Alone black hole-related theorem

The alone black hole-related theorem (black hole ゆいいつせいていり, black hole uniqueness theorem) is a theorem for the black hole measurement that Einstein Equation of the general theory of relativity gives as a solution. The axis symmetry routine solution shows that it becomes the car solution (car black hole).

The naturally occurring steady black hole shows that it is a car solution if I think with a cosmic censorship hypothesis. In addition, it is concluded that a black hole formed in the natural world is settled down to a car measurement if I think with a black hole hair loss theorem.

Table of contents

I it for the space-time that is static (static)

Alone black hole-related theorem (Israel, 1967) in the static space-time

A ball is symmetric, and the thing meeting three next conditions agrees on a vacuum of Einstein Equation in Schwarz silt solution among static solutions.

1. It is flat asymptotically.
2. I have an event horizon.
3. I do not have a space-time singular point outward in an event horizon.

In addition, it is shown that the solution becomes the Reisner ノルドシュトロム solution if it is said that I include it more until an electromagnetic field under this condition.

I write theorems to be known as a theorem of Berkoff for your information jointly next.

Theorem (Birkoff, 1923) of Berkoff

The vacuum solution of the ball symmetry fits it in Schwarz Sild solution (even if I do not do a supposition to be static).

I it for the space-time that is steady (stationary)

There are some versions, but lists next.

Alone black hole-related theorem (Cartar, 1971) in the regular space-time

The thing meeting the next condition agrees on a vacuum, axis symmetry of Einstein Equation in a car solution among steady solutions.

1. It is flat asymptotically.
2. The aspect, the outside of the event horizon${\displaystyle S^{2}\times R^{2}}$ と aspect.
3. I do not have a space-time singular point outward in an event horizon.

In addition, it is shown that the solution becomes the car Newman solution if it is said that I include it more until an electromagnetic field under this condition.

References

• W. Israel, Phys. Rev., 164 (1967), 1776.
• B. Carter, Phys. Rev. Lett. 26 (1971), 331

Allied item

• The theory of relativity | General theory of relativity
• Black hole | Solution of the Schwarz silt | Reisner ノルドシュトロム solution | Car solution | Car Newman solution
• Black hole hair loss theorem | Cosmic censorship hypothesis

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