From our experience, we know that light travels along straight paths. However, light gets deflected by the gravitational field of massive objects.
Then, according to Newton's 'actio equals reactio', light must also be the source of a gravitational field.
The gravitational properties of light is the topic of our article, “Gravitational properties of light – The gravitational field of a laser pulse”.
We use the model of a laser pulse of length L and very small beam diameter. The pulse travels from its emission point to its absorption point.
We use the framework of linearized Einstein gravity, where it is assumed that the spacetime metric, g,only differs by a small perturbation, h ,from the background metric, eta. We assume the background to be that of flat spacetime.
We solve the resulting equations analytically. In the laboratory frame, the non-zero components of the resulting metric perturbation only differ by sign.
Here, we a video of the evolution of their absolute value. The video starts shortly before the pulse emission and ends shortly after its absorption.
In the dark purple regions the metric perturbation vanishes. The high values of the metric perturbation, seen as a yellow spot, coincide with the pulse position. The perturbations due to the pulse propagate spherically with the speed of light from its position. Because the pulse also propagates at the speed of
light, it is always at the front of its effect on the metric.
An interesting observation is the effect of the polarization of the laser pulse. We find that the metric perturbation shows modulations for linear but not for circular polarization.
Because the whole problem is rotationally symmetrical, the metric perturbation is independent of the polarization direction.
The physical effect of the metric perturbation can be extracted from the Rieman curvature tensor R.
The curvature tensor provides us with information about the spread and the contraction of neighbouring trajectories of test particles.
Here, we see a particular component of the curvature tensor evolving in time. Red corresponds to negative values and blue to positiv values. Our most interesting observation is that the curvature tensor is only non-zero in spherical shells. These shells expand with the speed of light and are causally disconnected from the pulse during its free propagation. This means that a gravitational effect is only induced during emission and absorption.
The gravitational effect of emission is an attractive force. The gravitational effect of absorption is a repulsive force.
In contrast to the gravitational force due to a massive object, the gravitational force due to a laser pulse decreases only with the inverse of the distance to the pulse.
It is interesting to note that two parallel propagating light pulses attract each other if they counterpropagate but not if they co-propagate.
A periodically pulsed laser leads to an oscillating gravitational field. In our article, we compare the corresponding curvature to that expected for gravitational waves from cosmic sources.
The gravitational effect of a laser pulse is extremely weak, and, at the moment, there seems to be no way to detect it.
However, as light plays a fundamental role in modern physics, insights into its gravitational field are of great importance. For all the interesting details and magnitudes of the effects, have a look at our article, which is freely available in New Journal of Physics.