A longitudinal component in massive gravitational waves arising from a bimetric theory of gravity

Abstract

After a brief review of the work of de Paula, Miranda and Marinho on massive gravitational waves arising from a bimetric theory of gravity, in this paper it is shown that the presence of the mass generates a longitudinal component in a particular polarization of the wave. The effect of this polarization on test masses is performed using the geodesic deviation. A the end of this paper the detectability of this particular polarization is also discussed, showing that its angular dependence could, in principle, discriminate such polarization with respect the two ones of general relativity, if present or future detectors will achieve a high sensitivity.

On the longitudinal response function of interferometers for massive gravitational waves from a bimetric theory of gravity

“…where m g is the mass of the graviton, and (g 0 ) µν the non-dynamical background metric (note: differently from [15] in this paper we work with G = 1, c = 1 and = 1, exactly like in [14]). In this way the field equations can be obtained in an einstenian form like…”

“…An extension of linearized general relativity which takes into account massive gravitons gives a weak-field stress-energy tensor [14,15] …”

“…Detectors for GWs will be important for a better knowledge of the Universe and also to confirm or ruling out the physical consistency of General Relativity or of any other theory of gravitation [9,10,11,12,13,14,15]. This is because, in the context of Extended Theories of Gravity, some differences between General Relativity and the others theories can be pointed out starting by the linearized theory of gravity [9,10,12,14,15].…”

“…This is because, in the context of Extended Theories of Gravity, some differences between General Relativity and the others theories can be pointed out starting by the linearized theory of gravity [9,10,12,14,15]. In this picture, recently, some papers in the literature have shown that, from a bimetric theory of gravity, it is possible to produce massive gravitational waves which generate a longitudinal component in a particular polarization of the wave [14,15]. After a review of previous works (i.e.…”

“…After a review of previous works (i.e. the work of de Paula, Miranda and Marinho [15] and my previous research [14]) on this topic, which is due to provide a context to bring out the relevance of the results, in this paper the longitudinal response function of interferometers for this particular polarization of the wave is computed in its full frequency dependence and in two different gauges, showing the gauge invariance, with specific application to the Virgo and LIGO interferometers.…”