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Seminararbeit Seminar: Gekrümmter Raum Und Gedehnte Zeit Seminararbeit Seminar: Gekrümmter Raum und gedehnte Zeit Historischer Überblick zur Erforschung Schwarzer Löcher Institut für Physik Wintersemester 2015/2016 Universität Regensburg Vorgelegt von: Paul M. E. Unger Matrikelnummer: 1691694 E-Mail: [email protected] Eingereicht bei: Prof. Dr. Wolfgang Gebhardt Abgabetermin: 15.10.2015 Inhaltsverzeichnis 1. Die ersten Überlegungen im 18. Jhdt…………………………………………………….. 2 2. Die Jagd nach der Feldgleichung und deren Lösung im frühen 20. Jhdt…. 3 3. Die Untersuchung des Sternentodes ab dem Jahr 1930…………………..……. 5 4. Erste Sichtungen Schwarzer Löcher von 1940 bis 1943…………………………. 8 5. Ohne Schwarze Löcher geht’s nicht – Wheeler mitte des 20. Jhdts.………. 8 6. Weitere Sichtungen extrem massereicher Objekte im Jahr 1962……….……9 7. Die Beschreibung Schwarzer Löcher schreitet weiter ins 21. Jhdt. Fort…10 Anhang………………………………………………………………………………………………….……… 14 1 1 Die ersten Überlegungen im 18. Jhdt. Bei der Thematik der Erforschung Schwarzer Löcher denkt man heutzutage sofort an Namen wie Albert Einstein, John Wheeler, Stephen Hawkings und Roger Penrose. Doch die Reihe der Wissenschaftler, die einen wichtigen Beitrag zur Erforschung Schwarzer Löcher beitrugen, ist wesentlich länger und beginnt bereits Ende des 18ten Jahrhunderts. Die ersten schriftlichen Überlegungen zu Objekten, deren Masse so groß ist, dass man eine Fluchtgeschwindigkeit höher als die Lichtgeschwindigkeit benötigt, um ihrem gravimetrischen Potential zu entkommen, lassen sich auf John Mitchell zurückführen. Er wurde (vermutlich) 1724 in Nottingham geboren,1 studierte an der Universität Queens in Cambridge, an welcher er später auch lehrte, und wurde schließlich Pfarrer in Thornhill. Er befasste sich weiterhin stark mit naturwissenschaftlichen Themen wie Magnetismus und Gravitation, sagte voraus, dass sich Erdbeben wellenartig ausbreiten, und befasste sich auch mit Astronomie.2 1783 beschrieb er in einem Brief an Henry Cavendish folgende Überlegung: „ […] if the semi-diameter of a sphere of the same density with the sun were to exceed the sun in the proportion of 500 to 1, a body falling from an infinite height to it, would have aquired at its surface a greater velocity than that of light, and consequently, supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it, by its own proper gravity.“3 Dies wird heute als erste schriftlich festgehaltene Überlegung zu Schwarzen Löchern angesehen. Einige Jahre danach kam Pierre-Simon Laplace, geboren am 28. März 1749 in Beaumont-en- Auge in der Normandie und uns heute bekannt für seine Arbeiten in der Wahrscheinlichkeitstheorie und mit Differentialgleichungen, zu ähnlichen Überlegungen. Laplace begann 1769 auf Empfehlung von Jean-Baptiste le Rond d’Alembert in Paris zu studieren, wurde 1773 mit 24 Jahren an der Académie française aufgenommen und 1785 ordentliches Mitglied der Académie des sciences. 1796 veröffentlichte er in seinem Buch „Exposition du Système du Monde“ folgende Theorie.4 Er betrachtete einen Stern, der die 1 Sir Archibald Geikie, „Memoir of John Michell, M.A., B.D., F.R.S., fellow of Queens' college, Cambridge, 1749, Woodwardian professor of geology in the university 1762“, 1918, S.3, Veröffentlicht von: Cambridge, University press, URL: https://archive.org/details/memoirofjohnmich00geikrich, Stand: 28.09.2015. 2 Alan Chodos, „1783: John Michell anticipates black holes“, 2009, Veröffentlicht von: American Physical Society NEWS, URL: http://www.aps.org/publications/apsnews/200911/physicshistory.cfm, Stand: 28.09.2015. 3 John Michell, „On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose. By the Rev. John Michell, B. D. F. R. S. In a Letter to Henry Cavendish, Esq. F. R. S. and A. S.“, Philosophical Transactions of the Royal Society of London, Vol. 74 (1784), S.42, Veröffentlicht von: The Royal Society, URL: http://www.jstor.org/stable/106576, (Stand: 28.09.2015. 4 Eintrag zu Pierre Simon Laplace (1749 - 1837), Marquis de Laplace im Archiv der Royal Society, URL: https://collections.royalsociety.org/Dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqDb=Persons&dsqSearch=Code== %27NA5191%27&dsqCmd=Show.tcl, Stand: 28.09.2015. 2 gleiche Dichte wie die Erde aufweisen sollte, jedoch mit einem 250mal größeren Durchmesser. Er folgerte, dass die Gravitation eines solchen Objektes nach Newton so groß wäre, dass keine „Lichtpartikelchen“, wie sie damals im newtonschen Sinne betrachtet wurden, mehr dessen Oberfläche entfliehen könnten und dieses Objekt folglich nicht sichtbar zu erkennen wäre: „Un astre lumineux du même densitè que la terre et dont diamètre serais deux cents cinquante plus grand que celui du soleil, ne laisserait, en vertu de son attraction, parvenir aucune de ses rayons jusqu’a nous; il est donc possible que le plus grands corps lumineux de l’univers soient, par cela même, invisibles.“5 Durch Laplaces Beschreibung wurde zu dieser Zeit der Begriff „Schwarze Sterne“ für die heute als „Schwarze Löcher“6 bekannten Objekte geprägt. Das Interesse an der näheren Untersuchung Schwarzer Sterne schwand jedoch zunehmend im 19ten Jahrhundert. Der Grund hierfür war, dass die Wellentheorie durch Augustin Jean Fresnel immer mehr Anerkennung fand, während die Theorien von Laplace und Michell noch auf der von Newton geprägten Teilchenvorstellung des Lichtes basierten. 2 Die Jagd nach der Feldgleichung und deren Lösung im frühen 20. Jhdt. Erst mit Albert Einstein, geboren am 14. März 1879 in Ulm, gewann die Erforschung Schwarzer Sterne wieder Aufwind. Einstein begann 1896 am Polytechnikum in Zürich ein Studium zum Fachlehrer für Mathematik und Physik, welches er 1900 mit Diplom abschloss. 1905, im Alter von 26 Jahren, reichte er seine Ergebnisse zur Untersuchung des Photoelektrischen Effekts und seine Abhandlung „Zur Elektrodynamik bewegter Körper“ bei den „Annalen der Physik“, einer physikalischen Fachzeitschrift, ein. Letztere Abhandlung enthält zusammen mit dem von Einstein hinzugefügten Nachtrag „Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?“ die berühmte Formel zur Äquivalenz von Masse und Energie und wird heute als „spezielle Relativitätstheorie“ bezeichnet.7 Durch die Einführung von Raum-Zeit-Koordinaten und die Prämisse, dass Licht sich in allen Bezugssystemen mit der selben Geschwindigkeit ausbreitet, Längen- und Zeitmaß jedoch abhängig vom Bezugssystem des Beobachters sind, gelang ihm die Verknüpfung mechanischer und elektrodynamischer Gesetze. Nach seiner Habilitation 1907 und seiner Aufnahme in die „Preußische Akademie der Wissenschaft“ 1913 fand Einstein die Zeit, sich intensiver mit den Folgen seiner Theorien für die Gravitation, die er selbst unter dem Begriff „Gravitationsproblem“ zusammenfasste, 5 Pierre-Simon Laplace, „Exposition du Système du Monde“, 1808, Veröffentlicht von: Oxford University, URL: https://archive.org/details/expositiondusys02laplgoog, Stand: 28.09.2015. 6 Der Begriff „Schwarze Löcher“ lässt sich auf John Wheeler zurückführen, der diesen bei einem öffentlichen Vortrag 1967 erstmals verwendete (siehe Seite 9). 7 Walther Lutz / Albrecht Kai-Britt, „Albert Einstein“, Veröffentlicht von: Lebendiges Museum Online / Deutsches Historisches Museum, URL: https://www.dhm.de/lemo/biografie/albert-einstein, Stand: 28.09.2015. 3 auseinander zu setzten. Am 25. November 1915 veröffentlichte er seine Gravitationstheorie vor der Preußischen Akademie. An dieser Stelle sei David Hilbert kurz erwähnt. Hilbert, geboren am 23. Januar 1862 in Königsberg, studierte an der Albertus-Universität in Heidelberg, an der er 1886 auch habilitierte. Er stellte 5 Tage vor Einstein, am 20. November 1915, der Göttinger Akademie der Wissenschaft ebenfalls eine richtige Lösung für das Gravitationsproblem vor. Hilbert hat jedoch Einsteins Priorität nie öffentlich angefochten und seine Arbeit ging als elegante Ableitung der heute bekannten Einsteinschen Gleichungen in die Literatur ein.8 Durch die Veröffentlichung der Allgemeinen Relativitätstheorie ergaben sich gänzlich neue Möglichkeiten zur Untersuchung Schwarzer Sterne. Karl Schwarzschild, am 09. Oktober 1873 in Frankfurt am Main geboren, reichte 19169 eine erste exakte Lösung der Einsteinschen Feldgleichungen außerhalb kugel-symmetrischer Massen ein. Er studierte an der Universität Straßburg Astronomie und promovierte 1896 an der Ludwig-Maximilians Universität in München, an der er schließlich 1899 habilitierte. Er befasste sich trotz seines Einsatzes in Belgien und Russland während des Ersten Weltkrieges weiterhin mit wissenschaftlichen Problemen, unter anderem mit der Gravitationstheorie. Mit seiner Lösung ließen sich statische, nicht-rotierende, ungeladene Schwarze Löcher erstmals genauer beschreiben. 1916 wurde er auf Grund einer Autoimmunerkrankung vom Kriegsdienst befreit und starb am 11.05.1916 an den Folgen dieser Erkrankung.10 Eine weitere Lösung für die Feldgleichung wurde noch im selben Jahr von Hans Jacob Reissner veröffentlicht. Reissner wurde am 18. Januar 1874 in Berlin geboren, studierte an der Technischen Hochschule Charlottenburg Maschinenbau und promovierte 1902 an der Technischen Hochschule Berlin. An dieser besuchte er zudem Seminare in theoretischer Physik und Mathematik bei Max Planck. Er arbeitete Zeit seines
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