Black Holes, Singularities, Confusion

Only for Scwarzschild geometry, young Padawan

Hi Ender, geat question Principally, NS occur in two situations: possibly as the end-state of Hawking Evaporation of an astrophysical (but microscopic) black hole; and as part of the parameter space of (i.e. one version of) the non-trivial black holes, such as Reisnner Nordstrom (charged), Kerr (spinning), Kerr-Newman (spinning AND charged) or some of the string theory inspired variants.The first case occurs because the mass of the black hole is reducing owing to Hawking Radiation. This reduces the size of the Horizon (via that bit of maths helpfully provided above). The evaporation rate is runaway - the smaller the black hole gets, the hotter it gets, the faster it evaporates, etc, etc. Eventually the horizon and singularity coalesce, and... we don't know. Maybe a bang (gamma-ray burster?), maybe a sniffle, maybe nothing left, maybe a naked singularity. It will take a lot more knowledge of quantum gravity before we know, but string theory provides some clues.I'll come back to the second case in a while.

Ok, from the perspective of an external observer, light travels at c, about 300,000,000m/s. If we choose units where we measure time in seconds and distance in light-seconds (300,000,000m) and we draw one second as the same length as a light-second, we get the 45 degree line.From the perspective of light, you are correct it doesn't age - but also it doesn't move either, because distance in the direction of travel has been Lorentz contracted to zero. This sort of makes sense... it doesn't age as it travels, but that's becasue it doesn't have to go anywhere! So no, even from the perspective of light itself, it doesn't think of itself as travelling "horizontally". From our perspective, light does travel through time, it just does not age as it does so. There is more than one kind of time

To add to NWRs explanation...Take a length of rope. Stand in the middle of a field and put a stake in the ground. Tie one end of the rope to the stake. Walk away from the stake paying out a length of rope, say 10 feet. With the rope taut, walk around the stake once, measuring the distance you walk. Compare your answer to what you would expect from C=2xPixR. It should match of course.Try it again with 50 feet of rope, then with 1000 feet, then 10 miles, then 100 miles, and finally 1000 miles. What do you notice? Your measured distances start to deviate from the usual formula for the circumference of a circle. Why?Of course, you are not dealing with flat circles. You are on the Earth's surface which is curved, and your deviations from the circle formula actully measure the curvature of the Earth.Now repeat the exercise, but make the Earth your centre point, and move off into space to make your circle. You will experience the same effect, owing to the curvature of space generated by the Earth. You can't see this curvature as it is slight, but you can measure its effect. The effect is much more pronounced and easily visible around a black hole.Rather than circles, you could draw triangles on the ground and measure the angles. Once your triangle become large enough you realise that the angles actually add to more than 180 degrees, revealing a positively curved ground. The same thing happens in space: you find that the angles of triangles with perfectly straight lines don't add up to 180 degrees.Edited by cavediver, : Finally remembered how to spell taut - actually, the wife pointed it out