In the current standard viewpoint small black holes are believed to emit
radiation as black bodies at the Hawking temperature, at least until they reach
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.Comment: 11 pages, 4 figures; Winner of 3rd Place in the 2001 Gravity Research
Foundation Essay Competitio
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.
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.
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 paper is primarily pedagogical, and its main goal is to give
physics students, non-specialists, engineers etc. 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.Comment: 22 pages and 6 figure
The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s 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.
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