# Event Horizon without black hole?

I'm curious if a black hole is a necessary precondition for an event horizon.

Could you have an active star that's massive enough that it would create an event horizon even before it collapses?

• how do you define "black hole"? it usually means "an object with an event horizon"... – AccidentalFourierTransform Jan 17 '17 at 18:31
• @AccidentalFourierTransform so accelerating particles and the universe are also black holes? – DilithiumMatrix Jan 17 '17 at 18:56
• @DilithiumMatrix sure, why not? it's astrophysics, no need to be precise ;-) – AccidentalFourierTransform Jan 17 '17 at 18:59

It isn't possible to have stable massive object with an event horizon around it.

The acceleration required to stay at a fixed distance $r$ from a spherically symmetric object can be calculated from the Schwarzschild metric. This is done in What is the weight equation through general relativity? but I'll just quote the result here:

$$a=\frac{GM}{r^2}\frac{1}{\sqrt{1-\frac{r_s}{r}}}$$

Where $M$ is the mass of the object and $r_s$ is the event horizon radius. So it is just the Newtonian gravitational acceleration multiplied by the extra term of $1/\sqrt{1-r_s/r}$.

The problem is that as $r \to r_s$ the acceleration $a \to \infty$, that is to hover at the event horizon requires an infinite acceleration. As soon as you go inside the horizon you simply can't hover at all. Inside the horizon it is impossible to resist being dragged inwards towards the singularity.

And that's why there can't be a stable massive star inside the horizon. The forces between the atoms/ions/whatever that make up the star are not strong enough to resist it being crushed inwards to form a singularity.

The fate of a collapsing star can be approximately modelled by the Oppenheimer-Snyder metric. This is only approximate because it assumes a constant density inside the star, but it gives us a rough idea of what happens. The event horizon actually starts at the centre of the collapsing object and grows outwards until it is greater than the radius of the collapsing star. The star then goes on to form the singularity at the centre of the black hole.

I'm curious if a black hole is a necessary precondition for an event horizon.

A black hole is a name for what an event horizon contains (in my limited understanding).

Could you have an active star that's massive enough that it would create an event horizon even before it collapses?

The problem would seem to be that fusion takes place in the core. If mass was so great that an event horizon formed, the rest of the star would instantly be cut-off from the fusion generating core and it would immediately collapse anyway. No fusion (outside the event horizon) means no energy to resist gravity.

I'm dubious that fusion could be said to happen in such a dense core anyway, as you're past the density at which fusion would have any meaning and into territory we don't fully understand (quark-gluon plasma and beyond I guess ?).

A black hole is defined by event horizon. What is inside EH, is black, and so black hole.

Terminology aside, to answer your question simply, and with an analogy - Possibly, yes, but momentarily even if it is possible.

Collapsing analogy - Suppose an object falls into a pre-existing event horizon. Now, there is an EH, but theoretically, the falling matter is still collapsing once it is past the EH. How long that collapse takes, I do not think any one can say for sure. That is why, I said momentarily.

As John Renee wrote, if the EH starts at the center, then, there is an EH while the star still looks like a star (not a BH) from outside for at least a moment. Can we say, there was no black hole when the EH started - NO! because, that is the terminology - Only EH defines the black hole. As EH was expanding, so was the BH.