Frame-dragging caused by a rotating object is predicted by the general theory of relativity. The experiment Gravity Probe B has been devoted to the testing of the frame dragging effect due to Earth’s rotation (although it is much smaller compared to that of a black hole). The final experimental result is consistent with the prediction of general relativity!

To further understand what the frame-dragging effect is, let us explore the difference between ray trajectories around a non-rotating black hole and a rotating black hole.


The above image shows rays around a non-rotating black hole. The sphere represents the event horizon of the black hole. The event horizon is a virtual surface, not a physical surface, inside which even light cannot escape to the outer Universe. An event horizon is a unique property of black holes.

[Try this]: show or hide the horizon by click the “horizon” box in the control panel.


The above image, on the other hand, shows rays around a rapidly rotating black hole. An additional structure (outside the event horizon) called the ergosphere now appears. The ergosphere is defined by a region inside which photons must co-rotate in the same direction that black hole rotates. The outer boundary of the ergosphere, called the static limit, is represented by the the transparent surface outside the event horizon. The static limit is named so because everything (even light) inside the static limit cannot  remain static with respect to a distant star.

[Try this]: show or hide the ergosphere by click the “ergosphere” box in the control panel.

The spin parameter, a , is used to describe how fast a black hole is spinning.  Defined by the total angular momentum of the black hole divided by its mass, the value of a falls into -1 < a < 1.

The black hole is non-rotating when a = 0, and the black hole is rapidly rotating when a → ±1.  Positive and negative sign of a mean the black hole rotates in opposite direction.

[Try this]: control the spin parameter by sliding the “spin” bar in the control panel.

With Odyssey_Edu, we can explore the frame-dragging effect by observing how ray trajectories vary with different black hole spins!

[Try this]: control the inclination angle for incoming rays by sliding the “inclination” bar in the control panel.

When the incoming rays originate from above a rotating black hole, the following image is what we will see (in order to make the trajectories clearer, the event horizon and ergosphere are hidden in this image)!