General Relativity Evolution of the Photons in Dielectrics

General Relativity Evolution of the Photons in Dielectrics

Copyright: © 2014 |Pages: 29
DOI: 10.4018/978-1-4666-4687-2.ch010
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Abstract

Basic Einstein general relativity equations are linearized and coupled with Maxwell electromagnetic field equations to produce local gravitationally corrected Minkowsky space metrics; fundamental application on gravity action of an intense laser beam upon a weaker parallel one in dielectrics is undertaken towards evaluating of the space deviation phase shift and confirming the general equivalence principle of inertia for phonons in nanomaterials.
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10.2. Equivalence Principle And Linear Einstein Equations Of Gravity

According with the principle of equivalence, for free fall coordinates of the system, , equations of motion follow “straight line” in curved space-time (Hawking & Ellis 1973; Hayashi & Shirafuji 1979):

(10.1) with proper time:

(10.2)

Considering any other local coordinate system, , which can be Cartesian on the local flat space etc, we will have the dependence:

(10.3)

With this relation (10.1) becomes:

(10.4)

Multiplying the relation with we obtain:

(10.5) and noting:
(10.6) and the affine connection:
(10.7) we will obtain:
(10.8) which is the equation of free fall in line according with the principle of equivalence in curved space time, meaning equation geodesy.

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