Cosmological Constant and the Speed of Light (original) (raw)

The Optical Properties of Gravity

Journal of Modern Physics

The resemblance between the equation for a characteristic hypersurface through which wavefronts of light rays pass and optical metrics of general relativity has long been known. Discontinuities in the hypersurface are due to refraction involving Snell's law, as opposed to discontinuities in time that would involve the Doppler effect. The presence of a static gravitational potential in the metric coefficients is accounted by an index of refraction that is entirely dependent on the space coordinates. The two-time Einstein metric must be reinterpreted as a two-space scale metric because of the two different speeds of light. It is shown that the Schwarzschild metric is incompatible with the laws of classical physics. Gravitational waves are identified with the transverse-transverse plane wave solutions to Einstein's equations in vacuum, which propagate at the speed of light. Yet, when energy loss is evaluated, his equations acquire, surprisingly, a source term. Poynting's vector, which is not a true vector, is defined in terms of the pseudo-gravitational tensor, and hence energy is neither localizable nor conserved. The solutions to the equations of motion are geodesics and, by definition, do not radiate. A finite speed of propagation implies that gravitational waves should aberrate, like their electromagnetic wave counterparts, and if they do not aberrate they cannot radiate.

A Note on the Effect of the Cosmological Constant on the Bending of Light

Modern Physics Letters A, 2013

We take another look at the equations behind the description of light bending in a Universe with a cosmological constant. We show that even within the impact parameter entering into the photon's differential equation, and which is defined here with exclusive reference to the beam of light as it bends around the central mass, lies the contribution of the cosmological constant. The latter is shown to enter in a novel way into the equation. When the latter is solved our approach implies, beyond the first two orders in the mass-term and the lowest-order in the cosmological constant, a slightly different expression for the bending angle from what is previously found in the literature.

Note on the relationship between the speed of light and gravity in the bi-metric theory of gravity

2005

Relationship between the speed of gravity c g and the speed of light c e in the bi-metric theory of gravity is discussed. We reveal that the speed of light is a function of the speed of gravity which is a primary fundamental constant. Thus, experimental measurement of relativistic bending of light propagating in time-dependent gravitational field directly compares the speed of gravity versus the speed of light and tests if there is any aether associated with the gravitational field considered as a transparent 'medium' with the constant refraction index.

Anisotropic velocity of light in noninertial reference frames

Up to now little attention has been paid to an expression for the velocity of light in a gravitational field derived by Einstein in 1911. It is shown that (i) this expression represents the proper velocity of light (since it is defined in terms of proper time and length), (ii) the proper velocity of light is anisotropic in non-inertial reference frames, and (iii) unlike the coordinate velocity of light (which is a function only of the gravitational potential of the point at which it is determined) the proper velocity of light depends on the difference of the gravitational potential of the source and observation points and is expressed in terms of the initial velocity with which a light signal is emitted at the source point. The proper velocity of light is of crucial importance for two reasons: (i) it is this velocity (not the coordinate velocity) that is involved in the verification of the equivalence principle by calculating the potential and the electric field of a charge in an accelerating reference frame N a and in a frame N g supported in a uniform gravitational field as well as the self-force acting on a charge in N a and N g on account of its own electric field, and (ii) the proper velocity of light demonstrates that the local velocity of light is not always c which contradicts the standard curved-spacetime interpretation of general relativity.

The cosmological constant and the gravitational light bending

General Relativity and Gravitation, 2011

The solution of the null non-radial geodesic in a Schwarzschild-de Sitter background is revisited. The gravitational bending of a light ray is affected by the cosmological constant, in agreement with the findings of some previous investigations. The present study confirms that the leading correction term depends directly not only on  but also on the impact parameter and on the angular distance to the source. Using the resulting lens equation, the projected mass of the lens was estimated for several systems displaying Einstein rings. Corrections on the masses due to  are, on the average, of the order of 2%, indicating that they are not completely negligible for lens systems at cosmological distances.

Propagation of light in a gravitational background

Physical Review D, 1997

We study the propagation of an electromagnetic field in a weak gravitational background generated by a rotating mass. The solution of the Maxwell equations beyond the geometrical optics shows, together with the well-known deflection and rotation of the polarization plane already present in the geometrical optics approximation, new classical dispersive effects. We analyze such effects at first order in the gravitational constant G. In the case of an incoming wave with linear polarization they consist in the development of a component of circular polarization, a breaking of the orthogonality of the electric and magnetic fields, and additional contributions to the deflection of the beam and the rotation of the polarization plane. ͓S0556-2821͑97͒06422-9͔

Wave propagation in a gravitational field

Physics Letters A, 1987

The geometric optics approximation in general relativity is critically examined. The well-known result that rays of radiation follow null geodesics of the gravitational field is shown to be valid only in the limit of vanishing wavelength. New covariant definitions for the frequency and wave vector of external radiation are presented, and it is pointed out that general relativity restricts the product of the magnitude of the wave vector and a suitably defined effective radius of curvature of spacetime to be greater than, or of the order of, unity.

The relevance of the cosmological constant for lensing

General Relativity and Gravitation, 2010

This review surveys some recent developments concerning the effect of the cosmological constant on the bending of light by a spherical mass in Kottler (Schwarzschild-de Sitter) spacetime. Some proposals of how such an effect may be put into a setting of gravitational lensing in cosmology are also discussed. The picture that emerges from this review is that it seems fair to assert that the contribution of to the bending of light has by now been well established, while putting the lightbending terms into a cosmological context is still subject to some interpretation and requires further work and clarification.