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
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
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
V0 = 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
and as is the mass M of the star divided by the radius r, we can obtain
(equation that nowadays is usually deduced from the Schwarzschild metric for the general relativity)
and as according to the equation (3) 2GM/r = ve2 being ve 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/c2 , 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:
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/c2 (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.
[black holes index]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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