Relativistic gravity incomplete? Big Bang singularity

[espen180]

I have a question regarding the conditions "prior" to the Big Bang. I realize tere is no empirical evidence for these conditions, only speculations.

At the point of the Big Bang, all of matter and energy was "infinitely" densely concentrated at a single point, correct? Even though GR breaks down at this singularity, are these not black hole conditions, in which nothing can exit the horizon?

What force must then have overpowered this enormously strong gravitational force in order to bring matter outside the horizon/expand the matter at the singularity point?

 

[mathman]

The big bang theory seems to be on solid ground right for t > tz (Planck time). However for t=0, it is much more speculative.

 

[JesseM]

Although GR is probably not the correct theory to use very close to the Big Bang, it is nevertheless true that on a purely theoretical level there is no problem in GR with the notion of a singularity which emits matter and energy. For one thing, GR theoretically allows for the possibility of "white holes" which behave like the time-reverse of black holes, the event horizon being one-way in the opposite direction (matter can be emitted by the central singularity and escape the horizon, but once you're outside the horizon it's impossible to enter it). Secondly, the Big Bang singularity differs from either a black hole or white hole singularity, as explained in this section of the Usenet Physics FAQ:

Why did the universe not collapse and form a black hole at the beginning?

Sometimes people find it hard to understand why the Big Bang is not a black hole. After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly. At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass. Nevertheless, the Big Bang manages to avoid being trapped inside a black hole of its own making and paradoxically the space near the singularity is actually flat rather than curving tightly. How can this be?

The short answer is that the Big Bang gets away with it because it is expanding rapidly near the beginning and the rate of expansion is slowing down. Space can be flat even when spacetime is not. Spacetime's curvature can come from the temporal parts of the spacetime metric which measures the deceleration of the expansion of the universe. So the total curvature of spacetime is related to the density of matter, but there is a contribution to curvature from the expansion as well as from any curvature of space. The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole. The Schwarzschild limit does not apply to rapidly expanding matter.

What is the distinction between the Big Bang model and a black hole?

The standard Big Bang models are the Friedmann-Robertson-Walker (FRW) solutions of the gravitational field equations of general relativity. These can describe open or closed universes. All of these FRW universes have a singularity at their beginning, which represents the Big Bang. Black holes also have singularities. Furthermore, in the case of a closed universe no light can escape, which is just the common definition of a black hole. So what is the difference?

The first clear difference is that the Big Bang singularity of the FRW models lies in the past of all events in the universe, whereas the singularity of a black hole lies in the future. The Big Bang is therefore more like a "white hole": the time-reversed version of a black hole. According to classical general relativity white holes should not exist, since they cannot be created for the same (time-reversed) reasons that black holes cannot be destroyed. But this might not apply if they have always existed.

But the standard FRW Big Bang models are also different from a white hole. A white hole has an event horizon that is the reverse of a black hole event horizon. Nothing can pass into this horizon, just as nothing can escape from a black hole horizon. Roughly speaking, this is the definition of a white hole. Notice that it would have been easy to show that the FRW model is different from a standard black- or white hole solution such as the static Schwarzschild solutions or rotating Kerr solutions, but it is more difficult to demonstrate the difference from a more general black- or white hole. The real difference is that the FRW models do not have the same type of event horizon as a black- or white hole. Outside a white hole event horizon there are world lines that can be traced back into the past indefinitely without ever meeting the white hole singularity, whereas in an FRW cosmology all worldlines originate at the singularity.

 

[espen180]

I see. Thank you very much. :)