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Unformatted text preview: Motion of a Charged Particle in a Non-symmetrical Gravitational Theory S. M. Saydur Rahman Department of Physics University of Cincinnati Cincinnati, Ohio 45221 December 3, 2001 Abstract A new theory of gravity in which the geometry of space-time has a non-symmetric field structure is described here. The combined electromagnetic and gravitational field in this theory maintain the validity of the weak equivalance principle. The field equations of the non-symmetric gravitational theory are derived by considering the presence of electromagnetic magnetic field by adopting a non-minimal coupling, which ensures the validity of equivalance principle. The static, spherically symmetric solution of a charged point particle is also obtained. 1 1 Introduction In 1979 Moffat  studied the nonsymmetrical gravitational theory (NGT). Soon after establishing the NGT, Moffat studied the field produced by an electric charge  adopting a minimal coupling of the electromagnetic field to gravitation. In 1989 Will  pointed that such a coupling violates the weak equivalance principle (WEP) because it predicts that the test body gravitational acceleration depends upon its internal structure. Then by writing a more general coupling, Mann et al.  were to able to maintain the validity of the WEP. In this paper we have studied the field of a charge particle in a non-symmetric gravitational theory, by using the Lagrangian given by Mann et al and Ragusa . In sec-2 we first study the consequences of this more general coupling on the electromagnatic field equations and corresponding energy-momentum tensor. In sec-3 we study the field produced by an electric charge in the new scheme. 2 The electromagnatic action The electromagnetic action given by Mann et al. is, I em =- 1 16 Z d 4 x - gfg g [ ZF F + (1- Z ) F F + Y F F ] (1) where, F = A - A , is the electromagnetic field tensor (with vector potential A )....
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