Reply to ``Comment on Model-dependence of Shapiro time delay and the `speed of gravity/speed of light' controversy''

To determine whether the Shapiro time delay of light passing near a moving object depends on the ``speed of gravity'' or the ``speed of light,'' one must analyze observations in a bimetric framework in which these two speeds can be different. In a recent comment (gr-qc/0510048), Kopeikin has argued that such a computation -- described in gr-qc/0403060 -- missed a hidden dependence on the speed of gravity. By analyzing the observables in the relevant bimetric model, I show that this claim is incorrect, and that the conclusions of gr-qc/0403060 stand.Comment: 3 page reply to gr-qc/051004

Statistical Mechanics and Black Hole Entropy

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.Comment: 10 pages, one figure in separate (uuencoded, compressed) tar file; factor of 2 corrected in eqn. (2.8

Kinetic Energy and the Equivalence Principle

According to the general theory of relativity, kinetic energy contributes to gravitational mass. Surprisingly, the observational evidence for this prediction does not seem to be discussed in the literature. I reanalyze existing experimental data to test the equivalence principle for the kinetic energy of atomic electrons, and show that fairly strong limits on possible violations can be obtained. I discuss the relationship of this result to the occasional claim that ``light falls with twice the acceleration of ordinary matter.''Comment: 11 pages, LaTeX; pedagogical paper sent to archive at students' reques

Dimension and Dimensional Reduction in Quantum Gravity

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by `dimension' in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon.Comment: For proceedings of the conference in honor of Martin Reuter: "Quantum Fields---From Fundamental Concepts to Phenomenological Questions"; 14 pages; based in part on my review article arXiv:1705.0541

Black Hole Thermodynamics

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 chapter I 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.Comment: Invited review article. A few parts based on an earlier review, arXiv:0807.4520. To appear in Int. J. Mod. Phys. D and in "One Hundred Years of General Relativity: Cosmology and Gravity," edited by Wei-Tou Ni (World Scientific, Singapore, 2015). v2: added references and appendi

Horizon constraints and black hole entropy

To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories as well, the imposition of a "stretched horizon" constraint alters the algebra of symmetries at the horizon, introducing a central term. Standard conformal field theory techniques can then then be used to obtain the asymptotic density of states, reproducing the Bekenstein-Hawking entropy. The microscopic states responsible for black hole entropy can thus be viewed as "would-be pure gauge" states that become physical because the symmetry is altered by the requirement that a horizon exist.Comment: 20 pages, to appear in "The Kerr spacetime: rotating black holes in general relativity," edited by S. Scott, M. Visser, and D. Wiltshire (Cambridge University Press