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

Near-horizon Bondi-Metzner-Sachs symmetry, dimensional reduction, and black hole entropy

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.

The (2+1)-Dimensional Black Hole

I review the classical and quantum properties of the (2+1)-dimensional black hole of Ba{\~n}ados, Teitelboim, and Zanelli. This solution of the Einstein field equations in three spacetime dimensions shares many of the characteristics of the Kerr black hole: it has an event horizon, an inner horizon, and an ergosphere; it occurs as an endpoint of gravitational collapse; it exhibits mass inflation; and it has a nonvanishing Hawking temperature and interesting thermodynamic properties. At the same time, its structure is simple enough to allow a number of exact computations, particularly in the quantum realm, that are impractical in 3+1 dimensions.Comment: LaTeX, 34 pages, 4 figures in separate fil

Statistical Mechanics and Black Hole Thermodynamics

Black holes are thermodynamic objects, but despite recent progress, the ultimate statistical mechanical origin of black hole temperature and entropy remains mysterious. Here I summarize an approach in which the entropy is viewed as arising from ``would-be pure gauge'' degrees of freedom that become dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees of freedom can be counted, and yield the correct Bekenstein-Hawking entropy; the corresponding problem in 3+1 dimensions remains open.Comment: 5 pages, LaTeX, uses espcrc2.sty; talk given at the Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, September 199

A Note on Black Hole Entropy in Loop Quantum Gravity

Several recent results have hinted that black hole thermodynamics in loop quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi parameter $\gamma=i$. This suggests a connection with $\mathrm{SL}(2,\mathbb{C})$ or $\mathrm{SL}(2,\mathbb{R})$ conformal field theories at the "boundaries" formed by spin network edges intersecting the horizon. I present a bit of background regarding the relevant conformal field theories, along with some speculations about how they might be used to count black hole states. I show, in particular, that a set of unproven but plausible assumptions can lead to a boundary conformal field theory whose density of states matches the Bekenstein-Hawking entropy.Comment: v2: added references; v3: slight addition to discussion of 3d gravity; v4: more references, typos fixe

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