It is stated in V. Mukhanov's book "Physical foundations of Cosmology" the following (page 44, after equation 2.25): "In contrast, for the dust dominated universe, where ηmax=2π, the event horizon exists only during the contraction phase when η>π." could someone please explain why is this true? the equation for the event horizon in a closed, dust dominated universe is (again from Mukhanov): de(t)=am(1-cosη)(ηmax-η),(am is a constant) which clearly has non-vanishing values for η≤π
I think the best way to see it is geometrically. if you send a light signal from any point with ηπ, it doesn't reach the observer. Hence the statement that the event horizon exists only when η>π, since then signals wont reach us. This is how I've seen it. Like to know your opinion.
Is this the Friedmann equation solution for the closed dusty universe? How are you extracting the location of the event horizon from these equations? I think you need to integrate to get the location of the horizon.
the scale factor is indeed the solution of the 3d Friedman equation for a closed dusty universe. the event horizon is defined as de(t)=a(t)*X, where X=integral from t to tmax of dt/a. so yes we have to integrate. My problem was with the meaning of the word "doesn't exist". Does it mean that the event horizon is 0 or is it not defined. I finally solved the problem, but thanks anyway :)
I think the best way to see it is geometrically. if you send a light signal from any point with ηπ, it doesn't reach the observer. Hence the statement that the event horizon exists only when η>π, since then signals wont reach us. This is how I've seen it. Like to know your opinion.
Thank you. I think I see what you are saying. I am one of the fringe of people who believe that the continued collapse approach to black holes is the right one so exclude all singular solutions and ones with event horizons as unphysical. Some argue this is all a matter of freedom of choice of coordinates and both such solutions are allowed and equivalent. I object because of concerns about infalling multipolar charge distributions and some of how interior numerical solutions are handled. I won't bore you with this. Staying fresh on these classical results is important to me and I appreciate the reminder.
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