[flr (OP)]

An object that just passed the event horizon of a BH have its own time arrow, and a far-away observer have its own time-arrow.

Are the time-arrows of objects inside and outside event horizon of BH connected, i.e. it's the same time arrow?
 

[yor_on]

Time is a function of locality to me. Nothing else. That mean that you will need to find some way to locally measure a time, before the EV, passing the EV and well past it, inside. If you have that measurement I'm sure you will find that the 'time' locally measured, behaved the exact same in all circumstances.

[dlorde]

An object that just passed the event horizon of a BH have its own time arrow, and a far-away observer have its own time-arrow.

Are the time-arrows of objects inside and outside event horizon of BH connected, i.e. it's the same time arrow?

There is a sense in which time and space directions change orientation - inside the event horizon, all directions inevitably lead to the singularity, so the singularity is a point in the future.

[yor_on]

That one is for a non rotating black hole, isn't it?
A Schwarzschild black hole.

Or can you use it for rotating black hole too?
And it's also a geometrical analogue to the mathematics generated, describing its properties, as I gather, would you agree to that?
=

The point is that I'm not sure how exact this sort of description is? For example it defines a 'singularity's center' to be 'stretched out infinitely', but how well would such a notion fit a real measurement outside a event horizon? Could I then expect 'gravity' to not point to a 'center' at all? Of the 'sphere' described by the event horizon, as I'm observing something in a free fall towards it?

(me at rest with the event horizon) Somehow, as I'm free to choose any point of entry that exist for that sphere, redefining that axle of infinite 'center', by choosing a different approach it seems to me that this definition speaks of the whole inside as being the singularity's 'center'?

And that seems to say that you must meet 'the center' as soon as you pass that event horizon?
Its weird, on the other hand, all singularities are weird
=

on the other hand this description also define it as the space inside (formerly time) also will become 'infinite'? So we have a infinite space, containing a infinite center then? Awhhh

[yor_on]

It wouldn't matter if this 'center' can be defined to be whole of the event horizon, will it? The shortest distance, and most likely path, to the EV will still be the same as if it had a normal definition of a center, if I'm thinking right? As it is not rotating. I think we need to define this one

[dlorde]

Sorry yor_on, I can't make out what you're asking / talking about. What defines a 'singularity's center' to be 'stretched out infinitely' ?

I don't think a singularity can really have a centre - as I understand it, mathematically it's an infinitely small point; although we don't really know quite what it is, as the maths of physics breaks down there.

But in all black holes, rotating or not, all paths inside the event horizon lead to the singularity.

[yor_on]

well yes, that was how I thought of it too, but take a look here.
Changing places - space and time inside a black hole.

[yor_on]

From that definition it seems possible to define everything, being behind a non rotating black holes event horizon, to become a 'center', as I read it?

[dlorde]

From that definition it seems possible to define everything, being behind a non rotating black holes event horizon, to become a 'center', as I read it?

I don't understand what you're getting at. Any point can be defined as a 'center', and I suppose the singularity is singularly qualified to be a center (not to have a center). But the event horizon is just the point at which the escape velocity becomes infinite; it has no special properties otherwise. You could cross the EH of a super-massive black hole without noticing, and continue for some time before tidal forces spaghettify you. How does it help to suggest you somehow reach a 'center' when you cross the EH?

[dlorde]

well yes, that was how I thought of it too, but take a look here.
Changing places - space and time inside a black hole.

The article you linked to describes the space-time inversion I was referring to - but in more detail and clarity. I see what you mean about being 'stretched out infinitely', but - if I read it correctly - that's the spatial extent of the singularity itself when the temporal axis has been swapped for a spatial axis.

[yor_on]

Your confusion mirrors mine D

"Likewise, if you think about the unstoppable collapse of a body to form a black hole, you might think that the body ends up with all its matter concentrated in a single point of space - the singularity.

But again, this picture of the spacepoint-singularity residing in the center of the black hole is simply wrong. Using our analogy, you can see why.

The singularity is the whole of the axis - and the axis represents a space direction. Hence, the singularity is not a point in space - it is infinitely extended!"

so 'space' is the 'singularities center' inside it, as I get it (plus a headache).

And to that we can add a spectacular new idea in where everything burns to cinders,being the singularities 'firewall', as soon as something are daft enough to dare to cross a Event Horizon.  Black Hole Firewalls Confound Theoretical Physicists. 

[yor_on]

Wonder how much physics that would have to be changed if we don't find those black holes, although we do have good indications for them. But still, they are so weird, rotating or not.

[dlorde]

Wonder how much physics that would have to be changed if we don't find those black holes, although we do have good indications for them. But still, they are so weird, rotating or not.

I guess they'd have to think up another name for those super-dense things at the centre of most galaxies that satisfy the properties of black holes and have no other explanation. IOW, there's little doubt they are black holes, because they're way too dense to be anything else. Having said that, it's quite possible that details of our current models of black holes may have to be revised as we get new data about them.

[Pmb]

An object that just passed the event horizon of a BH have its own time arrow, and a far-away observer have its own time-arrow.

Are the time-arrows of objects inside and outside event horizon of BH connected, i.e. it's the same time arrow?
 

It's not as if time has a spatial direction. What happens is that all timelike and lightlike worldlines which originate inside the event horizon stay inside the event horizon. I that what you mean? It's in that sense that the future lightcone dips into the event horizon.

[HellsMascot]

After reading some Hawking, Susskind, and Hooft, I don't even bother thinking about black holes anymore. They cause my mind to feel spaghettified.