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The possible detection of gravitational waves by interferometric observations of distant light sources is studied. It is shown that a gravitational wave affects the interferometric pattern of stellar light in a particular way. Michelson and Hanbury Brown-Twiss interferometers are considered, and it is shown that the latter is the most adequate for such a detection.

A gravitational wave (GW) could be detected indirectly by its interaction with the light emitted by astronomical objects. Thus, for instance, the passage of a GW produces a time delay in the signal received from distant sources (Estabrook and Wahlquist [

In this paper, we study the effect of GWs on the interferometry of stellar light. Two basic types of interfero- metric devices used in astronomy are considered: the Michelson (see, e.g., [

Section 2 of the present paper is devoted to the analysis of an electromagnetic wave in the presence of a plane fronted GW. The analysis is based on previous works (Hacyan [

The metric of a plane GW in the weak field limit is

where the two degrees of polarization of the GW are given by the potentials

In the following, quadratic and higher order terms in f and g are neglected, and we set

The direction of a light ray in the absence of a GW is k, with

thus defining the angles

In the short-wave length approximation, the electromagnetic potential is taken as

where S is the eikonal function satisfying the equation

The electromagnetic vector is [

where

and the eikonal function is

As in Ref. [

where

The four vector

where

Let us use a tetrad

Accordingly the tetrad components of

and

Notice in particular that

The electric field in tetrad components is

and of course

For an electromagnetic plane wave with wave vector

where

are Stokes parameters (

Consider two detectors with space-time coordinates

where

the subindexes a, b and j refer to the labels 1 and 2 of x and k.

A Michelson interferometer permits to measure the average intensity

where the second term is the interference term.

A Hanbury Brown-Twiss interferometer permits to measure the interference between intensities:

where the second term is the interference between the two intensities.

Define

With this notation, we have for a Michelson interferometer:

and for a Hanbury Brown-Twiss interferometer:

Define also the complex functions

and

Then

and

In the absence of GWs,

implying that

where

It should be noticed that the field correlation

highly oscillatory and hinder a precise measurement with a Michelson interferometer. On the other hand, such terms do not appear in the correlation of the intensities:

The time dependence is included only in the terms

As a particular application of the above formulas, we can calculate the temporal coherence of a single signal in the presence of a GW. This can be obtained setting

and

Explicitly, in this particular case,

which is the only relevant term for the time correlation of the intensity correlation, and is entirely due to the GW.

In the particular case of a sinusoidal monochromatic GW of frequency

where

As for a pulse of GW, it can be approximated by a delta function:

where

The main conclusion from the present results is that the passage of a GW produces a time-dependent perturbation in the intensity interference of a distant light sources, an interference which would otherwise have a

static pattern. Thus, a time variation of

Shahen Hacyan, (2016) Signature of Gravitational Waves in Stellar Spectroscopy. Journal of Modern Physics,07,552-557. doi: 10.4236/jmp.2016.76058