>$ $(-\infty \leq λ\leq \infty)$ is greatly affected due to the non-local effect of the magnetic flux although the Aharonov-Bohm flux does not have any dynamical significance in classical mechanics. In particular, the quantum fluctuation increases in the presence of the magnetic flux due to the Aharonov-Bohm effect. In addition, the Virial theory in quantum mechanics is also constructed for the spherically symmetric system under the Aharonov-Bohm effect.

quant-ph↗

arXiv2002

Rotational Perturbations of Friedmann-Robertson-Walker Type Brane-World Cosmological Models

First order rotational perturbations of the Friedmann-Robertson-Walker metric are considered in the framework of the brane-world cosmological models. A rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane is derived under the assumption of slow rotation. The mathematical structure of the rotation equation imposes strong restrictions on the temporal and spatial dependence of the brane matter angular velocity. The study of the integrable cases of the rotation equation leads to three distinct models, which are considered in detail. As a general result we find that, similarly to the general relativistic case, the rotational perturbations decay due to the expansion of the matter on the brane. One of the obtained consistency conditions leads to a particular, purely inflationary brane-world cosmological model, with the cosmological fluid obeying a non-linear barotropic equation of state.

hep-th↗

arXiv2002

Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux

The semiclassical quantization rule is derived for a system with a spherically symmetric potential $V(r) \sim r^ν$ $(-2<ν<\infty)$ and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with $ν= -1,0,2,\infty$. It is shown that the results provided by our method are in good agreement with previous results. One expects that the semiclassical quantization rule shown in this paper will provide a good approximation for all principle quantum number even the rule is derived in the large principal quantum number limit $n \gg 1$. We also discuss the power parameter $ν$ dependence of the energy spectra pattern in this paper.

quant-ph↗

arXiv2002

Stability of the Anisotropic Brane Cosmology

The stability of the Bianchi type I anisotropic brane cosmology is analyzed in this paper. We also study the effect of the brane solution by comparing the models on the 3-brane and the models in the conventional Einstein's space. Analysis is presented for two different models: one with a perfect fluid and the other one with a dilaton field. It is shown that the anisotropic expansion is smeared out dynamically for both theories in the large time limit independent of the models with different types of matter. The initial states are, however, dramatically different. A primordial anisotropic expansion will grow for the conventional Einstein's theory. On the other hand, it is shown that the initial state is highly isotropic for the brane universe except for a very particular case. Moreover, it is also shown that the Bianchi type I anisotropic cosmology is stable against any anisotropic perturbation for both theories in the large time limit.

hep-th↗

arXiv2001

Induced gravity with complex metric field

The possible existence of a complex metric tensor field is studied. We show that an effective scalar field is induced by an overall phase component of the complex metric tensor. The corresponding gauge field is shown to be a tachyon. Possible implications of this scalar field to the no hair theorem in a spherically symmetric space is also analyzed. We also study its impact on the evolution of the early universe.

hep-th↗

arXiv2001

Stability Analysis of Anisotropic Inflationary Cosmology

The stability analysis of an anisotropic inflationary universe of the four dimensional Neveu-Schwarz--Neveu-Schwarz string model with a nonvanishing cosmological constant is discussed in this paper. The accelerating expansion solution found earlier is shown to be stable against the perturbations with respect to the dilaton and axion fields once the dilaton field falls close to the local minimum of the symmetry-breaking potential. This indicates that the Bianchi I space tends to evolve to an isotropic flat Friedmann-Robertson-Walker space. This expanding solution is also shown to be stable against the perturbation with respect to anisotropic spatial directions.

hep-th↗

arXiv2001

Regular charged black hole with a charged de Sitter core

We show that there is a class of regular charged black hole with a charged de Sitter core similar to the de Sitter-Schwarzschild black hole. One can show that the total energy momentum tensor for the static and spherically symmetric photon field can be made conserved even the Coulomb like energy momentum tensor for photon is not conserved alone. Possible impact and the numerical solutions of the charged black hole will be shown in this paper.

hep-th↗

arXiv2001

Bianchi type I space and the stability of inflationary Friedmann-Robertson-Walker space

Stability analysis of the Bianchi type I universe in pure gravity theory is studied in details. We first derive the non-redundant field equation of the system by introducing the generalized Bianchi type I metric. This non-redundant equation reduces to the Friedmann equation in the isotropic limit. It is shown further that any unstable mode of the isotropic perturbation with respect to a de Sitter background is also unstable with respect to anisotropic perturbations. Implications to the choice of physical theories are discussed in details in this paper.

hep-th↗

arXiv2001

Friedmann Equation and Stability of Inflationary Higher Derivative Gravity

Stability analysis on the De Sitter universe in pure gravity theory is known to be useful in many aspects. We first show how to complete the proof of an earlier argument based on a redundant field equation. It is shown further that the stability condition applies to $k \ne 0$ Friedmann-Robertson-Walker spaces based on the non-redundant Friedmann equation derived from a simple effective Lagrangian. We show how to derive this expression for the Friedmann equation of pure gravity theory. This expression is also generalized to include scalar field interactions.

gr-qc↗

arXiv2000

A new look at the pair-production width in a strong magnetic field

We reexamine the process $γ\to e^++ e^-$ in a background magnetic field comparable to $B_c\equiv m_e^2/e$. This process is known to be non-perturbative in the magnetic-field strength. However, it can be shown that the {\it moments} of the above pair production width is proportional to the derivatives of photon polarization function at the zero energy, which is perturbative in $B$. Hence, the pair-production width can be easily obtained from the latter by the inverse Mellin transform. The implications of our approach are discussed.

hep-ph↗