 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  
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  
Type  
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  
Program  
Affiliation  
Degree Grantor 
University of British Columbia

Campus  
Scholarly Level 
Graduate

Aggregated Source Repository 
DSpace

Item Media
Item Citations and Data
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.