Rotation speed near light speed increasing gravity?

[SpiderET]

Based on special relativity object with speed nearing to speed of light has increased mass and also its gravity pull is increasing. But this is in special relativity calculated for linear moving objects, not for rotating objects.

Based on general relativity does increase mass and gravity of objects which are rotating at speeds near speed of light? Let's assume a star which is rotating so fast, that's on equator it almost reaches speed of light.

I don't mean rotational frame dragging effect (Thirring Lense effect). This effect is much smaller than potential mass/gravity increase caused by increased mass caused by speed near to speed of light.

 

[Jonathan Scott]

Based on special relativity object with speed nearing to speed of light has increased mass and also its gravity pull is increasing. But this is in special relativity calculated for linear moving objects, not for rotating objects.

Based on general relativity does increase mass and gravity of objects which are rotating at speeds near speed of light? Let's assume a star which is rotating so fast, that's on equator it almost reaches speed of light.

I don't mean rotational frame dragging effect (Thirring Lense effect). This effect is much smaller than potential mass/gravity increase caused by increased mass caused by speed near to speed of light.

The kinetic energy of rotation effectively adds on to the rest mass for purposes of determining the distant field. So do any other forms of internal energy.