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Black Holes

A brief overview of the Mathematics of Black Holes will provide you with some formulas concerning the computation of gravitational properties of black holes. A more detailed discussion of Black Holes and Singularities



Uncharged, non-rotating black holes are called Schwarzschild black holes. Uncharged rotating black holes are called Kerr black holes. Non spinning charged black holes are called Reissner-Nordström black holes. Charged, spinning black holes are called Kerr-Newman black holes. The Black Hole No Hair Theorem shows that mass, charge, and angular momentum are the only properties which a black hole can possess.

type of black hole mass angular momentum charge
Kerr Black Hole M > 0 J > 0 Q = 0
Kerr-Newman Black Hole M > 0 J > 0 Q > 0
Reissner-Nordström Black Hole M > 0 J = 0 Q > 0
Schwarzschild Black Hole M > 0 J = 0 Q = 0


In 1965, R. Penrose proved the Singularity Theorem which says that a singularity must reside inside every imploding star, and therefore every black hole. In 1969, Lifschitz, Khalatnikov, and Belinsky showed that tidal gravity oscillates chaotically near the singularity. They also found the particular type of singularity, now known as a BKL singularity. Thus, black holes can pulsate, as was recognized by Press (1971).

Falling Photon

What happens if a beam of light, just say a single photon, happens to pass near by. If it crosses the event horizon it will fall ultimately into the black hole. Just let us take a close look what happens to if a Falling Photon comes near a black hole.

Schwarzschild Black Hole

Schwarzschild Black Hole Schwarzschild Black Hole
The paths of the photons are distributed symmetrically around the black hole.

Kerr Black Hole

Rotating Black Hole Rotating Black Hole
The paths of the photons are follow the rotation of the black hole. A photon is deflected if the rotation lies in the distribution direction. If the rotation is directed opposite the direction of the photon it is captured more early than other photons.

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