 Library Home /
 Search Collections /
 Open Collections /
 Browse Collections /
 UBC Theses and Dissertations /
 Gravitational energy and conserved currents in general...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Gravitational energy and conserved currents in general relativity Keefer, Bowie Gordon
Abstract
The problem of the definition of gravitational energy is reconsidered. In the Einstein theory all matter and fields except gravity must have a well defined local distribution of energy that is described by the energymomentum tensor. A gravitational "energymomentum complex" may be defined in analogy to an energymomentum tensor. However there is an infinite number of expressions for the gravitational complex, and each expression must depend explicitly upon the choice of reference system. Following a review of earlier works, a study is made of physical and geometric considerations which might select usefully distinguished gravitational complexes and reference frames. This investigation is conducted within the vierbein formulation of general relativity. Conserved currents corresponding to generalized energy, momentum and spin are derived from action principles. These currents transform as vector densities under general coordinate transformations, but depend on the vierbein frame chosen. The expressions for the energy and momentum currents are not unique, as their general expression contains three arbitrary constants. Physical examples are ised to test possible choices of these constants and possible vierbein frames. The generalized vierbein energy and momentum currents are calculated for asymptotically flat, radiative spacetimes. The physical requirements that the energy of an isolated system cannot increase when there is no incoming radiation, and that there, be invariance under vierbein transformations respecting boundary conditions appropriate to the asymptotic symmetry group, are imposed on the generalized energy integral. These requirements determine a unique expression for the energy current which contains no second order field derivatives. Since the boundary conditions do not specify the vierbein frame everywhere, the distribution of gravitational energy is not well defined even when the concept of total energy is made legitimate by asymptotic spacetime symmetry. It has been conjectured repeatedly that a local density of gravitational energy could be defined even in the absence of spacetime symmetries through a suitable choice of gravitational complex and of reference frame. This is certainly attainable in a formal sense, as invariant vierbein frames are defined by the principal directions of the curvature tensor and of the energymomentum tensorof matter. It is shown by the consideration of gravitational radiation fields that such definitions will not suffice to localize gravitational energy.
Item Metadata
Title  Gravitational energy and conserved currents in general relativity 
Creator  Keefer, Bowie Gordon 
Publisher  University of British Columbia 
Date Issued  1971 
Description 
The problem of the definition of gravitational energy is reconsidered. In the Einstein theory all matter and fields except gravity must have a well defined local distribution of energy that is described by the energymomentum tensor. A gravitational "energymomentum complex" may be defined in analogy to an energymomentum tensor. However there is an infinite number of expressions for the gravitational complex, and each expression must depend explicitly upon the choice of reference system.
Following a review of earlier works, a study is made of physical and geometric considerations which might select usefully distinguished gravitational complexes and reference frames. This investigation is conducted within the vierbein formulation of general relativity. Conserved currents corresponding to generalized energy, momentum and spin are derived from action principles. These currents transform as vector densities under general coordinate transformations, but depend on the vierbein frame chosen. The expressions for the energy and momentum currents are not unique, as their general expression contains three arbitrary constants. Physical examples are ised to test possible choices of these constants and possible vierbein frames.
The generalized vierbein energy and momentum currents are calculated for asymptotically flat, radiative spacetimes. The physical requirements that the energy of an isolated system cannot increase when there is no incoming radiation, and that there, be invariance under vierbein transformations respecting boundary conditions appropriate to the asymptotic symmetry group, are imposed on the generalized energy integral. These requirements determine a unique expression for the energy current which contains no second order field derivatives. Since the boundary conditions do not specify the vierbein frame everywhere, the distribution of gravitational energy is not well defined even when the concept of total energy is made legitimate by asymptotic spacetime symmetry.
It has been conjectured repeatedly that a local density of gravitational energy could be defined even in the absence of spacetime symmetries through a suitable choice of gravitational complex and of reference frame. This is certainly attainable in a formal sense, as invariant vierbein frames are defined by the principal directions of the curvature tensor and of the energymomentum tensorof matter. It is shown by the consideration of gravitational radiation fields that such definitions will not suffice to localize gravitational energy.

Genre  Thesis/Dissertation 
Type  Text 
Language  eng 
Date Available  20110322 
Provider  Vancouver : University of British Columbia Library 
Rights  For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. 
DOI  10.14288/1.0084878 
URI  
Degree  Doctor of Philosophy  PhD 
Program  Physics 
Affiliation  Science, Faculty of; Physics and Astronomy, Department of 
Degree Grantor  University of British Columbia 
Campus  UBCV 
Scholarly Level  Graduate 
Aggregated Source Repository  DSpace 
Item Media
Item Citations and Data
License
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.