arXiv subjects

J. H. Yoon

Publications and source records attributed to J. H. Yoon.

23 records · Page 2Linked to original sources

arXiv1997

The Schwarzschild Solution in the 4-Dimensional Kaluza-Klein Description of The Einstein's Equations

The Kaluza-Klein formalism of the Einstein's theory, based on the (2,2)-fibration of a generic 4-dimensional spacetime, describes general relativity as a Yang-Mills gauge theory on the 2-dimensional base manifold, where the local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. As a way of illustrating how to use this formalism in finding exact solutions, we apply this formalism to the spherically symmetric case, and obtain the Schwarzschild solution by solving the field equations.

gr-qc↗

arXiv1996

4-Dimensional Kaluza-Klein Approach to General Relativity in the (2,2)-Splitting of Spacetimes

We propose a Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-splitting of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. In this Kaluza-Klein formalism we find that general relativity of 4-dimensional spacetimes can be interpreted in a natural way as a (1+1)-dimensional gauge theory. In a gauge where the (1+1)-dimensional metric can be written as the Polyakov metric, the action is describable as a (1+1)-dimensional Yang-Mills type gauge theory action coupled to a (1+1)-dimensional non-linear sigma field and a scalar field, subject to the constraint equations associated with the diffeomorphism invariance of the (1+1)-dimensional base manifold. Diffeomorphisms along the fibre directions show up as the Yang-Mills type gauge symmetries, giving rise to the Gauss-law constraints. We also present the Einstein's equations in the Polyakov gauge and discuss them from the (1+1)-dimensional gauge theory point of view. Finally we show that this Kaluza-Klein formalism is closely related to the null hypersurface formalism of general relativity.

gr-qc↗

arXiv1993

A Proposal of Positive-Definite Local Gravitational Energy Density in General Relativity

We propose a 4-dimensional Kaluza-Klein approach to general relativity in the (2,2)-splitting of space-time using the double null gauge. The associated Lagrangian is equivalent to the Einstein-Hilbert Lagrangian, since it yields the same field equations as the E-H Lagrangian does. It is describable as a (1+1)-dimensional Yang-Mills type gauge theory coupled to (1+1)-dimensional matter fields, where the minimal coupling associated with the diffeomorphism group of the 2-dimensional spacelike fibre space automatically appears. Written in the first-order formalism, our Lagrangian density directly yields a non-zero local Hamiltonian density, where the associated time function is the retarded time. From this Hamiltonian density, we obtain a positive-definite local gravitational energy density. In the asymptotically flat space-times, the volume integrals of the proposed local gravitational energy density over suitable 3-dimensional hypersurfaces correctly reproduce the Bondi and the ADM surface integral, at null and spatial infinity, respectively, supporting our proposal. We also obtain the Bondi mass-loss formula as a negative-definite flux integral of a bilinear in the gravitational currents at null infinity.

gr-qc↗

arXiv1992

(1+1)-Dimensional Methods for General Relativity

This is an article contributed to the Brill Festschrift, in honor of the 60th birthday of Prof. D.R. Brill, which will appear in the Vol.2 of the Proceedings of the International Symposia on Directions in General Relativity. In this article we present the (1+1)-dimensional method for studying general relativity of 4-dimensions. We first discuss the general formalism, and subsequently draw attention to the algebraically special class of space-times, following the Petrov classification. It is shown that this class of space-times can be described by the (1+1)-dimensional Yang-Mills action interacting with matter fields, with the spacial diffeomorphisms of the 2-surface as the gauge symmetry. The constraint appears polynomial in part, whereas the non-polynomial part is a non-linear sigma model type in (1+1)-dimensions. It is also shown that the representations of $w_{\infty}$-gravity appear naturally as special cases of this description, and we discuss briefly the $w_{\infty}$-geometry in term of the fibre bundle.

gr-qc↗

arXiv1992

Algebraically Special Class of Space-Times and (1+1)-Dimensional Field Theories

We present the (1+1)-dimensional description of the algebraically special class of space-times of 4-dimensions. It is described by the (1+1)-dimensional Yang-Mills action interacting with matter fields, with diffeomorphisms of 2-surface as the gauge symmetry. Parts of the constraints are identified as the gauge fixing condition. We also show that the representations of $w_{\infty}$-gravity appear naturally as special cases of this description, and discuss the geometry of $w_{\infty}$-gravity in term of the fibre bundle.

hep-th↗