Out stargazing with the naked eye,if I focus on a particular star,I can see it pretty clearly but if I shift my focus slightly to the side of that star it appears to be brighter and even more focused than before. Is this effect explainable using GR or could it be an aberration of my eyesight?

It has to do with the anatomy of the eye. In low light, rod cells are picking up the light from the stars, and the rod cells are primarily located away from the center of the eye. Hence, looking slightly off center engages more rod cells, which picks up more light.

Brilliant. Thank you,Zapatos.

Just to fill in the details a bit. You have both rods and cone receptors. Rods can only sense light intensity (black and white) while cones can distinguish color. Rods are more light sensitive than cones. When you are looking directly at something the image is focused at the center of the retina where there are more cone than rods. But is the periphery region around that, there are more rods than cones, so that region is more light sensitive. Thus you can see faint objects better if you look at then out of the side of your eye and are not looking directly at them. You are trading light sensitivity for color sense.

Thank you too,Janus. No need for Albert after all,lol.

Okay, so this phenomenon is not to be confused with "twinkling" of stars, right? Because from what I know that is caused by refraction of light due to the atmosphere.

 

Please do clarify.

Okay, so this phenomenon is not to be confused with "twinkling" of stars, right? Because from what I know that is caused by refraction of light due to the atmosphere.

 

Please do clarify.

You are correct. Twinkling of stars is an external effect caused by variable refraction related to atmospheric "turbulence". The phenomenon discussed here is internal, related to our optical system.

Okay, so this phenomenon is not to be confused with "twinkling" of stars, right? Because from what I know that is caused by refraction of light due to the atmosphere.

 

Please do clarify.

It's noticeable on stars that are of too low magnitude for the cones but not the rods i.e. when you move your eyes they pop in and out of visibility as they cross the two zones of light receptors.