INTRODUCTION / HOW THE BLACK HOLES ARE FORMED / SPECIAL RELATIVITY AND BLACK HOLES / GENERAL RELATIVITY AND BLACK HOLES / BLACK HOLES DETECTION / The NON- PUNCTUAL BLACK HOLE / SPACE-TIME graphics on STAR COLLAPSE / HOLES In ETERNAL FORMACION, ETERNAL BLACK HOLES And OTHER MATHEMATICAL CONCEPTS

**GENERAL RELATIVITY And THE
BLACK HOLES **(© Angel Torregrosa
Lillo)**
**[versión
española]

According to the Einstein's general relativity theory, in the proximities of a great mass the time lapses more slowly due to the gravitational action.

Einstein deduced (how we could read in their book "The meaning of relativity") the following formula

(7)

being

x=8p G/c²

t'= elapsed time at a distance r from the gravity center of the mass (a star) producing the gravitational field

t= supposed objective time (elapsed far away in the remoteness of the gravitational field)

s = density of the sta

V_{0 }= Volume of the
star

r = distance from the center of the star until the point of the space that we are analyzing.

Then substituting x by their value we can obtain

(8)

and as is the mass M of the star divided by the radius r, we can obtain

(9)

*(equation that nowadays is
usually deduced from the Schwarzschild metric for the general
relativity) *

and as according to the equation (3) 2GM/r = v_{e}^{2} being v_{e}
the classical escape velocity at the distance r from the center
of the star, we obtain

(10) (Is possible to make another deduction of this formula, more didactic, through the equivalence principle)

From here is deduced that **as a body
approach a star, the time elapse more slowly** for this
body, as a function of the escape velocity in the star (from a
classical point of view), so that when you aer in a point in wich
the classical escape velocity is equal to the speed of light, the
time will stop for the object located in that place. That is for**
r=2GM/c**^{2} , the called **Schwarchild
radius**..We can see that if we isolate the term M / r, it gives the same ratio as obtained by classical physics and speed limit of light in the section on special relativity and black holes. Therefore the values in the table in that paragraph are valid, because the equation for the radius of Schwarchild luckily is the same if calculated using general relativity or by means of classical mechanics and the speed limit of light .

Thus appears a spherical
surface around the black hole in which the time stops. This
spherical surface is the called **event horizon **of
the black hole.

Crossing this horizon the time exists again but with imaginary components (the calculation of time elapsed inside the event horizon leads us to a square root of a negative number), which leads us to think that time elapses inside a black hole perhaps in a fifth dimension, perpendicular to the three spacial dimensions and to the normal time dimension.

Furthermore the
theory of the general relativity tells us that the **space
bends** around a mass in such a form that a light beam
that passes brushing that mass, would deviate double of de
deviation if it were affected for the gravity from a classical
point of view (like a particle). Thus Einstein obtained, carrying
out some approximations, that the deviation were:

(11)

that provide us an angle of 1.75 seconds of degree in a light beam that passes brushing the sun. This was checked through the observation of eclipses.

He
also obtained that the light emitted by a star should have some **redshift**
in his spectroscopical analysis, that is to say that the emitted
light will have a minor frequency than the normal light, because
all their electrons will vibrate slowly due to the partial
detention of the time, obtaining the formula:

We could
appreciate that if the radius were 2GM/c^{2} (radio of
the event horizon) the frequency would be zero and therefore we
would not see the light coming from the star. Another reason to
call it "black hole".

It's possible to calculate that for the mentioned radius the space bending would be such that the light would remain caught in the hole. In this way when we approach to the event horizon the three space normal coordinates are curved in a way that any movement in the interior of the hole only can go toward the center of the star.

In this way all thing surpassing the event horizon won't **never
leave**.

INTRODUCTION / HOW THE BLACK HOLES ARE FORMED / SPECIAL RELATIVITY AND BLACK HOLES / GENERAL RELATIVITY AND BLACK HOLES / BLACK HOLES DETECTION / The NON- PUNCTUAL BLACK HOLE / SPACE-TIME graphics on STAR COLLAPSE / HOLES In ETERNAL FORMACION, ETERNAL BLACK HOLES And OTHER MATHEMATICAL CONCEPTS

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