A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter

We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that $a^2+Q^2=M^2$ always holds provided that a continuous sequence of spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity $a=J/M$ is the black hole's intrinsic angular momentum per unit mass, $Q$ its electric charge and $M$ the well known black hole mass parameter introduced by Christodoulou and Ruffini.Comment: 19 pages, 2 figures, replaced with published versio

Nonthermal nature of incipient extremal black holes

We examine particle production from spherical bodies collapsing into extremal Reissner-Nordstr\"om black holes. Kruskal coordinates become ill-defined in the extremal case, but we are able to find a simple generalization of them that is good in this limit. The extension allows us to calculate the late-time worldline of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential fall-off of a nonextremal black hole. Therefore, although the vanishing of the stress tensor's expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.Comment: 13 pages, 2 epsf figures, RevTeX 3. Minor changes, version published in PR

Electrostatic boundary value problems in the Schwarzschild background

The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution. Boundary value problems are solved. With a multipole expansion the asymptotic property for the field of any charge distribution is derived. It is shown that one produces a Reissner--Nordstrom black hole if one lowers a test charge distribution slowly toward the horizon. The symmetry of the distribution is not important. All the multipole moments fade away except the monopole. A calculation of the gravitationally induced electrostatic self-force on a pointlike test charge distribution held stationary outside the black hole is presented.Comment: 18 pages, no figures, uses iopart.st

On classical super-radiance in Kerr-Newman-anti-de Sitter black holes

We study in detail the modes of a classical scalar field on a Kerr-Newman-anti-de Sitter (KN-AdS) black hole. We construct sets of basis modes appropriate to the two possible boundary conditions (``reflective'' and ``transparent'') at time-like infinity, and consider whether super-radiance is possible. If we employ ``reflective'' boundary conditions, all modes are non-super-radiant. On the other hand, for ``transparent'' boundary conditions, the presence of super-radiance depends on our definition of positive frequency. For those KN-AdS black holes having a globally time-like Killing vector, the natural choice of positive frequency leads to no super-radiance. For other KN-AdS black holes, there is a choice of positive frequency which gives no super-radiance, but for other choices there will, in general, be super-radiance.Comment: 23 pages, 3 figures, v2: minor changes, references adde

No static bubbling spacetimes in higher dimensional Einstein-Maxwell theory

We prove that any asymptotically flat static spacetime in higher dimensional Einstein-Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black holes in this theory. In particular, these results establish that there are no asymptotically flat static spacetimes with non-trivial topology, with or without a black hole, in Einstein-Maxwell theory.Comment: 9 pages. v2: minor edits, references adde

Can the Universe Create Itself?

The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a Big Bang explosion, the question of what happened before the Big Bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the Big Bang must have had a beginning also. Ultimately, the difficult question seems to be how to make something out of nothing. This paper explores the idea that this is the wrong question --- that that is not how the Universe got here. Instead, we explore the idea of whether there is anything in the laws of physics that would prevent the Universe from creating itself. Because spacetimes can be curved and multiply connected, general relativity allows for the possibility of closed timelike curves (CTCs). Thus, tracing backwards in time through the original inflationary state we may eventually encounter a region of CTCs giving no first-cause. This region of CTCs, may well be over by now (being bounded toward the future by a Cauchy horizon). We illustrate that such models --- with CTCs --- are not necessarily inconsistent by demonstrating self-consistent vacuums for Misner space and a multiply connected de Sitter space in which the renormalized energy-momentum tensor does not diverge as one approaches the Cauchy horizon and solves Einstein's equations. We show such a Universe can be classically stable and self-consistent if and only if the potentials are retarded, giving a natural explanation of the arrow of time. Some specific scenarios (out of many possible ones) for this type of model are described. For example: an inflationary universe gives rise to baby universes, one of which turns out to be itself. Interestingly, the laws of physics may allow the Universe to be its own mother.Comment: 48 pages, 8 figure

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference

The Farm, the city, and the emergence of social security

We study the social, demographic and economic origins of social security. The data for the U.S. and for a cross section of countries suggest that urbanization and industrialization are associated with the rise of social insurance. We describe an OLG model in which demographics, technology, and social security are linked together in a political economy equilibrium. In the model economy, there are two locations (sectors), the farm (agricultural) and the city (industrial) and the decision to migrate from rural to urban locations is endogenous and linked to productivity differences between the two locations and survival probabilities. Farmers rely on land inheritance for their old age and do not support a pay-as-you-go social security system. With structural change, people migrate to the city, the land loses its importance and support for social security arises. We show that a calibrated version of this economy, where social security taxes are determined by majority voting, is consistent with the historical transformation in the United States

Heat Shock Proteins and Amateur Chaperones in Amyloid-Beta Accumulation and Clearance in Alzheimer’s Disease

The pathologic lesions of Alzheimer’s disease (AD) are characterized by accumulation of protein aggregates consisting of intracellular or extracellular misfolded proteins. The amyloid-β (Aβ) protein accumulates extracellularly in senile plaques and cerebral amyloid angiopathy, whereas the hyperphosphorylated tau protein accumulates intracellularly as neurofibrillary tangles. “Professional chaperones”, such as the heat shock protein family, have a function in the prevention of protein misfolding and subsequent aggregation. “Amateur” chaperones, such as apolipoproteins and heparan sulfate proteoglycans, bind amyloidogenic proteins and may affect their aggregation process. Professional and amateur chaperones not only colocalize with the pathological lesions of AD, but may also be involved in conformational changes of Aβ, and in the clearance of Aβ from the brain via phagocytosis or active transport across the blood–brain barrier. Thus, both professional and amateur chaperones may be involved in the aggregation, accumulation, persistence, and clearance of Aβ and tau and in other Aβ-associated reactions such as inflammation associated with AD lesions, and may, therefore, serve as potential targets for therapeutic intervention