Black Holes and Beyond

TL;DR

The paper tackles the black hole information paradox by arguing that the semiclassical picture must break down at macroscopic scales due to the enormous black hole entropy, a breakdown realized in string theory via fuzzball microstates. It explains Hawking’s entanglement problem, demonstrates that small corrections cannot resolve it, and then presents fractionation and bound-state constructions (notably the D1D5 system) that yield horizonless, unitary microstate geometries whose entropy matches the Bekenstein bound. Through AdS/CFT and explicit microstate constructions, Mathur shows how radiation from fuzzballs can reproduce Hawking-like spectra without information loss, while also offering a coherent picture for Rindler and de Sitter entropies and a refined form of complementarity. The work links microstate structure to broader questions about the emergence of spacetime, infall, and early-universe dynamics, proposing a unified, unitary description of black holes and related horizons with broad cosmological implications.

Abstract

The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity do not exhibit any such breakdown, and this forces us into a difficult corner: either we must give up quantum mechanics or we must accept the existence of troublesome `remnants'. In string theory, however, the fundamental quanta are extended objects, and it turns out that the bound states of such objects acquire a size that grows with the number of quanta in the bound state. The interior of the black hole gets completely altered to a `fuzzball' structure, and information is able to escape in radiation from the hole. The semiclassical approximation can break at macroscopic scales due to the large entropy of the hole: the measure in the path integral competes with the classical action, instead of giving a subleading correction. Putting this picture of black hole microstates together with ideas about entangled states leads to a natural set of conjectures on many long-standing questions in gravity: the significance of Rindler and de Sitter entropies, the notion of black hole complementarity, and the fate of an observer falling into a black hole.

Figures (16)

• Figure 1: Electron positron pairs are created from the vacuum, and pass through the positive and negative grids. The two members of each pair are entangled with each other, generating an entanglement entropy $S_{ent}=N\ln 2$ between the left and right sides of the figure.
• Figure 2: The Penrose diagram of a black hole formed by collapse of the 'infalling matter'. The spacelike slices shown give a foliation of the geometry by 'good slices'.
• Figure 3: Eddington-Finkelstein coordinates for the Schwarzschild hole. Spacelike slices are $t=const$ outside the horizon and $r=const$ inside. Curvature length scale is $\sim 3 ~km$ all over the region of evolution covered by the slices $S_i$.
• Figure 4: The instability of 'outgoing geodesics' at the horizon. A null geodesic at $r=2M$ headed radially outwards stays stuck at $r=2M$, one slightly outside escapes to infinity while one slightly inside falls to $r=0$.
• Figure 5: (a) Momentum modes by themselves have energies $\sim {1\over L}$, but when bound to a multiwound string with winding $n_w$ the minimum allowed energy drops by a factor $n_w$. (b) Duality maps this simple observation to an interesting fact about branes: D1 branes bound to many D5 branes give rise to 'fractional tension' branes.