Falling into BH question

By 'infalling', I hope you mean 1) matter that is present in the interior when the event horizon forms, or 2) exterior matter that will find itself within the horizon if the Swarzchild radius increases, for instance.

Naturally, yes. At least it would in the idealized black hole that was already fully-formed. If there is no singularity, apparently, there is no true event horizon.

Update on the falling into a realistic black hole with Hawking radiation:

My old GR professor got back to me, and pointed out something that I had forgot to consider: it depends upon whether or not a singularity forms before the black hole evaporates. If the singularity forms, then yes, some of the matter will travel in and smack the singularity before evaporation. If not, then indeed, infalling matter will see the black hole evaporate before it. Apparently the question as to whether or not the singularity will form in an evaporating black hole is still open.

Yes. I think that your old GR professor has described the problem nicely.

If an event horizon is something that anything can fall through, then it's inevitable that a singularity will form.

The photon emitted at the limit of the horizon will be received in infinite time measured by the distant observer, ie. never (supposing the purely classical case without evaporation). You're apparently considering this problem within special relativity, but that only allow to talk about flat spacetime with no gravity, where black holes do not exist indeed. I friendly recommend a reading of the beautiful and accessible introductory text by James Hartle, "Gravity: An Introduction to Einstein’s General Relativity", Addison Wesley (2002) (available on Amazon).


I was supposed to mean that in terms of the distant observer clock, the photons which he would expect to receive much sooner if the spacetime was flat, will be received much later. This is again a manifestation of spacetime curvature, not a modification of properties of light which always move locally at the speed of light c. That the travel time of light increases within a strong gravitational field is one of the classic tests of general relativity which has been confirmed experimentally with a precision of about 0.1%.

Naty1

I raised the question of how an object is able to cross the event horizon because I don't understand how it happens and what seems logical to me is at odds with the widely accepted interpretation of black hole geometries. Certainly I accept that observers in different reference frames don't always agree on observed time,distance,mass,etc. but I also believe that events in one reference frame can be mathematically transformed into any other reference frame to explain what those observers see. To suggest that simply because observers in different reference frames disagree about time, distance or mass, is sufficient reason to accept an ad hoc instance of differing observations without providing some sort of transformation between the reference frames is less than scientific.

I also raised the question hoping that someone here could point out the errors in my logic. The references I've seen, like xantox's posts, don't address the issue of the evaporation of the black hole during the extremely dilated time an object experiences as it falls towards the event horizon. Briefly put, is time infinitely dilated at the event horizon and if so, how does an object cross that event horizon in finite time? If it crosses in finite time in one frame of reference but not in another, what is the transformation between those reference frames that permits that?

Your suspicions are valid for a test particle. A massive object that perturbs the event horizon may be different.

In addition to this, a central singularity is often invoked, but not proven nor motivated.

Imagine you are halfway between two black holes that are approaching each other. To a observer the horizons merge, with you inside. Apparently the size of the black hole must increase for something to cross an event horizon--which, come to think about it, is nearly a tautalogy, anyway.


Why should it be dense? At the time of collapse, the mass is not all stuck at one point in space. Put enough air together at standard density and it's a blackhole.

Using the contemporary view of what happens when things fall to black holes, the apparent velocity (with respect to the black hole) of an infalling particle approaches the speed of light.

Does this not yield a Relativistic mass increase?

The Schwarzschild metric relates radius to mass: R = M (2G/c²)

Since radius and mass are directly proportional, the mass density of a Schwarzschild black hole drops with radius. Density is proportional to R^-2.

Interestingly, (according to the WMAP 5-year results) the mass density of a Schwarzschild black hole with a radius equal to that of the observable universe would equal the density of the observable universe.

In fact, our observable universe satisfies all requirements for a Schwarzschild black hole:

• Spherically symmetrical
• No electrical charge.
• No spin.
• R = M (2G/c²)

Wilkinson Microwave Anisotropy Probe:
http://map.gsfc.nasa.gov/universe/WMAP_Universe.pdf

Presuming that it's possible to have "matter that is present in the interior <of an> event horizon" sort of bypasses the whole core of any discussion of whether it's possible to fall through an event horizon.

Using the contemporary view of what happens when things fall to black holes, the apparent velocity (with respect to the black hole) of an infalling particle approaches the speed of light.

Just in case anyone missed it, The Schwazschild metric applies to space without any matter in it. The Schwarzchild metric is equally applicable to the space around the Earth, for instance. It's just not applicable within the Earth itself. All that is required of it, is that the mass be mass be spherically symmetric and unchanging in qauantity over time.

There is nothing that requires the central mass to occupy a single point.

Basically there's no such thing in General Relativity of an object's velocity that is far away from the observer. Relative velocities are only well-defined if computed at the same point in space-time. You just can't subtract velocities at different points, so this sort of question is meaningless.

Furthermore, the idea of the relativistic mass is no longer used, as it leads to too many mistakes. This would be one of them, because the energy of the infalling object certainly does not diverge at it crosses the event horizon.

I don't know where you are getting your facts. The velocities at assymtotic infinity are infinite in the reference frame of the horizon.

I'm not suggesting that the velocities of infalling objects would subtract, somehow, from each other. I'm suggesting that relativistic mass increase is inevitable for an infalling object.

Regarding "the idea of the relativistic mass is no longer used", perhaps I should refer to "momentum" or "energy"?