Perhaps standard effective field theory arguments are right, and vacuum fluctuations really do generate a huge cosmological constant. I show that if one does not assume homogeneity and an arrow of time at the Planck scale, a very large class of general relativistic initial data exhibit expansions, shears, and curvatures that are enormous at small scales, but quickly average to zero macroscopically. Subsequent evolution is more complex, but I argue that quantum fluctuations may preserve these properties. The resulting picture is a version of Wheeler's "spacetime foam," in which the cosmological constant produces high curvature at the Planck scale but is nearly invisible at observable scales.

Wheeler's conjectured 'spacetime foam' - large quantum fluctuations of spacetime at the Planck scale - could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of 'foamy' initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.

The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this paper, will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox.

It is well known that the Euclidean black hole action has a boundary term at the horizon proportional to the area. I show that if the horizon is replaced by a stretched horizon with appropriate boundary conditions, a new boundary term appears, described by a Schwarzian action similar to the recently discovered boundary actions in “nearly anti-de Sitter” gravity.

Near the horizon, the obvious symmetries of a black hole spacetime-the horizon-preserving diffeomorphisms-are enhanced to a larger symmetry group with a three-dimensional Bondi-Metzner-Sachs algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry and show that it is strong enough to determine the black hole entropy in any dimension.

In an earlier short paper [Phys. Rev. Lett. 120, 101301 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.101301], I argued that the horizon-preserving diffeomorphisms of a generic black hole are enhanced to a larger three-dimensional Bondi-Metzner-Sachs symmetry, which is powerful enough to determine the Bekenstein-Hawking entropy. Here, I provide details and extensions of that argument, including a loosening of horizon boundary conditions and a more thorough treatment of dimensional reduction and meaning of a "near-horizon symmetry."

Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this context, summarize the evidence for dimensional reduction, and discuss possible physical explanations.

Results from a number of different approaches to quantum gravity suggest that the effective dimension of spacetime may drop to d = 2 at small scales. I show that two different dimensional estimators in causal set theory display the same behavior, and argue that a third, the spectral dimension, may exhibit a related phenomenon of 'asymptotic silence.'

Supertranslations, and at least in 2 + 1 dimensions superrotations, are asymptotic symmetries of the metric in asymptotically flat spacetimes. They are not, however, symmetries of the boundary term of the Einstein-Hilbert action, which therefore induces an action for the Goldstone-like fields that parametrize these symmetries. I show that in 2 + 1 dimensions, this action is closely related to a chiral Liouville action, as well as the 'Schwarzian' action that appears in two-dimensional near-AdS physics.

I review a new (and still tentative) approach to black hole thermodynamics that seeks to explain black hole entropy in terms of microscopic quantum gravitational boundary states induced on the black hole horizon.