Relativity Lite

Gravity Lite | 63 calculations, * that the astronaut will hardly feel them at all. [Sh]e will survive, almost unscathed, right up to the edge of the probabilistic quantum gravity singularity. Only at the singularity’s edge, just as [s]he comes face-to-face with the laws of quantum grav- ity, will the astronaut be killed—and we cannot even be absolutely sure [s]he gets killed then, since we do not really understand at all well the laws of quantum gravity and their consequences.” † There may even be a way to avoid a singularity completely. If the collapsing star were spinning, it would collapse onto a ring of no thickness (whose radius increases with the ratio of the rotational velocity to the mass of the black hole ‡ ) rather than a point of no thickness. § In fact, it’s very unlikely that a star would form with zero spin, or lose its spin as it collapses, so these Kerr black holes, ¶ with their ring singularity, would be the norm. Our astronaut could conceivably pass through the center of the ring and miss the singularity. But then what? Einstein’s equations allow a solution in which our astronaut would pass through the ring into a region called a white hole because time is reversed there so everything near the ring singularity travels out of a different one-way membrane into a flat region of our universe other than the one it started in or into another universe. I emphasized the word “allow” because one would actually have to “start” with the two flat regions of spacetime connected by a singularity so that the collapse of a star is unlikely to lead to such a wormhole . ** No white hole has ever been seen. Supposing such a wormhole is found, and our astronaut falls in, appearing redder and redder and seeming to take forever to do so to the outside world. She looks out and sees the outside universe appearing bluer and bluer and watches their clocks speed up. She sees an inconceivable number of years pass outside while it takes a few minutes of her time for her to pass through the wormhole into some other part of the same universe she left, in the * A. Ori, Phys. Rev. Lett. 67 , 789 (1991). † Kip S. Thorne, From Black Holes to Time Warps: Einstein’s Outrageous Legacy (W. W. Norton, New York, 1994), p. 479. ‡ Robert M. Wald, General Relativity (University of Chicago Press, Chicago, 1984), p. 314–15, gives the ring singularity at r Mc = GJ 3 , where J is the total angular momentum of the collapsed star and its gravitational field (Steven Weinberg, Gravita- tion and Cosmology: Principles and Applications of the General Theory of Relativity [Wiley, New York, 1972], p. 240) and G is the gravitational constant. § For a spinning Kerr black hole, the surface of infinite time dilation and the one-way membrane are two different ellipsoidal surfaces, whereas for a nonspinning black hole, these are combined into the spherical shell at the Schwarzschild radius. We will see infinite time dilation for an astronaut passing through the outermost ellipsoid of revolution, r + , but she could reemerge from this surface. The inner ellipsoid of revolution, r − , is the one-way surface of the Kerr black hole. Once she passes through r − , our astronaut is lost to us. But interestingly, maybe not lost to herself. See Ronald Adler, Maurice Bazin, and Menachem Schriffer, Introduction to General Relativity (McGraw-Hill, New York, 1975), p. 265. ¶ Roy P. Kerr, Phys. Rev. Lett. 11 , 237–38 (1963). ** Robert M. Wald, General Relativity (University of Chicago Press, Chicago, 1984), p. 155.