JOURNEEY TO A BLACK HOLE

This section will describe a trip to the most compact star imaginable: a black hole. A black hole can be thought of as any star compressed so greatly that it not only has a photon sphere but also an event horizon. The black hole discussed here will be considered to be non-rotating so that gravity external to its event horizon is described by the Schwarzschild metric and the analysis given above. Although radial distances will be given from the black hole in both Schwarzschild radii (R_S) and kilometers (km), please note that one cannot simply measure this distance with a series of meter sticks. This is because, for one reason, any meter stick closer than the event horizon could not be seen by an observer outside the event horizon. A better way of visualizing radial distance is to picture orbiting the black hole at a fixed distance, measuring the circumference of the orbit, and dividing by 2 pi.

Far from the black hole an undistorted night sky is visible with a very small patch of fuzz in the center. As the viewer nears the black hole the fuzzy patch becomes discernable as an unusual conglomeration of stellar images.

The first sky Einstein ring, is an invisible circle centered on the black hole and dividing the first complete set of images (those angularly furthest from the disk of the black hole which lie between the zeroth and first Einstein rings) from the second complete set of images. Each image in the first set is always brighter than the corresponding image in the second set. The second sky Einstein ring appears in the conglomeration of stellar images near the apparent photon sphere position, just outside the photon sphere. A complete image of the sky can be seen between these two Einstein rings. Note that typically stellar images get much dimmer as one looks closer to the apparent photon sphere position, but the average surface brightness of the sky there remains unchanged.

The viewer now does an orbit around the black hole at the radius of 10 R_S (42 km).

Remember, an entire single image of the sky is contained between the zeroth and first sky Einstein rings. It is therefore impossible for an image to leave this region - it cannot just "go" across this ring and end up between the first and second Einstein rings. Stars (in reality) approaching the nadir point below the black hole from the viewer (moving slowly) have images that appear to approach the Einstein ring and get very bright (moving rapidly), eventually receding from this Einstein ring and dimming.