Aspects of electrostatics in a weak gravitational field |
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Authors: | Hamsa Padmanabhan and T Padmanabhan |
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Institution: | 1.Fergusson College,Pune University,Pune,India;2.IUCAA,Pune University Campus,Pune,India |
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Abstract: | Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using
the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent
procedures and are interpreted in an intuitive manner. Specifically: (a) We discuss possible definitions of the electric field
in curved spacetime (and noninertial frames), argue in favour of a specific definition for the electric field and discuss
its properties. (b) We show that the electrostatic potential of a charge at rest in the Rindler frame (which is known and
is usually expressed as a complicated function of the coordinates) is expressible as A
0 = q/λ where λ is the affine parameter distance along the null geodesic from the charge to the field point. (c) This relates well with the
result that the electric field lines of a charge coincide with the null geodesics; that is, both light and the electric field
lines ‘bend’ in the same manner in a weak gravitational field. We provide a simple proof for this result as well as for the
fact that the null geodesics (and field lines) are circles in space. (d) We obtain the sum of the electrostatic forces exerted
by one charge on another in the Rindler frame and discuss its interpretation. In particular, we compare the results in the
Rindler frame and in the inertial frame and discuss their consistency. (e) We show how a purely electrostatic term in the
Rindler frame appears as a radiation term in the inertial frame. (In part, this arises because charges at rest in a weak gravitational
field possess additional weight due to their electrostatic energy. This weight is proportional to the acceleration and falls
inversely with distance—which are the usual characteristics of a radiation field.) (f) We also interpret the origin of the
radiation reaction term by extending our approach to include a slowly varying acceleration. Many of these results might have
possible extensions for the case of electrostatics in an arbitrary static geometry. |
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