Black holes as quantum bound states

We present a new quantum description for the Oppenheimer-Snyder model of gravitational collapse of a ball of dust. Starting from the geodesic equation for dust in spherical symmetry, we introduce a time-independent Schrödinger equation for the radius of the ball. The resulting spectrum is similar to that of the Hydrogen atom and Newtonian gravity. However, the non-linearity of General Relativity implies that the ground state is characterised by a principal quantum number proportional to the square of the ADM mass of the dust. For a ball with ADM mass much larger than the Planck scale, the collapse is therefore expected to end in a macroscopically large core and the singularity predicted by General Relativity is avoided. Mathematical properties of the spectrum are investigated and the ground state is found to have support essentially inside the gravitational radius, which makes it a quantum model for the matter core of Black Holes. In fact, the scaling of the ADM mass with the principal quantum number agrees with the Bekenstein area law and the corpuscular model of Black Holes. Finally, the uncertainty on the size of the ground state is interpreted within the framework of an Uncertainty Principle.

Worte der Wahrheit und des Friedens an die gesammte jüdische Nation : vorzüglich an diejenigen, so unter dem Schutze des glorreichen und großmächtigsten Kaysers Josephs II. wohnen

[Naphtali Herz Wessely.] Aus dem Hebr. [von David Friedländer]

Feyerliche Dankrede eines hebräischen Großrabbiners ... bey Gelegenheit der höchsterfreulichen Krönung eines römischen Königs ... des Prinzen Josephs v. Oesterreich, des Sohnes Franzens und Theresiens ... in dem Jahre ... 1764 ... gesprochen

durch Ben-Issatai in d. gangbare Deutsch übers.

Die Sage vom Sarge Josephs und der Bericht Benjamins von Tudela über Daniels schwebenden Sarg

Bernhard Heller

Der Name Josephs

M. Schwarzauer

Josephs Verkauf [Illustration]

Scan von Monochrom-Mikroform

Oratorium nach der Composition des Stabat Mater &c. : aufgeführt den 21. März 1790 in der evangelischen Hauptkirche zu Frankfurt am Mayn, bey dem wegen des Ablebens weil. Sr. Kaiserl. Majestät Josephs II. glorwürdigsten Andenkens, auf Befehl E. Hochedlen Raths veranstalteten Trauerfeste

von Joseph Haydn

Susanne Dombois als Sulamith, Rollenbild, in: Richard Strauss: Josephs-Legende

Signatur des Originals: S 36/F03478

National-Theater u. Max Josephs-Platz, München

Signatur des Originals: S 36/F08016

{[N.N.] als Joseph {[u.a.], Szenenfoto, Gruppenbildnis, in: Richard Strauss: Josephslegende: Die Folterung Josephs, Berlin, 1921, Uraufführung

Signatur des Originals: S 36/F11993

Intoleranz des katholischen Klerus gegen die ungarischen Protestanten nach zuverlässigen Aktenstücken : oder Ideen zur gebührenden Schätzung der Verdienste der beyden grossen Kaiser Josephs und Leopolds um die protestantischen Kirche in Ungarn, ein Pendant zum Manch-Hermäon.

Mode of access: Internet.

Augsburgs geschichte von erbauung der stadt bis zum tode Maximilian Josephs, ersten königs von Bayern, 1825.

With engraved half-title-page. The covers of vol. 1 are engraved.

Studien zur kirchlichen Reform Josephs II : mit besonderer Berucksichtigung des vorderosterreichischen Breisgaus.

Thesis (doctoral)--Albert-Ludwigs-Universitat zu Freiburg im Breisgau.

Part of "Widows Mite" lying in the co. of Washington D.C. ; The above 2 plats represent two separate parts of that portion of a tract of land called Josephs Park, lying in Montg. Co. Md. /

Both tracts border on Rock Creek.

Novel Pathogenic Mutations and Copy Number Variations in the VPS13A Gene in Patients With Chorea-Acanthocytosis

Chorea-acanthocytosis (ChAc) is a rare autosomal recessive neurodegenerative disorder caused by loss of function mutations in the vacuolar protein sorting 13 homolog A (VPS13A) gene that encodes chorein. It is characterized by adult-onset chorea, peripheral acanthocytes, and neuropsychiatric symptoms. In the present study, we performed a comprehensive mutation screen, including sequencing and copy number variation (CNV) analysis, of the VPS13A gene in ChAc patients. All 73 exons and flanking regions of VPS13A were sequenced in 35 patients diagnosed with ChAc. To detect CNVs, we also performed real-time quantitative PCR and long-range PCR analyses for the VPS13A gene on patients in whom only a single heterozygous mutation was detected. We identified 36 pathogenic mutations, 20 of which were previously unreported, including two novel CNVs. In addition, we investigated the expression of chorein in 16 patients by Western blotting of erythrocyte ghosts. This demonstrated the complete absence of chorein in patients with pathogenic mutations. This comprehensive screen provides an accurate and useful method for the molecular diagnosis of ChAc. (C) 2011 Wiley-Liss, Inc.