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- Title
Hamiltonian approach to frame dragging.
- Authors
Kenneth Epstein
- Abstract
Abstract A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson–Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials.
- Subjects
HAMILTONIAN systems; INHOMOGENEOUS materials; LORENTZ transformations; RELATIVITY (Physics)
- Publication
General Relativity & Gravitation, 2008, Vol 40, Issue 7, p1367
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-007-0535-y