Ronald J. Adler

The Generalized Uncertainty Principle and Black Hole Remnants

In the current standard viewpoint small black holes are believed to emit black body radiation at the Hawking temperature, at least until they approach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system. Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse: the collapse is prevented, not by symmetry, but by dynamics, as a minimum size and mass are approached.

ON GRAVITY AND THE UNCERTAINTY PRINCIPLE

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.

Black hole remnants and dark matter

We argue that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse. Specifically we invoke the GUP to obtain a modified Hawking temperature, which indicates that there should exist non-radiating remnants (BHR) of about Planck mass. BHRs are an attractive candidate for cold dark matter. We investigate an alternative cosmology in which primordial BHRs are the primary source of dark matter.

Six easy roads to the Planck scale

We give six arguments that the Planck scale should be viewed as a fundamental minimum or boundary for the classical concept of spacetime, beyond which quantum effects cannot be neglected and the basic nature of spacetime must be reconsidered. The arguments are elementary, heuristic, and plausible and as much as possible rely on only general principles of quantum theory and gravity theory. The main goal of the paper is to give physics students and nonspecialists an awareness and appreciation of the Planck scale and the role it should play in present and future theories of quantum spacetime and quantum gravity.

Vacuum catastrophe: An elementary exposition of the cosmological constant problem

Quantum field theory predicts a very large energy density for the vacuum, and this density should have large gravitational effects. However these effects are not observed, and the discrepancy between theory and observation is an incredible 120 orders of magnitude. There is no generally accepted explanation for this discrepancy, although numerous papers have been written about it. As usually stated the problem requires a knowledge of quantum field theory and general relativity, topics not normally studied by undergraduates. We have tried to make the problem accessible to undergraduates by using only the simplest ideas of quantum theory, such as the uncertainty principle and the theory of the harmonic oscillator, and classical gravitational theory. We believe that such simplification is not only an amusing pedagogical exercise but clarifies how basic is the conflict between quantum theory and gravitational theory. We do not here discuss various proposed solutions to the problem, beyond the trivial and unsat...

Simple analytical models of gravitational collapse

Most general relativity textbooks devote considerable attention to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. Only a few discuss the dynamical process of gravitational collapse by which black holes and singularities form. We present two simple analytical models that describe this process. The first involves collapsing spherical shells of light and is analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid and is analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is simplicity and algebraic completeness, but we also present a few more sophisticated results such as the collapse of a light shell in Kruskal-Szekeres coordinates.

The Gravity Probe B test of general relativity

The Gravity Probe B mission provided two new quantitative tests of Einsteins theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earths orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

General Treatment of Orbiting GyroscopePrecession

We review the derivation of the metric for a spinning body of any shape andcomposition using linearized general relativity theory (LGRT), and also obtainthe same metric using a transformation argument. The latter derivation makes itclear that the linearized metric contains only the Eddington α and γ parameters,so no new parameter is involved in frame-dragging or Lense—Thirring effects.We then calculate the precession of an orbiting gyroscope in a general weakgravitational field described by a Newtonian potential (the gravitoelectric field)and a vector potential (the gravitomagnetic field). Next we make a multipoleanalysis of the potentials and the precession equations, giving all of these interms of the spherical harmonics moments of the density distribution. The analysisis not limited to an axially symmetric source, although the Earth, which is themain application, is very nearly axisymmetric. Finally, we analyze the precessionin regard to the Gravity Probe B (GP-B) experiment, and find that the effect ofthe Earths quadrupole moment (J2) on the geodetic precession is large enoughto be measured by GP-B (a previously known result), but the effect on theLense—Thirring precession is somewhat beyond the expected GP-B accuracy.

Finite Cosmology and a CMB Cold Spot

The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 x 10{sup 23}M{sub {circle_dot}} and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.

The nearly flat universe

We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single constant flatness parameter ɛ that quantifies the notion of nearly flat. Observations can only place an upper limit on ɛ, and always allow the possibility that the Universe is infinite with k = −1 or finite with k = 1. We use current observational data to obtain a numerical upper limit on the flatness parameter and discuss its implications, in particular the “naturalness” of the nearly flat Universe.