The Ultimate Future of the Universe, Black Hole Event Horizons, Holography, and the Value of the Cosmological Constant

Abstract

Hawking has shown that if black holes were to exist in a universe that expands forever, black holes would completely evaporate, violating unitarity. I argue this means unitarity requires that the universe exist for only a finite future proper time. I develop this argument, showing that unitarity also requires the boundaries of all future sets to be Cauchy surfaces, and so no event horizons can exist. Thus, the null generators of the surfaces of astrophysical black holes must leave the surface in both time directions, allowing non-spherical topologies for black hole surfaces. Since all information eventually escapes astrophysical black holes, and since the null surfaces defining astrophysical black holes are Cauchy surfaces, holography automatically holds. I further show that unitarity requires the effective cosmological constant to be zero eventually, since otherwise the universe would expand forever.