Roh-Suan Tung - Academia.edu (original) (raw)
Papers by Roh-Suan Tung
arXiv (Cornell University), Oct 1, 2000
In the Tetrad Representation of General Relativity, the energymomentum expression, found by Mølle... more In the Tetrad Representation of General Relativity, the energymomentum expression, found by Møller in 1961, is a tensor wrt coordinate transformations but is not a tensor wrt local Lorentz frame rotations. This local Lorentz freedom is shown to be the same as the six parameter normalized spinor degrees of freedom in the Quadratic Spinor Representation of General Relativity. From the viewpoint of a gravitational field theory in flat space-time, these extra spinor degrees of freedom allow us to obtain a local energy-momentum density which is a true tensor over both coordinate and local Lorentz frame rotations.
arXiv (Cornell University), Sep 4, 2001
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially... more We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector field. For existence of a well-defined Hamiltonian variational principle taking into account a spatial boundary, it is necessary to modify the standard Arnowitt-Deser-Misner Hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field. The most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obtained from the symplectic current pulled back to the hypersurface boundary of the spacetime region. A main result is that we obtain a covariant derivation of Dirichlet, Neumann, and mixed type boundary conditions on
arXiv (Cornell University), Sep 4, 2001
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Rela... more We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for wide generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying "energy-momentum" vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the
International Journal of Modern Physics, Oct 18, 2012
We generalize the big-bang model in a previous paper by extending the real vacuum scalar field to... more We generalize the big-bang model in a previous paper by extending the real vacuum scalar field to a complex vacuum scalar field, within the FLRW framework. The phase dynamics of the scalar field, which makes the universe a superfluid, is described in terms of a density of quantized vortex lines, and a tangle of vortex lines gives rise to quantum turbulence. We propose that all the matter in the universe was created in the turbulence, through reconnection of vortex lines, a process necessary for the maintenance of the vortex tangle. The vortex tangle grows and decays, and its lifetime is the era of inflation. These ideas are implemented in a set of closed cosmological equations that describe the cosmic expansion driven by the scalar field on the one hand, and the vortex-matter dynamics on the other. We show how these two aspects decouple from each other, due to a vast difference in energy scales. The model is not valid beyond the inflation era, but the universe remains a superfluid afterwards. This gives rise to observable effects in the present universe, including dark matter, galactic voids, non-thermal filaments, and cosmic jets.
arXiv: General Relativity and Quantum Cosmology, Nov 17, 2010
We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as t... more We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as the source of gravity a Halpern-Huang real scalar field, which was derived from renormalizationgroup analysis, with a potential that exhibits asymptotic freedom and spontaneous symmetry breaking. Both properties are crucial to the formulation of the problem. Numerical solutions show that the universe expands at an accelerated rate, with the radius increasing like the exponential of a power of the time. This is relevant to "dark energy" and "cosmic inflation". Extension to the complex scalar field will make the universe a superfluid. The vortex dynamics that emerges offers explanations for other cosmological problems, namely, matter creation, galactic voids, and the "dark mass".
Abstract. We discuss earlier unsuccessful attempts to formulate a positive gravitational energy p... more Abstract. We discuss earlier unsuccessful attempts to formulate a positive gravitational energy proof in terms of the New Variables of Ashtekar. We also point out the difficulties of a Witten spinor type proof. We then use the special orthonormal frame gauge conditions to obtain a locally positive expression for the New Variables Hamiltonian and thereby a “localization ” of gravitational energy as well as a positive energy proof.
Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other... more Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed. PACS number(s): 04.20.Cv, 04.20.Fy Typeset using REVTEX
On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), 2002
We present a gauge theory of the super SL(2,C) group. The gauge potential is a connection of the ... more We present a gauge theory of the super SL(2,C) group. The gauge potential is a connection of the Super SL(2,C) group. A MacDowell-Mansouri type of action is proposed where the action is quadratic in the Super SL(2,C) curvature and depends purely on gauge connection. By breaking the symmetry of the Super SL(2,C) topological gauge theory to SL(2,C), a metric is naturally defined.
The Quadratic Spinor Lagrangian (QSL)1,2,3,4 was shown to be equivalent to GR|| the teleparallel ... more The Quadratic Spinor Lagrangian (QSL)1,2,3,4 was shown to be equivalent to GR|| the teleparallel (tetrad) reformulation of General Relativity...
Physical Review D, 1994
Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other... more Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed.
![Research paper thumbnail of Erratum: “Covariant Hamiltonian boundary conditions in General Relativity for spatially bounded space–time regions” [J. Math. Phys. 43, 5531 (2002)]](https://attachments.academia-assets.com/92961285/thumbnails/1.jpg)
](Journal of Mathematical Physics, 2004
In the second line of Section III (Some Notes On Physics), 1 the correct expression of the energy... more In the second line of Section III (Some Notes On Physics), 1 the correct expression of the energy-momentum tensor of a perfect fluid is T i j = pg i j + (p + µ)u i u j .
![Research paper thumbnail of Erratum: “Properties of the symplectic structure of general relativity for spatially bounded space–time regions” [J. Math. Phys. 43, 3984 (2002)]](https://attachments.academia-assets.com/92961292/thumbnails/1.jpg)
](Journal of Mathematical Physics, 2004
The sentences before and after Eqs. ͑4.53͒-͑4.55͒, ͑4.62͒-͑4.65͒, ͑4.79͒-͑4.81͒, and ͑4.89͒-͑4.91... more The sentences before and after Eqs. ͑4.53͒-͑4.55͒, ͑4.62͒-͑4.65͒, ͑4.79͒-͑4.81͒, and ͑4.89͒-͑4.91͒ all refer to 2-spheres S that lie outside any horizon. The sentence after Eq. ͑4.91͒ should refer to the normal part of P a. In Eq. ͑4.37͒, the log expressions are missing a term R 2 : i.e., ln͑R 2 ϩ͑u ͒/͑ v ͒͒.
Journal of Mathematical Physics, 2002
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially... more We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector field. For existence of a well-defined Hamiltonian variational principle taking into account a spatial boundary, it is necessary to modify the standard Arnowitt-Deser-Misner Hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field. The most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obtained from the symplectic current pulled back to the hypersurface boundary of the spacetime region. A main result is that we obtain a covariant derivation of Dirichlet, Neumann, and mixed type boundary conditions on
Journal of Mathematical Physics, 2002
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Rela... more We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for wide generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying "energy-momentum" vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the
Classical and Quantum Gravity, 2008
A class of boundary conditions for canonical general relativity are proposed and studied at the q... more A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities for the quasi-local regions. If on the boundary the evolution vector normal to the 2-surface is chosen to be proportional to the dual expansion vector, we obtain a generalization of the Hawking energy associated with a generalized Kodama vector. This vector plays the role for the stationary untrapped boundary conditions which the stationary Killing vector plays for stationary black holes. When the dual expansion vector is null, the boundary conditions reduce to the ones given by the non-expanding horizons and the null trapping horizons.
Technische Mechanik, Apr 2, 2000
A simple Cosserat model is used to explore the coupled planar flexural and axial vibrations of a ... more A simple Cosserat model is used to explore the coupled planar flexural and axial vibrations of a slender rod clamped at one end with a heavy attached mass free to move at the other. By assuming that the inertia of the rod is small compared to that of the attached mass it is shown how the equations of motion reduce to a dynamical system. The effects of gravity on the rod can be incorporated within this framework and the linearised stability of the system discussed in terms of solutions to the Mathieu-Hill equation.
Extracta mathematicae, Aug 1, 1999
1. IntroDUCtion In [6] we have shown how a drill-string in a typical rig may be modelled in terms... more 1. IntroDUCtion In [6] we have shown how a drill-string in a typical rig may be modelled in terms of a space curve with structure. This structure defines the relative orientation of neighbouring cross-sections along the drill-string. Specifying a unit vector (which may be identified with the normal to each cross-section) at each point along the drill-string centroid enables the state of flexure to be related to the angle between this vector and the tangent to the space-curve. Specifying a second vector orthogonal to the first vector (thereby placing ...
arXiv (Cornell University), Oct 1, 2000
In the Tetrad Representation of General Relativity, the energymomentum expression, found by Mølle... more In the Tetrad Representation of General Relativity, the energymomentum expression, found by Møller in 1961, is a tensor wrt coordinate transformations but is not a tensor wrt local Lorentz frame rotations. This local Lorentz freedom is shown to be the same as the six parameter normalized spinor degrees of freedom in the Quadratic Spinor Representation of General Relativity. From the viewpoint of a gravitational field theory in flat space-time, these extra spinor degrees of freedom allow us to obtain a local energy-momentum density which is a true tensor over both coordinate and local Lorentz frame rotations.
arXiv (Cornell University), Sep 4, 2001
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially... more We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector field. For existence of a well-defined Hamiltonian variational principle taking into account a spatial boundary, it is necessary to modify the standard Arnowitt-Deser-Misner Hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field. The most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obtained from the symplectic current pulled back to the hypersurface boundary of the spacetime region. A main result is that we obtain a covariant derivation of Dirichlet, Neumann, and mixed type boundary conditions on
arXiv (Cornell University), Sep 4, 2001
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Rela... more We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for wide generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying "energy-momentum" vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the
International Journal of Modern Physics, Oct 18, 2012
We generalize the big-bang model in a previous paper by extending the real vacuum scalar field to... more We generalize the big-bang model in a previous paper by extending the real vacuum scalar field to a complex vacuum scalar field, within the FLRW framework. The phase dynamics of the scalar field, which makes the universe a superfluid, is described in terms of a density of quantized vortex lines, and a tangle of vortex lines gives rise to quantum turbulence. We propose that all the matter in the universe was created in the turbulence, through reconnection of vortex lines, a process necessary for the maintenance of the vortex tangle. The vortex tangle grows and decays, and its lifetime is the era of inflation. These ideas are implemented in a set of closed cosmological equations that describe the cosmic expansion driven by the scalar field on the one hand, and the vortex-matter dynamics on the other. We show how these two aspects decouple from each other, due to a vast difference in energy scales. The model is not valid beyond the inflation era, but the universe remains a superfluid afterwards. This gives rise to observable effects in the present universe, including dark matter, galactic voids, non-thermal filaments, and cosmic jets.
arXiv: General Relativity and Quantum Cosmology, Nov 17, 2010
We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as t... more We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as the source of gravity a Halpern-Huang real scalar field, which was derived from renormalizationgroup analysis, with a potential that exhibits asymptotic freedom and spontaneous symmetry breaking. Both properties are crucial to the formulation of the problem. Numerical solutions show that the universe expands at an accelerated rate, with the radius increasing like the exponential of a power of the time. This is relevant to "dark energy" and "cosmic inflation". Extension to the complex scalar field will make the universe a superfluid. The vortex dynamics that emerges offers explanations for other cosmological problems, namely, matter creation, galactic voids, and the "dark mass".
Abstract. We discuss earlier unsuccessful attempts to formulate a positive gravitational energy p... more Abstract. We discuss earlier unsuccessful attempts to formulate a positive gravitational energy proof in terms of the New Variables of Ashtekar. We also point out the difficulties of a Witten spinor type proof. We then use the special orthonormal frame gauge conditions to obtain a locally positive expression for the New Variables Hamiltonian and thereby a “localization ” of gravitational energy as well as a positive energy proof.
Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other... more Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed. PACS number(s): 04.20.Cv, 04.20.Fy Typeset using REVTEX
On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes), 2002
We present a gauge theory of the super SL(2,C) group. The gauge potential is a connection of the ... more We present a gauge theory of the super SL(2,C) group. The gauge potential is a connection of the Super SL(2,C) group. A MacDowell-Mansouri type of action is proposed where the action is quadratic in the Super SL(2,C) curvature and depends purely on gauge connection. By breaking the symmetry of the Super SL(2,C) topological gauge theory to SL(2,C), a metric is naturally defined.
The Quadratic Spinor Lagrangian (QSL)1,2,3,4 was shown to be equivalent to GR|| the teleparallel ... more The Quadratic Spinor Lagrangian (QSL)1,2,3,4 was shown to be equivalent to GR|| the teleparallel (tetrad) reformulation of General Relativity...
Physical Review D, 1994
Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other... more Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed.
Journal of Mathematical Physics, 2004
In the second line of Section III (Some Notes On Physics), 1 the correct expression of the energy... more In the second line of Section III (Some Notes On Physics), 1 the correct expression of the energy-momentum tensor of a perfect fluid is T i j = pg i j + (p + µ)u i u j .
Journal of Mathematical Physics, 2004
The sentences before and after Eqs. ͑4.53͒-͑4.55͒, ͑4.62͒-͑4.65͒, ͑4.79͒-͑4.81͒, and ͑4.89͒-͑4.91... more The sentences before and after Eqs. ͑4.53͒-͑4.55͒, ͑4.62͒-͑4.65͒, ͑4.79͒-͑4.81͒, and ͑4.89͒-͑4.91͒ all refer to 2-spheres S that lie outside any horizon. The sentence after Eq. ͑4.91͒ should refer to the normal part of P a. In Eq. ͑4.37͒, the log expressions are missing a term R 2 : i.e., ln͑R 2 ϩ͑u ͒/͑ v ͒͒.
Journal of Mathematical Physics, 2002
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially... more We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector field. For existence of a well-defined Hamiltonian variational principle taking into account a spatial boundary, it is necessary to modify the standard Arnowitt-Deser-Misner Hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field. The most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obtained from the symplectic current pulled back to the hypersurface boundary of the spacetime region. A main result is that we obtain a covariant derivation of Dirichlet, Neumann, and mixed type boundary conditions on
Journal of Mathematical Physics, 2002
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Rela... more We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for wide generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying "energy-momentum" vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the
Classical and Quantum Gravity, 2008
A class of boundary conditions for canonical general relativity are proposed and studied at the q... more A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities for the quasi-local regions. If on the boundary the evolution vector normal to the 2-surface is chosen to be proportional to the dual expansion vector, we obtain a generalization of the Hawking energy associated with a generalized Kodama vector. This vector plays the role for the stationary untrapped boundary conditions which the stationary Killing vector plays for stationary black holes. When the dual expansion vector is null, the boundary conditions reduce to the ones given by the non-expanding horizons and the null trapping horizons.
Technische Mechanik, Apr 2, 2000
A simple Cosserat model is used to explore the coupled planar flexural and axial vibrations of a ... more A simple Cosserat model is used to explore the coupled planar flexural and axial vibrations of a slender rod clamped at one end with a heavy attached mass free to move at the other. By assuming that the inertia of the rod is small compared to that of the attached mass it is shown how the equations of motion reduce to a dynamical system. The effects of gravity on the rod can be incorporated within this framework and the linearised stability of the system discussed in terms of solutions to the Mathieu-Hill equation.
Extracta mathematicae, Aug 1, 1999
1. IntroDUCtion In [6] we have shown how a drill-string in a typical rig may be modelled in terms... more 1. IntroDUCtion In [6] we have shown how a drill-string in a typical rig may be modelled in terms of a space curve with structure. This structure defines the relative orientation of neighbouring cross-sections along the drill-string. Specifying a unit vector (which may be identified with the normal to each cross-section) at each point along the drill-string centroid enables the state of flexure to be related to the angle between this vector and the tangent to the space-curve. Specifying a second vector orthogonal to the first vector (thereby placing ...