Giddings replies:Emil Mottola and Ruslan Vaulin emphasize that there are different versions of massive remnant scenarios—with horizonless star-like objects replacing black holes. Fuzzballs, firewalls, and gravastars are examples. A black hole may form and then transition into a massive remnant, or a collapsing object may transition into a massive remnant just before it reaches the horizon. (Fuzzball supporters have varied between these possibilities.) In my article, space limited discussion to the first version, but many believe the latter version faces comparable challenges with locality and with observation.
Consider gravitational collapse of a fluid ball of mass M. Its density at horizon formation is around 1016 (M☉/M)2 g/cm3, where M☉ is the mass of the Sun. With M the mass of our galactic black hole, Sgr A*, that density is about 1000 g/cm3; for the largest known black holes, it is about 10−4 g/cm3. Both densities are within well-explored regimes—the latter is less than the density of air.
In the conventional picture, a fluid element crossing the horizon is nearly freely falling. To avoid black hole formation, the element must suddenly accelerate enormously, enter a new state, and maintain sufficient acceleration to avert horizon crossing. If a static remnant were so produced, the external state and stress tensor could well be approximated by those of D. G. Boulware (Mottola and Vaulin’s reference 1). The big question is what could provide a plausible dynamical mechanism for that drastic transition.
Apparently, the mechanism would have to be nonlocal, to stop the fluid just before the horizon, since the horizon is not a local construct. If a collision or explosion blew off the material on one side of the fluid during collapse, the ultimate horizon would be smaller, and a fluid element on the opposite side would have to nonlocally know not to suddenly accelerate. Such scenarios seemingly involve even more extreme and fanciful departures from conventional physics—including locality—than a small effect that allows information to “leak” from a black hole. Moreover, the latter nonlocality does not necessarily imply asymptotic acausality;1 symmetries of the black hole are different from those of Minkowski space.
If a scenario in which a physical surface replaces the horizon were realized, one would expect radiation from accreting matter impacting the surface. Indeed, Avery Broderick, Abraham Loeb, and Ramesh Narayan constrain such radiation2 to less than 1% of infalling energy for Sgr A* and conclude that it is all but certain that a surface replacing the horizon does not exist. Clearly, though, experimental constraints are improving.
Tarun Biswas points out that Karl Schwarzschild used different coordinates. Schwarzschild’s r should not be thought of as the usual radius; in his coordinates a geodesic continues through r = 0 to negative r. In general relativity, physics is independent of choice of coordinates, but the more easily interpreted choice for a radial coordinate is the conventional one determining areas of spheres.
