I have read in numerous places  that an object in free fall into a black hole will be travelling the speed of light when it passes the event horizon.  How is it possible to go this fast?  Does it continue accelerating, faster than light until it is crushed by the singularity?
43997
Imagine we have something very heavy (i.e supermassive black hole) and some object that we can throw with 0.999999 speed of light (i.e proton). We are throwing our particle in the direction of hole. The black hole is so heavy that we can assume that in some moment acceleration of gravity would be say 0.0001 speed of light/s^2. So the question is what will be the speed of proton in few a seconds later, assuming we have such distances that it will not hit the black hole before.
59587
I have found these two formulas:  $v = at + v_0$  $x = \frac{1}{2}at^2 + v_0t + x_0$   a is the acceleration v is the velocity x is the position t is the time $v_0$ is the initial velocity $x_0$ is the initial position   The problem is that with an acceleration of $10$ m.s$^{-2}$ (for example) the object would surpass the speed of light in $3 \times 10^7$ s = $11$ months and $11$ days, which should not be possible.  Is there some other formula that gives the position of an object depending on its acceleration and on the time, but which works and does not allow the speed of the object to surpass the speed of light?
15219
A question has recently come up that goes beyond my knowledge of special relativity.  Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant acceleration, and he has a magical engine that can maintain the thrust needed to accomplish such acceleration even as the vehicle acquires mass.  He measures his acceleration at periodic intervals and sums it up as he goes.  Observers perceive the rocket to increase in speed and gradually approach the speed of light (but never reach it). Two possibilities are being debated for what the pilot observes, and my preference is for the first:   Time dilation gives him the impression that the summation of his readings are approaching light speed at a constant rate, but there is an asymptote involved here even in the inertial frame such that he never actually perceives himself to reach, let alone exceed, $c$, because time slows down to a crawl (as seen from the reference frame) before this can happen. Although to observers he is only approaching $c$, it is possible for the summation of the measurements on his accelerometer to indicate that he has surpassed $c$ and is now traveling faster than light.  From the reference frame he is approaching $c$ and his instruments in the inertial frame tell him that he has surpassed it.   I assume (1) is true beyond a doubt?  If so, is there a straightforward explanation for this?
113155
This is related to  and  The idea is to shine a beam of light from a clock towards a heavy mass, like a black hole, in some manner such that the curvature of spacetime around the mass is sufficient to &quot;bend&quot; the light directly back to the clock. That is, to send the light along a self-intersecting geodesic using a sufficiently curved spacetime. Note that in this case the source and the detector are the same object, so no clock synchronization is required. Hypothetically, this should measure the one-way speed of light. None of the given refutations from the similar posts on this site are convincing. Here are some of the main refutations, as I understand them, and my counter to them: (1) In being curved by spacetime, the light is actually changing direction, hence this is not the one-way speed. To my understanding of General Relativity, the light travels along a geodesic; that is, a curve such that, ignoring technicalities of Differential Geometry, its tangent direction is constant. There is no reflection or acceleration. So in this sense, how can the light with a constant tangent direction be said to change direction? One might say that the path deviates from a straight line in Euclidean space, but given that spacetime is not Euclidean, has no , and has no global notion of direction, this is the only definition of straight or &quot;one direction&quot; that makes sense. Thus, either the light does not change direction and is &quot;one-way,&quot; or we need to be clearer about what exactly we mean by &quot;one-way&quot; in the context of General Relativity. (2) Such an experiment would be impossible or impractical. I think some posters were saying this because the original questions implied that the clock would have to be at the event horizon of a black hole, which is of course impossible or impractical; however, I don't think such an extreme closeness to the black hole is required. Given that the  of a black hole, where light orbits in a circle, is outside of the event horizon, shining the light at some distance outside of the photon sphere should be sufficient to curve the light back to the clock, regardless of the distance of the clock from the black hole (see my rough illustration). At the extreme, we could place the clock directly on the photon sphere, which should be theoretically possible. Regardless, the question is not about practicality, but whether the one-way speed is theoretically measurable.  Update: Essentially what this argument boils down to, I think, is that the average speed of light along a single self-intersecting geodesic may differ from the average speed of light along a non-geodesic self-intersecting path, which is always c. Put that way, however, it does seem a little ridiculous. It is hard to see how the anisotropy of the speed could be defined in such a way as to be consistent with this pathological case. Presumably, we could approximate a single self-intersecting geodesic with a non-geodesic path arbitrarily closely, so, logically, the average speeds over each path should be approximately the same, i.e., c. Furthermore, how would the &quot;preferred direction&quot; of the speed of light behave around a black hole, for instance? Regardless, I still think this experiment does actually solve the problem for the given notion of &quot;direction&quot;. Though the problem is usually posed in the flat spacetime of Special Relativity, with a global notion of direction, so the apparent unanswerability of this question should be seen as a limitation of Special Relativity only, which is then solved by General Relativity.
79828
A thought experiment:   Take an object that is massive enough so we can detect it's position in space by measuring its gravitation field (for example, by sending almost tangential laser beams and measure how they deviate in the object's gravitation field).  Take a simple (non-rotating, non-charged) black hole. Send this object to the black hole. While the object falls into the black hole, measure the object's gravitation field (therefore, the object's position).   I'm wondering what will we see when the object:   Is getting closer to the event horizon. Crossing the event horizon. Fails to the singularity under the event horizon.   My intuition tells me following:   As time around the black hole slows down for an external observer, we may see that the object (i.e. its gravitation field) is always in the place it touched the black hole. (EDIT: According to "", this will not happen.) If my previous assumption is wrong, we may see how the object falls down to the singularity behind the event horizon. Also, the shape of the event horizon will deviate from an ideal sphere and by measuring these deviations we will see a position of the object under the horizon, which seems to contradict to the definition of the event horizon.   My questions are:   In any generally recognized theory that describes this situation? What will happen to the object and its gravitation field according to this theory (theories)? How confident we can be in the description given by this theory?
105833
I recently watched  by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assumption in his famous 1905 paper where he assumes that the speed of light is same in all directions. This made me ask this question is taking the speed of light same in all directions an axiom of some sort? As I've often read no information can be sent at more than the speed of light but here one-way taking the speed to infinite makes no difference. So are all of our physics theories based on the assumption and what would happen if light turns out to be moving at different speeds in different direction? Will that enable transfer of information faster than the speed of light and is there any way for us knowing that the transfer happens faster than the speed of light? The video takes a Earth Mars case where he says it isn't possible for us to every realize this discrepancy but is there a more general proof which says it isn't possible
5561
I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them.   How and why is this possible?   Also, why can't anything travel faster than light?
113650
I'm quite familiar with SR, but I have very limited understanding in GR, singularities, and black holes. My friend, which is well-read and is interested in general physics, said that we can "jump" into another universe by entering a black hole.  Suppose that we and our equipments can withstand the tidal forces near black holes. We jumped from our spaceship into a black hole. As we had passed the event horizon, we couldn't send any information to the outside anymore.   Can this situation be interpreted as that we were in another universe separate from our previous universe? Is there corrections or anything else to be added to above statement?
16595
This question was prompted by . Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone falling into the black hole reaches the event horizon, so could that person see the universe age by an infinite time?  To be more precise, suppose the observer starts falling from rest at time $t = 0$ and some initial distance $r &gt; r_s$. If we wait for some time $T$ then shine a light ray at the falling observer. Will the light ray always reach the falling observer before they cross the event horizon? If not, what is the formula for the longest time $T$ that we can wait and still be sure the ray will catch the observer? If $T$ is not bounded it implies that observer could indeed see the end of the universe.  I can think of a qualitative argument for an upper limit on $T$, but I'm not sure how sound my argument is. The proper time for the observer to fall to the event horizon is finite - call this $\tau$. The proper time for the light ray to reach the horizon is zero, therefore the light ray will reach the observer before they cross the event horizon only if $T &lt; \tau$. Hence $T$ is bounded and the observer won't see the end of the universe.  I think a more rigorous approach would be to determine the equations of motion (in the Schwarzschild coordinates) for the falling observer and the light ray, and then find the condition for the light to reach the falling observer at some distance $\epsilon$ from the event horizon. Then take the limit as $\epsilon \rightarrow 0$. In principle this seems straightforward, but in practice the algebra rapidly defeated me. Even for a light ray the radial distance:time equation isn't closed form (Wolfram claims it needs the $W$ function) and for the falling observer the calculation is even harder.
32721
I am not a professional physicist, so I may say something rubbish in here, but this question has always popped in my mind every time I read or hear anyone speak of particles hitting singularities and "weird things happen".   Now to the question at hand, please follow my slow reasoning... As far as I've learned, to reach a black hole singularity, you must first cross an event horizon. The event horizon has this particular property of putting the external universe on an infinite speed to the falling observer. Now due to the Hawking radiation, and knowing that the cosmic background radiation is slowly dimming, sooner or later every black hole in this particular instance of inflation we are living in will evaporate, according to an external observer of said black holes.  This means that every black hole has a finite timespan, as long as this universe survives that long. Now if we go back to the falling observer, we had already established that such an observer would see the outside universe "speed up" infinitely. This means that when the falling observer "hits" the event horizon, he will (or it if we speak about particles, which is clearer in this case), be immediately transported in time towards the final evaporation moment of the black hole. Either this or the particle gets some weird treatment. My point is, such a particle never gets to the singularity, because it has no time to get to it. The moment it crosses the event horizon, the black hole itself evaporates.  Where am I wrong here?
29658
I have looked online to no avail.  There is two competing answers and I am curious to know which one is right.  Someone asked me this question.  If you are traveling at the speed of light can you see your reflection in a mirror in front of you?  My answer to the question is no, I would figure that in order for that to happen the light reflecting off you that would appear in the mirror must travel faster than the speed of light to actually reach the mirror (which we all know is impossible).  He says the answer is yes, that it is all relative to the current frame of reference.   Can anyone validate the correct answer with possible references?
54513
As explained in the answers to  post, photons apparently exert a gravitational pull on other objects. It has also been explained on this site, that gravity propagates at the speed of light.  I'm wondering, though, how do you reconcile these two facts? I'm trying to imagine the gravitational field made by a photon and it seems like there are some paradoxes. For example, how can gravity propagate ahead of the photon at the speed of light, if the photon is also travelling at the speed of light? My guess is the solution is probably found in relativity, but I certainly can't figure it out.   Right now, the best I can do is to think about gravity as sound, and a photon as an object travelling at the speed of sound. Can anyone help me out?
55626
I recently read an article that said that the event horizon telescope took a picture of a black hole (Sagitarius A*) and it will be presented on the 10th of April. I was wondering how this picture is taken and what a picture of a black hole even means?   The only explanation I could think of was that the telescope took pictures of the stars surrounding the black hole and then a sudden absence of stars pointed that a black hole is present.  Can anyone explain how black hole photos are taken or how does event horizon telescope work?
5251
I've read a lot of conflicting answers in these forums. However, today saw the awesome announcement of gravitational waves. Two black holes merged:   Not only that, they merged FAST. In 1/5th of a second revolving around each other 250 times a second. The entire event was quicker than a heartbeat. Moreover, we observed this happening as distant outsiders. So now we can say for sure:   Objects approaching the event horizon DO NOT appear to slow down Black holes CAN merge in a finite (and quick) amount of time And all this is wrt a frame of reference far, far away   To quote the NYTimes article:  One of them was 36 times as massive as the sun, the other 29. As they approached the end, at half the speed of light, they were circling each other 250 times a second.  And then the ringing stopped as the two holes coalesced into a single black hole, a trapdoor in space with the equivalent mass of 62 suns. All in a fifth of a second, Earth time.  However, everything I've read so far has let me to believe that an outside observer should never be able to measure the collision happening in a finite time. So what exactly is happening here? I must have read at lest 5 different versions of this so far everywhere in these forums over the past several years.
25518
How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but how exactly does that massive gravity slow down time?
1453
How much extra distance would I have to travel through space to get from Earth to a stellar mass event horizon? (compared to the same point in space without a black hole)
9332
Are black holes in a sense transparent? Meaning, they don't 'hide' any stars that happen to be 'behind' them?  A regular object obviously blocks a point source of light emanating from 'behind' it. Meaning it creates an area of space photons cannot get to us from. But a massive object curves space, and so via gravitational lensing we can sometimes see distant stars that are 'behind' other stars (by behind I mean that if the star in the middle would suddenly vanish, the trajectory of photons traveling from the distant star to Earth would have passed through the volume now occupied by the middle star).  My thinking, is that black holes curve space so much, that from ANY source of light outside it, light has a trajectory to reach us on Earth (assuming of course no other object blocks it on its way).  The reasoning for this is: Suppose we draw the straight line between us and the light source (as if the black hole wasn't there at all). Photons from our light source crossing the event horizon would obviously 'fall' inside. A photon in theory traveling exactly tangent to the event horizon would in a sense go 'into orbit' around the black hole (obviously there is no such thing, because the black hole isn't perfectly spherical, and there are quantum effects and so forth. But I'm focusing on the geometry), crossing our straight line exactly at the intersection of our line and the event horizon. Any photon passing near the event horizon, but a bit farther, would follow a curve that intersects our line a little farther from the event horizon. Continuing this, there would be at last be a photon that would exactly curve our way.