five fallacies used to link black holes to einstein\'s relativistic space-time.

[Einstein]1]
List the field equations that describe matterfreefield.
Carl Schwartz, German officer [2]
Shortly before his death, the solution of the field equation of the spherical symmetric static gravitational field was derived.
The solutionis of shiwazhilde is called the shiwazidu. Einstein [3]
Indicates that the substance cannot be compacted below the critical radius defined by the Schwarzschild metric. Weller [4]
It is shown that the formation of black holeresults by compacted matter below the critical radius violates the conservation of momentum and energy.
So why do many people believe that there are black holes in Einstein\'s relativity space-time?
This belief seems to be based at least in part on an incorrect description of the journey of the particle\'s radial fall to the assumed mass below the critical radius.
The description is incorrect because the particles arrive and pass through the critical radius.
This paper discusses five fallacies used to describe particle journeys.
The initial resolution of these errors reveals why particles will never reach a critical radius.
Figure 2 coordinate time t to local time [tau]
For particles with a supposed mass below the radial fall to critical radius, the mapping of the coordinate time t of the distant observer based on the radial distance r to the particle local time t is shown in Fig. 1.
Data shown in Figure 1
1 can be obtained using the Schwarzschild metric. [
Figure 1 slightly]
In particular, for compact mass M with a schwtz sub-radius R, reference space coordinates can be used to represent the schwtz sub-metric (r, 6,0)
Coordinate time t and local time t (
Usually referred to as the appropriate time t), i. e. , [c. sup. 2]d[[tau]. sup. 2]=[c. sup. 2](1 -R/r)d[t. sup. 2]-d[r. sup. 2]/(1 -R/r)-[r. sup. 2]d[[theta]. sup. 2]-([r. sup. 2][sin. sup. 2][theta])d[[phi]. sup. 2]. (1)
Reference coordinates (r, [theta], []phi, t)
When a particle uses local time coordinates [to detect the passage of time], the space and time coordinates used by distant observers to make measurements are [tau].
Radial fall of particles D [theta]= d[theta]= 0, (2)
So in (1)reduces to [c. sup. 2]d[[tau]. sup. 2]= [c. sup. 2(i-]r)d[t. sup. 2]-d[r. sup. 2]/(1-R/r), (3)
Indicates the relationship between radial position r, local time [tau]
And coordinate time t.
According to the relationship expressed (3)
For each radio assignmentr. sub. i]
Arrive from the starting position [r. sub. S]
Coordination time [t. sub. i]
Reach the radial position [r. sub. i]
It can be calculated with an integral [
Mathematical expressions that cannot be reproduced in ASCII](4)where [f. sub. 1](r)
Is a function of r from (3)[5, p. 667].
Local time [[tau]. sub. i]
Need to reach the radial position [r. sub. i]
Can be calculated with integral
Mathematical expressions that cannot be reproduced in ASCII](5)where [f. sub. 2](r)
Is a function of r from (3)[5, p. 663].
When the radial position [r. sub. i]
Set to a critical radius equal [r. sub. C]
[Integrated [f. sub. 1](r)
For points in (4)
[Integrated [f. sub. 2](r)
For points in (5)are undefined;
However ,(5)
Points in (4)doesnot.
This indicates the critical radius [r. sub. C]
Arrive at local time [[tau]. sub. C]
But could not arrive within the finiteSchwarzschild coordination time.
Calculation results using integral (4)
Points (5)
Summarize in the figure. 1.
As shown in the figure.
1. Based on (4)and (5)
Any value of coordinate time t, 0 [
Less than or equal to]t [
Less than or equal to][]
Unlimited, you can map the corresponding value of local time [tau], 0 [
Less than or equal to]t [
Less than or equal to][[tau]. sub. C]
Based on radial position r.
Figure 3 pause to check the correctness of the diagram
1 at this point, readers are encouraged to stop and look at the picture
1, and perform an obvious check to confirm why the data in the figure
Must be correct.
The main points are as follows: * infinite coordinate time is required (i. e.
* Limited local time [[tau]. sub. C]
Reach the critical radius [r. sub. C];
* Local time [tau]
And with the reduction of r, the coordination time t is carried out monotonous;
* Reach each radial position [r. sub. i]
Coordination time required [[tau]. sub. i]
Completion and local time t complete;
* Based on radial position [r. sub. i]
Value of coordinate time [t. sub. i]
Map to local time [[tau]. sub. i].
Readers who understand why
1 must be an accurate description of the data from the Schwarzschild metric, some changes have been made, and if persisted, this will provide an intuitive basis for understanding the rest of the paper
There is only one small modification to the diagram.
This is necessary to reveal why the critical radius cannot be crossed.
This is the theme of the next section. 4 Fig.
1 modified to consider the limited duration of the compression quality
1 describes the data of the Schwarzschild metric for the assumed compact mass, which is considered to be present forever in the coordination time.
But what happens when the compact mass is replaced by a more realistic entity?
For example, replace the compact mass with a theoretical black hole with a finite lifetime.
The results are shown in the figure. 2.
Because Hawking radiation [6]
, It is estimated that a black hole will evaporate well in 10 minutes (100)years.
So, add to the diagram.
Time of finite coordinates [t. sub. E]
This is assuming the coordinate time required for the black hole to completely evaporate [7].
Use the mapping shown in the figure
1. Radial position can be identified [r. sub. E]-where [r. sub. E]> [r. sub. C]--
Particles will evaporate at the same time as the coordinate time and the black hole [t. sub. E]. Fig.
2 show local time [[tau]. sub. E]
Indicates the local time required for the particle to arrive [r. sub. E]. Local time[[tau]. sub. E]
Corresponding to [Coordinate Time]t. sub. E]--
The coordination time required for the black hole to completely evaporate. Local time[[tau]. sub. C]
Press (5)
, Indicating the local time required for the particle to reach the critical radius [r. sub. C]. Because[[tau]. sub. E]< [[tau]. sub. C]
Particles will experience in local time 【tau]
The black hole will evaporate before reaching the critical radius. [
Figure 2:
The meaning of Figure 52 Fig.
2, according to the data from the Schwarzschild metric, it is shown that no matter what coordinates are used to measure the passage of time, particles falling vertically will never pass through the critical radius of the compressed mass.
For each radial position where the particle arrives (i. e. , [r. sub. S][
Greater than or equal to]r [
Greater than or equal to][r. sub. E]
, There is corresponding coordinate time t and corresponding local time to reach the target position [tau]
Wireless distribution is achieved.
The final destination of the particle does not depend on which measurement of time is used to timing the journey. Fig.
2 An example is proposed that meets the basic requirements of general relativity. -
It is indeed a coherent universe. -
There is a single reality of the logical order of events.
The logical order of events is not changed by the observed reference frame. Fig.
2 is an anchor from which to show how each of the five fallacies discussed below induce deviation from a coherent reality, in which, the logical sequence of events is consistently a coherent reality for each reference frame, in which physical events vary according to the observed reference frame.
In the following fallacious discussion, the evaporation of black holes is used as a convenient method to explain the finite life of the hypothetical mass compacted below the critical radius.
However, it can be clearly seen from Figure 1
2, the particle cannot pass through the critical radius, so, as [pointed out]3]
The mass will never compress its critical radius.
For what this means for collapsing stars, see the discussion below about fallacy 4. [
Figure 3 slightly]
6 Fallacy 1: show the critical radius of the particle after evaporation through the black hole, for the journey of the particle to the black hole, using (4)and (5)
Usually not represented as shown in the figure.
2, but as shown in the figure3 [5, p. 667]. Fig. 3, like Fig. 1 and Fig.
2, is from (4)and (5). However, Fig.
Because Figure 3 is considered a mistake.
3 includes additional data not shown in figure 31 or Fig. 2.
This misrepresents the journey of particles.
Especially in the picture.
3. Trajectory representing local time [tau]
Beyond [[tau]. sub. c]
, Local time required to reach the critical radius [r. sub. C].
The general rule of mathematics cannot be used to generate extradata for local time t that occurs after the critical radius [r. sub. C]isreached.
This is because in (5)
Not defined in [r. sub. C].
However, a new \"principle of the pendulum needle wheel\"5, See pp. 663-664]
Used to generate these additional data.
However, just showing how to generate additional data mathematically does not overcome the logical sorting problem introduced by adding additional data to Figure 1. 3.
Additional data display [r. sub. C]
Can arrive and cross at local time [[tau]. sub. C].
However, this is not possible as shown in the figure
2. Black holes will evaporate at local time [[tau]. sub. E]
So the critical radius [r. sub. C]
The presence will stop until the particles arrive.
A horizontal line is included in the figure.
Indicates the location of the inFig.
The evaporation of the black hole happened.
As shown in the figure.
3. Evaporation of black holes in radial position [r. sub. E], local time[[tau]. sub. E]
And Coordination time [t. sub. E]
Logic occurs before radial position [r. sub. C], local time [[tau]. sub. C]
Coordinate time * coordinates of reference frames using radial propagation photons ,(e. g.
Edington-
Finkestan coordinates and krascar-
Szekeres coordinates).
For each class of specially selected coordinates, it is shown that their reference frames cannot pass through the critical radius within the time of black hole evaporation.
Use the coordinates of the free falling particle reference frame: Share the coordinates of the reference frame with the particles, such as the Novikov coordinates, and also share the same time coordinates.
So the local time was coordinated [tau]
Measuring the local coordinates of novikov coordinates [and the time lapse of the reference frame]5, p. 826].
Measure the time required for black hole evaporation according to Time coordinates [tau]--
This is the time coordinate of the reference frame shared by the shared Novikov coordinates and local coordinates--
Has been proved to be [[tau]. sub. E]. See Fig. 2.
As stated above ,[[tau]. sub. E]< [[tau]. sub. C]
Indicates that a black hole will evaporate at local time [[tau]. sub. E]
Before the reference frame of the Novikov coordinates, the particles will be able to reach the critical radius at local time [[tau]. sub. C].
Using the coordinates of the photon reference frame: Enter the reference frame of Edington-
Finkestan coordinates and krascar-
The Szekeres coordinate is a radial-propagating photon. [5, See pp. 826-832].
The coordinate time t for the photon to reach its critical radius can be calculated very simply from the Schwarzschild metric (1).
Because photons are radial. theta]= d[theta]= 0.
Because there is no progress in the local time of the photon, d [tay]= 0.
Therefore, by setting d [, obtain the form of the Schwarzschild metric used to calculate the coordinate time t valuetheta]= d[phi]= d[tau]= 0 in (1)yielding 0 = [c. sup. 2(1 -R/r]d[t. sup. 2]-d[r. sup. 2]/(1 -R/r), (6)
Points in (4)
It can be used to calculate the coordinate time t of the photon passing through according to the radial distance. Integrand f1(r)
In the terms of Isobtained re-ordering (6), i. e. , [f. sub. 1](r)= dt/dr = 1/c(l -R/r)(7)
When the photon reaches r = R, the product function is (7)
It\'s uncertain. The points are (4)
No convergence.
Therefore, in the limited coordinate time, the photons traveling in the radial direction will not reach R.
Black holes that evaporate in finite coordinate time [t. sub. E]
, Will evaporate when the photon reaches the radial position [r. sub. L]
Outside R.
When the photon reaches the radial position [r. sub. L]
Coordination time]t. sub. E]
, The radial distribution of particles in [r. sub. E]
Beyond the critical radius [r. sub. C]
As shown in the figure. 2.
In the frame of reference of the photon, when the photon reaches the radial position [the black hole will evaporate]r. sub. L]
Before the photon reaches its critical radius R.
As in all reference frames, the reference frame of the photon cannot reverse the critical radius before the black hole evaporates.
9 fallacy 4: the existence of the surface that claims to be trapped under the last asurface that affects Misner et al. [5, pp. 873-874]
The argument is made that once the surface of the collapsed star passes through the critical radius, the light reflected from the surface is still trapped below the critical radius.
This is because the surface of the collapsed star will never pass through the radius. 3].
The last particle on the surface passing through the critical radius can be modeled approximately by the radial falling particle in figure 12.
From the perspective of a distant observer (
Coordination time in figure2)
, Before the infinite coordinate time required for the last particle to pass through the critical radius, the collapsed star evaporates within a limited time.
From the perspective of particles on the surface (
Local time2)
When the particle reaches the critical radius, the collapsed star evaporates very suddenly.
It is interesting to imagine the experience of particles, because the surface of the collapsed star will immediately break down into radiation near the critical radius.
Such an unimaginable proportion of Hell is often covered up by extreme gravity near the critical radius.
But with the burning of the sun\'s surface, the mass of collapsed stars is reduced. -
Causing the critical radius to retreat further below the collapsed star surface-
It may be possible to post a shorter view of the expansion of Hell, which may provide an explanation for the sudden appearance of the Astral.
Since the surface of the collapsed star cannot pass through its critical radius within a finite coordinate time t, Misner et al. [5, pp. 873874]
Reference frame for measurement ingoingedington-
Finkestan coordinates
As described in the previous section, use ingoing Eddington-
The Finkelstein coordinates prove that the critical radius can be crossed, which leads to a problem.
The ingoingEddington-
Finkelstein coordinates do not pass through the Schwazer metric of the collapsed star before the collapsed star evaporates.
This should be particularly clear for examples of collapsing stars, as the surface located outside its critical radius will be an unpenetrating barrier that can stop any photon as an ongoing Eddington-
Starting from the critical radius at R, the finkestan coordinates.
10 fallacy 5: It is an illusion to claim the infinite coordinate time to reach the critical radius. It was asserted that free-fall travellers quickly reached the critical radius, according to the appropriate time measurement.
For distant observers, due to the illusion of light propagation, it seems that it takes an infinite coordinate time to reach the critical radius. 5, pp. 874-875].
Fallacy 5 is a departure from general relativity, because in general relativity, the difference between local time and coordinate time is not only the result of the delay caused by light propagation.
In general relativity, time is carried out at different speeds, depending on the strength of the gravity field that is being measured. Einstein [8, p. 106]
Explanation: \"We have to use clocks with non-similar structures to measure the time in places with different gravity potential.
\"This principle of relativity is reflected in the spatial metric of the rate at which gravity changes time to advance [2].
For an accurate description of how the schwtz metric gravity based on momentum and energy conservation affects time, see [4, Eq. 8].
Because fallacy 5 does not correctly explain the effect of gravity on time, it does not conform to the general theory of relativity or the Schwartz-based metric, and the results predicted by fallacy 5 are inconsistent with the results calculated using the Schwarzschild metric.
The assumptions in the following section illustrate this.
11 a hypothesis that illustrates the logical contradiction introduced by fallacy 5 according to the fallacy 5, measured at the appropriate time, a radial descending traveler quickly arrives and passes through the critical radius of the ablack hole.
The reality that travelers quickly reach the critical radius seems to distant observers that it takes an infinite amount of time due to the propagation of light.
Fallacy 5\'s description of reality is inconsistent with the calculations made using the Schwarzschild metric.
For example, a reflector is placed on the back of the traveler, allowing the distant observer to periodically transmit a beam of light to the traveler.
Using the Schwarzschild metric to calculate the radial position of a beam that moves faster will exceed the slower-moving beam and reflect back to indicate the position of the traveler to the remote observer.
No matter how much the traveler starts before turning on the light (
Measured using coordinate time, even trillions of years or more)
According to the Schwarzschild metric, the light will always exceed the traveler before reaching the critical radius.
Whether it is calculated using local time or coordinate time, the other position that the traveler has been surpassed is the same, providing the start time and override time for each beam is measured with the same time coordinate.
Based on the data patterns obtained from the Schwarzschild metric, this result is inevitable, as shown in the figure1.
As shown in the figure.
2, before the distant observer observes the black hole evaporation, the distant observer can continue to shine the beam of the traveler.
Feedback from the reflected beam will tell the distant observer that when the black hole evaporates slowly during the coordination time, the traveler will stay outside the black hole and quickly evaporate at local time.
This contradicts the claim of fallacy 5 that it is easy for travelers to reach and pass through the critical radius.
In this experiment, remote observers do not even need to shine the beam because the background radiation reflected from the traveler provides exactly the same information.
Hawking radiation also provides the same information.
When distant observers see travelers outside the critical radius, distant observers will also observe Hawking radiation from evaporation black holes, before reaching distant observers, it must first be assigned by the traveler\'s radio.
This shows to distant observers that before distant observers, travelers will experience the radiation emitted during the collapse of the black hole.
In addition, the radiation passed by the traveler will constantly bring information about the location of the traveler to the distant observer, confirming the information from the beam.
Each radiation photon of the vaporized black hole passed by the traveler is a progress report of the traveler\'s position, which will confirm to the distant observer that the traveler has not yet passed the radio through the critical radius traveler.
This progress report will continue until the black hole is completely evaporated.
Beams, background radiation and Hawking radiation from distant observers will all intercept travelers outside the critical radius ---
According to the shivasi regulations--
Regardless of the coordinates used for measurement.
This result contradicts the claim of fallacy 5 that the critical radius is quickly crossed, and because of the propagation of light, it takes only infinite time in the view of distant observers.
Submitted on November 16, 2010/accepted Douglas L on December 15, 2010. Weller E-
Email: Physics @ howweller
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