How does the geodesic equation of a charge change in the presence of an electromagnetic field?
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The geodesic equation of a charge is modified in the presence of an electromagnetic field. The Lorentz force law is included in the gravitational equations of geodesic motion, leading to the motion of charged particles in the electromagnetic field . The canonical momentum is used in the mass/momentum relationship, where the kinetic momentum is replaced by the canonical momentum, which includes the electromagnetic vector potential . This modification allows for the motion of charged particles in the electromagnetic field to be obtained through variational calculus . The presence of the electromagnetic field affects the behavior of geodesics, causing the horizon to shrink and modifying the radial and circular trajectories of both massless and massive particles . The radius of the innermost circular orbit also shrinks due to the presence of the electromagnetic field .
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| The provided paper does not discuss the geodesic equation of a charge in the presence of an electromagnetic field. | |
6 Citations | The geodesic equation of a charge in the presence of an electromagnetic field is the same as the classical equations of motion of a relativistic particle with charge Z in the electromagnetic background. |
Open access•Posted Content | The paper explains that in the presence of an electromagnetic vector potential, the Lorentz force can be obtained by replacing the kinetic momentum with a canonical momentum in the mass/momentum relationship. The motion of charged particles in this potential can then be obtained using variational calculus. |
Open access 01 Jan 1999 | The geodesic equations for a charged particle in the unified theory of gravitational and electromagnetic interactions are the same as the equations of motion for a charged particle in general relativity. |
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