Kerr Solution

“In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein’s equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound.

The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time. And since the general theory of relativity provides only a single unique family of solutions for their descriptions, they are the simplest objects as well. The unique two-parameter family of solutions which describes the space-time around black holes is the Kerr family discovered by Roy Patrick Kerr in July, 1963. The two parameters are the mass of the black hole and the angular momentum of the black hole. The static solution, with zero angular momentum, was discovered .by Karl Schwarzschild in December, 1915.

I do not know if the full import of what I have said is clear. Let me explain.

Black holes are macroscopic objects with masses varying from a few solar masses to millions of solar masses. To the extent they may be considered as stationary and isolated, to that extent, they are all, every single one of them, described exactly by the Kerr solution. This is the only instance we have of an exact description of a macroscopic object. Macroscopic objects, as we see them all around us, are governed by a variety of forces, derived from a variety of approximations to a variety of physical theories. In contrast, the only elements in the construction of black holes are our basic concepts of space and time. They are, thus, almost by definition, the most perfect macroscopic objects there are in the universe. And since the general theory of relativity provides a single unique two-parameter family of solutions for their descriptions, they are the simplest objects as well.

Turning to the physical properties of the black holes, we can study them best by examining their reaction to external perturbations such as the incidence of waves of different sorts. Such studies reveal an analytic richness of the Kerr space-time which one could hardly have expected. This is not the occasion to elaborate on these technical matters 22. Let it suffice to say that contrary to every prior expectation, all the standard equations of mathematical physics can be solved exactly in the Kerr space-time. And the solutions predict a variety and range of physical phenomena which black holes must exhibit in their interaction with the world outside.

The mathematical theory of black holes is a subject of immense complexity; but its study has convinced me of the basic truth of the ancient mottoes,

The simple is the seal of the true
Beauty is the splendour of truth.”

— Subrahmanyan Chandrasekhar

The meaning

“the day was sufficient to itself, and so was the life.”

Frühen Morgen

“Wenn du zur Arbeit gehst am frühen Morgen
Wenn du am Bahnhof stehst mit deinen Sorgen
Da zeigt die Stadt dir asphaltglatt
Im Menschenrichter Millionen Gesichter
Zwei fremde Augen, ein kurzer Blick
Die Braue, Pupillen, die Lider
Was war das? Vielleicht dein Lebensglück
Vorbei, verweht, nie wieder.

Du gehst dein Leben lang auf tausend Straßen
Du siehst auf deinem Gang, die dich vergaßen
Ein Auge winkt, die Seele klingt
Du hast’s gefunden, nur für Sekunden
Zwei fremde Augen, ein kurzer Blick
Die Braue, Pupillen, die Lider
Was war das?
Kein Mensch dreht die Zeit zurück
Vorbei, verweht, nie wieder.

Du musst auf deinem Gang durch Städte wandern
Siehst einen Pulsschlag lang den fremden Andern
Es kann ein Feind sein, es kann ein Freund sein
Es kann im Kampfe dein Genosse sein
Es sieht hinüber und zieht vorüber
Zwei fremde Augen, ein kurzer Blick
Die Braue, Pupillen, die Lider
Was war das?
Von der großen Menschheit ein Stück
Vorbei, verweht, nie wieder.”


Eles disseram que está tudo acabado? Hein, hein? Os sonhos das pessoas, não tem fim!


Es gibt keinen Menschen ohne Schuld

Authority in science

‘Never rely on an authority in science. Even the greatest genius can be wrong – whether he has one or two Nobel Prizes, or none.’

Die Zeit

Die Zeit ist nicht barmherzig.

Money, fame or power is irrelevant

“Every one of us is going to die eventually, but we as a species will stick around for a while. That’s why I think accumulating money, fame or power is irrelevant.”

Und am Ende

Nicht nur die Vergangenheit beeinflusst die Zukunft. Sondern auch die Zukunft die Vergangenheit.

La jetée

Rien ne distingue les souvenirs des autres moments: ce n’est que plus tard qu’ils se font reconnaître, à leurs cicatrices. Ce visage qui devait être la seule image du temps de paix à traverser le temps de guerre, il se demanda longtemps s’il l’avait vraiment vu, ou s’il avait créé ce moment de douceur pour étayer le moment de folie qui allait venir…


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maio 2022

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