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For a long time, I'm having difficulties understanding some problems of black hole physics, so maybe someone here could help me out. Standard story goes something like this : while a massive star's undergoes gravitational collapse, it's core goes through phase transition (p+e -> n +v) transforming itself into neutron star. Let's say it's mass is over x solar masses, than collapse will go on until it reaches state of a black hole. Nothing can exit it, it has singularity point of a infinite spacetime curvation where laws of physics can't be defined.
Basically, existence of singularity is what I don't understand.
Let's say I'm *really* good in calculus and I take a well-localized mass distribution of total 10 (or whatever ) solar masses of 'ideal fluid'. I throw it in field equation and I receive black hole metrics in limit of t -> oo , measured by a distant observer, right?
Ok, now let's go a bit back in time , to phase transition between radiation dominated and matter dominated era after the Big Bang. If we plug in different equations-of-state of radiation and matter in Friedmann equations, we will get different dynamics of metrics e.g. time dependence of a scale-of-space changes. (term is translated from croatian, maybe not correct)
Now, in Big Bang physics it is obvious that a dynamics of such system *will* depend on equation of state of it's mass distribution that contribute to energy density. How come black hole's doesn't ? Late Big Bang physics, as I see it, is all about introducing detailed equation of state into Einstein's field equations to reproduce visible consequences in t ~ 10^10 years.
OTOH, for some unknown (maybe only to me) reason, it's reasonable to approximate core of a collapsing star with a ideal fluid of a quite impotent equation of state that gives a singular "core" instead of a quark-gluon-graviton plasma enclosed with a Schwarzschild surface=) I'm kidding about the "plasma", but I hope you get the point. I am not challenging validity of a Schwarzschild solution to *some* extent and I understand that system of a coupled, nonlinear , partial differential equation are hard to solve so approximations are a life-style. But then, physicist are cautious when talking about consequences of a models that incorporate such *strong* assumptions, except when they talk about BH singularities as if they are experimental fact and not remnant of a wild assumption that disregards all others forces of nature except gravity! So...what am I missing?
Basically, existence of singularity is what I don't understand.
Let's say I'm *really* good in calculus and I take a well-localized mass distribution of total 10 (or whatever ) solar masses of 'ideal fluid'. I throw it in field equation and I receive black hole metrics in limit of t -> oo , measured by a distant observer, right?
Ok, now let's go a bit back in time , to phase transition between radiation dominated and matter dominated era after the Big Bang. If we plug in different equations-of-state of radiation and matter in Friedmann equations, we will get different dynamics of metrics e.g. time dependence of a scale-of-space changes. (term is translated from croatian, maybe not correct)
Now, in Big Bang physics it is obvious that a dynamics of such system *will* depend on equation of state of it's mass distribution that contribute to energy density. How come black hole's doesn't ? Late Big Bang physics, as I see it, is all about introducing detailed equation of state into Einstein's field equations to reproduce visible consequences in t ~ 10^10 years.
OTOH, for some unknown (maybe only to me) reason, it's reasonable to approximate core of a collapsing star with a ideal fluid of a quite impotent equation of state that gives a singular "core" instead of a quark-gluon-graviton plasma enclosed with a Schwarzschild surface=) I'm kidding about the "plasma", but I hope you get the point. I am not challenging validity of a Schwarzschild solution to *some* extent and I understand that system of a coupled, nonlinear , partial differential equation are hard to solve so approximations are a life-style. But then, physicist are cautious when talking about consequences of a models that incorporate such *strong* assumptions, except when they talk about BH singularities as if they are experimental fact and not remnant of a wild assumption that disregards all others forces of nature except gravity! So...what am I missing?
