Time is supposed to stop at the black hole event horizon. So the question is what happens inside the black hole, does time for instance go back wards as some theorists believe.
Let's start with the fact that the black hole is a mathematically nonsensical object.
Time on the event horizon does not exist. Inside a black hole, time flows backwards.
A black hole is not a necessary consequence of the general theory of relativity.
Return to the initial version of Einstein's equations (1913) + additional postulate provides a smooth solution of the equations.
https://www.researchgate.net/publication/303844514_Gravitational_field_equations_and_relativistic_homogeneous_gravitational_field
New article now only Russian
https://www.researchgate.net/publication/307608989_Uravnenia_gravitacionnogo_pola_Vytalkivausee_resenie_Temnaa_energia
Preprint Gravitational field equations and relativistic homogeneous g...
Preprint Уравнения гравитационного поля. Выталкивающее решение. Темная энергия
Article interesting
· Going to Classical Mechanics, for the simple pendulum period [T sec] :
T= 2π[ sqrt (l/g)]
i.e. time [ PERIOD OF OSCILLATIONS] is a function of length and acceleration of gravity
[l = length ( in m) of the pendulum, and g is the local acceleration of gravity im m/s^2].
LHS [units seconds] = RHS [units seconds].
Half period t/2 [in sec] may be replaced by the circle’s 2πl, arc lθ = L [in meters] i.e. arc defined by bob’s center reciprocation between the two end of movement limits [ and θ the small sector angle of reciprocation ].
If T/2[ in seconds] is substituted by L[in meters ] then g in m/s^2 units has to be substituted by m^(-1) i.e. 1/m.
Then l/g units will take value of m*[1/m] = m^2 and sqrt[m^2] = m
Tthus LHS [in meters] = RHS [in meters].
Note 1.The interest of the formula " T= 2π[ sqrt (l/g)] " is that increased values of g, result into decreased values of periods [ or increased frequencies] i.e in STRONG GRAVITATIONAL FIELDS [e.g. black holes] time does not tend to ZERO but PERIOD OF OSCILLATIONS does or : FREQUENCY tends to INFINITY! *
* Relativity specifies that, as such [ i.e in strong gravitation fields] “ time tends to zero”.
Note 2. A similar, quantified measure of time, in our local environment, is that of the gravitational flow of sand in a clepsydra.
Regardsfrom Athens,
Panagiotis Styefanides
------------------------------------------------
The World I understand
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No-the singular behavior of coordinates at the horizon depends on the observer, it doesn't have invariant meaning. For a freely falling observer, time behaves as usual, up to the singularity, that's an event at finite proper time for this observer. For the accelerated observer, that cannot observe the singularity, time behaves as usual, forever. For the accelerated observer that can observe the singularity, time behaves as usual, up to the singularity, that, once more, occurs at finite proper time for this observer. Time isn't an invariant quantity, that's all, so it doesn't make sense to compare how it is defined by different observers.
There isn't any ``inside'' (or ``outside'') of a black hole, because the horizon isn't a space-like surface, it's a light-like surface. There is just a black hole spacetime, that contains a singularity, for certain observers.
One shouldn't identify the star, whose collapse gives rise to the black hole spacetime, with the black hole.
In a spherical coordinate system the event horizon is a bad defined surface. Making a change of coordinates helps understanding what´s happen on this surface. In general relativity Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere outside the physical singularity.
Check out this coordinates, it helps understanding what happens on the event horizon.
@ stam
To answer "No" to an open question - that describes your approach exactly.
A well described standard rote answer.
But you say there is no connection between the collapsing star and the black hole it forms
When there is clearly a close connection to the collapsing star and the black hole it forms.
Please examine your logic - not that you will ever understand the concept of that in any case. That is logic or the possibility of examining it.
The properties of a black hole spacetime are independent of the properties of the star that collapsed-the metric of the former is independent of the equation of state of the latter. So an observer in a black hole spacetime can't deduce the detailed properties of the star that collapsed.
By gravitational collapse-and that's been computed since the 1930s by Oppenheimer and his students and has been used for templates for sources of gravitational waves-that's how it could be deduced that the source of gravitational waves measured by LIGO was the merger of stars that had suffered gravitational collapse. However the equation of state of the stars in question isn't relevant; that's why they are identified as black holes. The words are ambiguous, it's the mathematical description that's relevant.
But LIGO was able to measure the mass of the black holes, and by definition that is dependant on the mass of the progenitor stars
But not on their composition-that's what ``equation of state'' means. So it isn't true that this is by definition-it's the result of the procedure of collapse.
The fact that, in the recent measurements, each black hole had a mass of 29 or 36 times the mass of the Sun, for example, doesn't imply anything about what kind of stars these were, before they collapsed-nor, in fact, on the mass of the stars themselves.
These points, incidentally, don't have anything to do with the question.
"For the accelerated observer, that cannot observe the singularity, time behaves as usual, forever."
his is not true.
Look at the work of Einstein in 1907. 5. Einstein A. Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen. Jahrb. d. Radioaktivitat u. Elektronik, 4, 411—462 (1907).
It is from this work started GRT. there is considered accelerated system. It is shown that the time depends on the position hours.
There is a classic work...Møller C. Theory of Relativity. Oxford University Press; 2nd edition, (1972).
The metric proposed by Meller has a feature similar to the feature of the Schwarzschild metric.
I started with a non-inertial systems. It turned out that the majority of them are not described in Euclidean geometry. For example uniformly accelerated system has a non-zero Riemann curvature. It turned out that the Einstein tensor is also non-zero. This makes it possible to ascribe the gravitational field of the energy-tension tensor. And on the basis of this return to the original version of Einstein's equations. .
The result - instead of the Schwarzschild metric obtained smooth
Time is a coordinate-it doesn't have an invariant meaning, in special, or general relativity. That's what matters. The only difference the black hole singularity makes is that there exist observers that have the singularity in their future at finite proper time (free falling and certain accelerating observers) and other accelerating observers that do not have the singularity in their future at any finite proper time.
Yes, but inside the black hole time it does not make sense.
The black hole was originally mathematically meaningless. Such was left now.
The black hole does not follow from the theory. It follows from the simplified equations of the gravitational field.
The known black hole metrics (Schwarzschild, Reissner-Nordstrom, Kerr) are exact solutions of the full Einstein equations and don't involve any approximation-the mathematics was and is unambiguous, the physics was, initially, unclear.
Once more: there's no such notion of ``inside'' or ``outside'' a black hole, since the event horizon isn't a space-like surface, like the surface of a star; there's a black hole spacetime, in which certain observers encounter a singularity in finite proper time and others do not. One shouldn't confuse history with mathematics. And one shouldn't confuse the star, whose collapse gives rise to the spacetime, with the black hole. The star is an object, the black hole isn't.
While there is some confusing terminology that's used, most notably ``near horizon geometry'', that can lead to the mistaken conclusion that the horizon is a place, what matters is the mathematical description, that's unambiguous and describes a certain class of observers in a black hole spacetime. These observers aren't ``near'' any object, however.
"The known black hole metrics (Schwarzschild, Reissner-Nordstrom, Kerr) are exact solutions of the full Einstein equations..."
- Undoubtedly
"The star is an object, the black hole isn't. "
- Perfectly. So why do it? I think we are doing nothing for many years ...
Basic theory of progress was due to the failure of the exact equations, 1915. The grand success made us forget about the "little things" - the field of energy. Reasonable principle put forward by Einstein in 1913, forgotten.
Modern Einstein's equation does not contain the energy of the gravitational field. It is permissible for small fields and unacceptable in strong fields. Therefore Schvartsshilda metric gives good results in small fields and meaningless at strong.
It rather depends what you mean by "inside a black hole". If you mean "at a black hole singularity" then the question is something which General Relativity does not answer -- presumably, a proper extension of GR and quantum mechanics is needed to understand and perhaps answer such questions at or near the classical singularity. But if you mean "inside the event horizon" then there is a clear classical answer. Recall that the event horizon of a black hole is the surface beyond which even light cannot escape the gravitational effects of the black hole. Within the event horizon, but away from the singularity, time measured along the world-line of an observer is quite well defined. An observer would simply see her clock continue to tick as normal, as she passed through the event horizon (which she would not initially realise she had done). As you suggest, an observer outside the event horizon watching the first observer's clock would however see it slow down and in the long run appear (almost) to stop.
The notion "time" inside a black hole has in principle another sense than the observed time. The calculations in frames of GR show that the time at the surface of black hole is stopped. It means that the time does not flow from the past to the future as in our observed Universe. It is difficult to understand this situation in frames of the usual notions. It means formally that the observer is inside the observed space-time. It is evidently, we cannot feel? what world is inside black hole. We can suppose for example that the time inside black hole flows in the opposite direction, i.e. the inner space is the mirror reflection of the usual (observed) world. This conclusion is obtained from the mathematical calculations as for the Schwarzschild solution in the empty space so for the de Sitter space. But these calculations are only mathematical speculations. Really we cannot live inside the black hole, therefore we cannot observe this space. It is possible to assume that the space is related to the space possessing another geometric and physical characteristics.
Take the expression for the Kerr metric: https://arxiv.org/pdf/0706.0622.pdf (eq.(3)), for instance. Compute the LHS of Einstein's equations. Compare with 0 (the RHS, in vacuum).
There's no point in speculating, when it's possible to calculate. And there's no point in refusing to realize that individual coordinates are not invariant under general coordinate transformations, nor that there no such ``places'' as ``outside'' or ``inside'' a black hole. So any discussion in these terms is meaningless-as is the statement about ``living inside (or outside) a black hole''.
Of course it's possible to make observations that can lead to conclusions about the geometry of spacetime and, whether this spacetime is a black hole spacetime.
The spacetime of our Universe has been measured to be described by the Friedmann-Robertson-Walker-Lemaître metric, for instance. This metric describes a spacetime in accelerated expansion from a singularity. It's a past singularity, not a future singularity, which is that of a black hole spacetime.
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