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I was wondering about the characteristics of a black hole, and I know they have mass, spin, and an insanely strong gravitational force. But, as far as I know, basically all black holes possess the event horizon. In fact, according to Wikipedia and our friend, Stephen Hawking:

"the absence of event horizons means that there are no black holes"

So...does that make the EH the defining characteristic of a black hole? Or can I say something is a black hole if it has an equal gravitational strength? Thanks!

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    $\begingroup$ Re. "Stephen Hawking says there are no black holes" – see physics.stackexchange.com/a/95395 $\endgroup$
    – jng224
    Aug 30, 2021 at 10:18
  • $\begingroup$ Is a naked singularity a black hole? $\endgroup$
    – throx
    Aug 31, 2021 at 2:32

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All black holes have an event horizon, but not all event horizons are associated with a black hole. If you fly on a rocket that accelerates at a constant rate, your path follows a hyperbola that never crosses a particular line in spacetime called the Rindler Horizon. No event that happens after the Rindler Horizon can ever send any signal to the rocket - even at the speed of light, it can never catch up. As far as the observer on the rocket is concerned, this line acts like a black hole's event horizon. Once something crosses it you'll never see it again. But to a stationary observer, there is nothing there. It's just the future.

As for what is the defining characteristic, there are a number of definitions. For example, one way to define it is as a region from which it is impossible to escape to the infinite future. (So the Rindler horizon doesn't count, because it is easy to get to infinity from there.) Of course, that depends on the universe being infinite...

The problem with definitions is that you presumably want to exclude regions like 'the future' or 'the whole universe' which are also impossible to escape from. (And which also contain singularities.) There are various other regions that can be associated with black holes besides the event horizon, like the ergosphere. And when black holes are charged and spinning, their internal structure gets more complicated, with the possibility of Kerr black holes with internal wormholes opening up into other universes beyond our own that make the definitions even murkier. It's quite tricky to come up with a definition that captures all the cases of interest and excludes everything else.

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A black hole is a region of spacetime that nothing can escape from. There is no direction that you can travel in that leads from inside the black hole to a point outside the black hole. The event horizon marks the boundary of this region of spacetime. So all black holes have an event horizon. Whether you call the event horizon the defining characteristic, or whether you call the region inside the event horizon from which nothing can escape the defining characteristic is a matter of preference. The boundary can't exist without the interior; the interior can't exist without a boundary.

If something has "equal gravitational strength" then it would have an event horizon.

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  • $\begingroup$ Nice short answer. One thing you could add: the feature that distinguishes a black hole from, say, a en.wikipedia.org/wiki/Event_horizon#Cosmic_event_horizon is that every path any particle or light can take inside the black hole's horizon is leading towards the singularity. This is a bit stronger than just saying that you cannot go outside, and in some sense you could IMO take this as a defining characteristic. $\endgroup$
    – AnoE
    Aug 31, 2021 at 11:17
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Is the event horizon the defining characteristic of a black hole?

Yes, it's the only widely accepted definition.

This definition has the disadvantage that it's nonlocal. That is, it defines a black hole based on whether or not light can escape to infinity, which means that you can't judge it based on the properties of the spacetime near the black hole. So for example, if you're doing a numerical simulation of gravitational collapse to form a black hole, there is nothing you can look at easily in your simulation to define where the event horizon is or whether it has formed yet.

An advantage of the standard definition is that for an object that is a black hole by that definition, we can prove no-hair theorems. Observationally, it also connects directly to criteria we can use to tell whether a given object is a black hole.

There have been attempts to come up with alternative definitions: http://arxiv.org/abs/gr-qc/0508107

Or can I say something is a black hole if it has an equal gravitational strength?

No, this won't work because there is nothing special about the gravitational strength of a black hole (assuming you define that as the gravitational field g at some fixed distance). For example, if a star undergoes gravitational collapse to a black hole, the strength of its gravitational field, at a fixed distance, is the same before and after collapse. The equivalence principle also tells us that the gravitational field g is not a very useful concept to work with in general relativity, because it can have any value you like (including zero) depending on your frame of reference.

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  • $\begingroup$ Why can't you tell in a simulation whether an event horizon has formed yet? I understand that the shape and possibly the existence of an EH is specific to each observer but after choosing a reference frame, shouldn't an EH be easily noticeable/determinable for any mass accumulation of some shape, rotation etc.? (As an abstract argument I'd say that the universe can be regarded a perfect simulation of itself, and we can detect/predict EHs.) $\endgroup$
    – Peter - Reinstate Monica
    Aug 30, 2021 at 13:57
  • $\begingroup$ @Peter-ReinstateMonica: The event horizon is defined as the boundary of all points for which a signal cannot escape to infinity at any point in the future. But this means that you need to know the entire future evolution of the spacetime to definitively say whether a point is inside or outside the event horizon. One can, however, define the notion of an apparent horizon whose properties are much more like those you describe: it's observer-dependent and can be determined without knowing the complete future of the spacetime. $\endgroup$
    – Michael Seifert
    Aug 30, 2021 at 15:08
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I was wondering about the characteristics of a black hole, and I know they have mass, spin, and an insanely strong gravitational force. But, as far as I know, basically all black holes possess the event horizon..... So, does that make the EH the defining characteristic of a black hole? Or can I say something is a black hole if it has an equal gravitational strength?

In general relativity, the gravitation of a black hole is not special or unique, per say. A Schwarzschild black hole has a coordinate (unphysical) singularity at its event horizon, and a gravitational (physical) singularity at its center. The tidal force felt by a particle near the event horizon is inversely proportional to the mass of the black hole, which is why supermassive black holes can tidally disrupt stars that have passed within their event horizons, whereas a stellar mass black hole could disrupt a star outside of its event horizon. The Kerr black hole differs from the Schw case in that it has rotation/spin resulting in the physical singularity as a ring structure.

There are many definitions of a black hole. The commonly used/known one is based on the notion of null infinity of R. Penrose and S. Hawking, who explored the singular structure of spacetime using path incompleteness and the singularity theorems, which essentially defines the black hole using its event horizon and avoiding the difficulties of the physical singularity. Saying that two objects have "equal gravitational strength" is rather vague, since it depends on all kinds of things: for example, in the large separation limit, the gravity of a slowly spinning star can be approximated by the Schw black hole reasonably well.

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In astronomy, observationally, we insist on two things:

  1. Evidence of infall/outflow/orbit velocities approaching the speed of light.

  2. Evidence that the object is not a neutron star: usually a mass beyond the most generous theoretical limit for neutron star mass.

The horizon is an entirely theoretical concept, unobservable if the theory is correct.

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