Browsing by Author "Padmanabhan, Hamsa"

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Aspects of electrostatics in a weak gravitational ﬁeld
(Springer, 2009-11-13) Padmanabhan, Hamsa; Padmanabhan, T.
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 coor- dinates) is expressible as A0 = q/λ where λ is the afﬁne parameter distance along the null geodesic fromthe 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.
A comparison of CMB lensing e ciency of gravitational waves and large scale structure
(IUCAA, 2015-02) Padmanabhan, Hamsa; Rotti, Aditya; Tarun, Sauradeep
Nonrelativistic limit of quantum field theory in inertial and noninertial frames and the principle of equivalence
(American Physical Society, 2011-10-18) Padmanabhan, Hamsa; Padmanabhan, T.
We discuss the nonrelativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, and attempt to highlight and clarify several subtleties. In particular, we study the following issues: (a) While the action for a relativistic free particle is invariant under the Lorentz transformation, the corresponding action for a nonrelativistic free particle is not invariant under the Galilean transformation, but picks up extra contributions at the end points. This leads to an extra phase in the nonrelativistic wave function under a Galilean transformation, which can be related to the rest energy of the particle even in the nonrelativistic limit . We show that this is closely related to the peculiar fact that the relativistic action for a free particle remains invariant even if we restrict ourselves to Oð 1=c2 Þ in implementing the Lorentz transformation. (b) We provide a brief critique of the principle of equivalence in the quantum mechanical context. In particular, we show how solutions to the generally covariant Klein-Gordon equation in a noninertial frame, which has a time-dependent acceleration, reduce to the nonrelativistic wave function in the presence of an appropriate (time-dependent) gravitational field in the c !1 limit, and relate this fact to the validity of the principle of equivalence in a quantum mechanical context. We also show that the extra phase acquired by the nonrelativistic wave function in an accelerated frame, actually arises from the gravitational time dilation and survives in the nonrelativistic limit. (c) While the solution of the Schro¨ dinger equation can be given an interpretation as being the probability amplitude for a single particle, such an interpretation fails in quantum field theory. We show how, in spite of this, one can explicitly evaluate the path integral using the (nonquadratic) action for a relativistic particle (involving a square root) and obtain the Feynman propagator. Further, we describe how this propagator reduces to the standard path integral kernel in the nonrelativistic limit. (d) We show that the limiting procedures for the propagators mentioned above work correctly even in the presence of a weak gravitational field, or in the Rindler frame, and discuss the implications for the principle of equivalence.