Hi,Would you please help me in this case:
According to relativity , the clocks work slower in a gravitational field and the stronger the field is, the slower the clock works.It means in the frame of an observer far from the event horizon of a blackhole, it takes an infinite time for an object(a spacecraft for example) to reach the event horizon so
the mass of a blackhole should never increase during the time because in our frame no object has fallen onto the event horizon.
Is this true?

This is a popular misconception.It just appear to have not fallen, in fact it has already fallen there and so the gravitational field changes accordingly with increasing mass.
Gravity fields are curvatures in spacetime, more mass = deeper curvature.

Hope that helps.

BTW sorry if my grammar is very bad in some posts, I don't know how to properly formulate some things as I am a foreign speaker.

See this recent thread, and the links in it.

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"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

There's a lot of misconceptions, but this is not one of them. Well, there are misconceptions about how it works and the meaning of it all. "Already fallen in". Well, GR plays some crazy games with temporal based notions such as "already".

In Schwarzschild coordinates, and indeed the coordinates based on the local ruler and clock of any external observer whose own world line does not itself cross the horizon, events past the horizon *never happen* in finite time. According to the simultaneity of all those external observers, the sense of where in their notion of space things are at their notion of "now", nothing ever crosses the horizon. Things only asymptotically approach it. The moment of horizon crossing occurs at t = infinity. Events past there *never happen*.

If you're on a world line that crosses the horizon, it happens in finite time and that world line terminates in short order at the singularity. But again, those events never happen in the frames of external observers. Events inside the horizon are causally disconnected, and this is how that plays out.

This is no problem for the external gravity. The more stuff falls in, the more mass is down there sitting frozen and gravitating externally. Additional mass leaves "more gravity behind" as it falls in.

And this violence to our Newtonian/Galilean notions of space and time is no restricted to real gravity. An accelerating observer perceives an event horizon behind which events never occur in his frame as well. An inertial observer perceives that as due to the fact that light beyond a certain point can only asymptotically catch that accelerating observer. Light can never reach him.

And that's the same thing inside a black hole horizon. Light can never get out to catch any external observers.

-Richard

So would we be able to experience the gravitational effect yet not see the visual effect i.e if we were close enough to witness a star being sucked into a black hole we could detect the increased gravity from the now more dense black-hole but the star seems not to have been sucked in yet?

Well, if light can't get to you, then changes in gravity can't either. In GR, gravity propagates at the speed of light.

Note I said "changes in". What is the external field of a spherical mass M confined to radius 2R vs that of one at radius R? It's the same. As mass falls in a black hole, it leaves behind the additional gravity so to speak. All those events that increase the gravitational field the external observer perceives occur before it crosses the horizon.

In this coordinate view, fretting about what happens inside the horizon is meaningless. Events inside never occur. So how can you worry about effects of events that never occur? That's how it is as far as causal effects go.

-Richard

I worry about all the effects, even the ones that don't happen!
but on a serious note yes i see your point. thanks

The key word here is "slower", which prompts the obvious question: Slower with respect too what? The answer is slower with respect to distant clock in a much weaker gravitational field. That means if I am standing way out here in safety, looking at a clock way over there near the black hole event horizon, I will say that clock is running slow compared to my clock. But what about an observer sitting next to the clock near the event horizon? What is the standard by which that observer decides their clock is running "slow" (as opposed to "slower"; the distinction is important)? So now we dig down to the real question: Near the event horizon, is time really "slow", by some absolute standard, or does it just look slower to the distant observer?

This is the basis of a lesson on two different kinds of time: coordinate time and proper time. Coordinate time is the time coordinate in an equation, maybe an equation of motion, or a field equation. Proper time is the time recorded by a clock in free fall. The two are not the same, and are used differently in physics. This is what publius is getting at when he talks about world lines ...

Imagine that the "world line" is a trajectory through spacetime, from here to there. If here & there are both outside the event horizon, then "events past the horizon *never happen* in finite time". If on the other hand, "here" is outside the event horizon, and "there" is inside the event horizon, the events inside the event horizon do indeed happen in finite time.

And this all comes from the difference between coordinate time & proper time. My clock sitting next to me at rest with respect too me give me proper time. Any other "time" anywhere else in the universe is, with respect too me, a coordinate time. So the coordinate time near a black hole stops ticking altogether at the event horizon, were a distant observer would say that time "stops". However, if I now connect myself and that clock at the event horizon with a trajectory (world line) that I proceed to move along simply by falling through the gravitational field from here to there, my clock will never seem "slow" to me. It will tick just fine, and I will fall through the event horizon into the black hole, increasing its mass. An outside observer will say that I never fell in, eventually stopping at the event horizon.

So it's just an appearance, and m1omg is right ...

But do note, even if we allow that I never fall into the black hole, my mass will be hanging around the event horizon, as seen by some distant observer. So the black hole would still increase in mass, according to the distant observer.

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Don't try this at home - We're what you call "professionals" - MythBusters.

Much of what has been said in this thread is correct, but there is a considerable amount that is based on misconception of black-hole dynamics. I'll describe an experiment, first from the point of view of an observer watching at a safe distance from the event horizon and one from the point of view of an observer in free fall into the black hole:

In the first case, you're stationary at a safe distance outside the event horizon of a black hole with a pair of identical synchronized clocks A and B. Clock B, a deep saturated violet in color, is attached to a long massless measuring tape free to unwind from a frictionless drum.

You release clock B and watch it fall toward the event horizon of the black hole, unreeling the measuring tape as it falls. At first, its speed increases but after a while slows, becomes momentarily constant, then begins to decrease. Throughout this time, the movement of its hands gradually slows. Its initially bright violet color gradually fades progressively through paler shades of spectral colors indigo, blue, green, yellow, orange, and red, the intensities of the colors simultaneously fading into invisibility. Then, through use of a sequence of infra-red, microwave, radio-wave, and x-ray, and finally gamma-ray detectors, you try to follow it for awhile, but finally lose it altogether long before you reach the end of this sequence of detectors. The combined outputs of all of your observations reveal that the distance of the clock from the event horizon has been approaching the event horizon asymptotically but will never reach it. Throughout this time, the hands on the clock have been slowing at a rate that would bring them to a full stop by the time the clock reached the event horizon. The measuring tape reveals that the slowing of the descent toward the event horizon is an illusion. The clock is actually falling more and more rapidly as is revealed by the increasing rotational speed of the windless from which the windless is paying out the tape. Eventually, although the descent rate of the clock appears to have stopped altogether, the windless is paying out tape faster and faster. This process continues indefinitely.

In the second case, you are in free fall toward the event horizon along with clock B. You neither see nor sense anything unusual in your immediate surroundings most of the way down although your descent is accelerating steadily. Clock B continues to run at the same rate as before, but you see clock A at its fixed distance from the event horizon running faster and faster, its hands eventually whirling around so fast that they become a nearly invisible blur, like the propeller of an airplane with the engine running at full throttle. The speed of your fall toward the event horizon will increase at an accelerating rate.

If the diameter of the event horizon is comparable to your own dimensions, you are in for additional unpleasantness: Whatever your orientation with the vertical, you'll feel yourself being stretched along a vertical axis and compressed in the horizontal plane. If the diameter of the event horizon is large compared with your own dimensions, you will have no way to detect your passage through the event horizon: It would look like a totally black circle as you approach it, hence the name "black hole". Once you fall through it, you'll still see nothing at first. Because of the reversal of the roles of time and distance in the direction toward the center of the black hole, I have no idea what you'd see and won't try to guess. All I can say is that it presumably wouldn't be pleasant and that you'd rather be somewhere else.