Field Energy in GEM Field Theory W J
- Slides: 10
Field Energy in GEM Field Theory W. J. Wilson Department of Engineering and Physics University of Central Oklahoma Edmond, OK 73034
Outline I. III. IV. V. VII. The Field Energy Problem of GR Linearized GR GEM Theory Analogy of GEM with Maxwell EM Theory Gravitational Field Energy in GEM Theory Gravitational Radiation in GEM Theory Stability of Gravitational Bound States in GEM Conclusions OAS Fall 2007 Technical Meeting 2/10
The Field Energy Problem of GR n n n There is no well-defined gravitational field energy in General Relativity (L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Sec. 96) Standard methods to obtain the energy-momentum tensor in GR do not work. They yield a pseudo-tensor that is not unique. Usually asserted on the basis of the principle of equivalence that the gravitational energy cannot be localized. (C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation) OAS Fall 2007 Technical Meeting 3/10
Linearized GR GEM Theory General Relativity (GR) Gravitoelectromagnetic Theory (GEM) For “weak” fields See Bahram Mashhoon, “Gravitoelectromagnetism: A Brief Review, ” ar. Xiv: gr-qc/0311030, 8 Nov 2003 And references therein. For “weak” fields OAS Fall 2007 Technical Meeting 4/10
Maxwell EM Theory GEM Theory Negative Sign OAS Fall 2007 Technical Meeting 5/10
Maxwell EM Theory Energy Flow GEM Theory Energy Flow Negative Sign OAS Fall 2007 Technical Meeting 6/10
Energy Flow in GEM Wave − + A “graviton” carries negative energy in the +k direction Equivalent to positive energy going in the –k direction OAS Fall 2007 Technical Meeting 7/10
EM- Radiation from Accelerating Charge Gravitational Radiation from Accelerating Mass Negative Sign Accelerating charge emits radiation that carries positive energy away. Emitting system loses energy. Accelerating mass emits radiation that carries negative energy away. Emitting system gains energy. OAS Fall 2007 Technical Meeting 8/10
Stability of Gravitational Bound States DE = - |DE| Energy R r R’ Em + |DE| M R Em m v E m → E m′ + D E Em = Em′ + DE Em′ = Em − DE = Em + |DE| OAS Fall 2007 Technical Meeting E m′ > E m 9/10
Conclusions Gravitational Radiation carries negative energy away from radiating (accelerating) sources n All gravitational bound states are slowly expanding n Possible physical explanation of Hubble expansion of the Universe n OAS Fall 2007 Technical Meeting 10/10
