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There is enough energy released by gravitational collapse to heat the Sun to its current temperature. You can do a more detailed analysis taking into account how much cooling occurs during the collapse, but the steep temperature dependence of the Stephan-Boltzmann law makes it difficult to lose heat to space until the object is already hot.
However, this involves a loss of energy to the environment and hence an overall increase in the entropy of the Universe. This crucial detail always seems to be missing from discussions of the Jeans mass and gravitational collapse. I was wondering if there are any nice, simplified models of this that can be easily expressed?
Gravitational collapse is a fundamental mechanism for structure formation in the universe. Over time an initial relatively smooth distribution of matter will collapse to form pockets of higher density, typically creating a hierarchy of condensed structures such as clusters of galaxies, stellar groups, stars and planets.
A partial answer only. Given a spherical collapse, and ignoring relativistic effects, the time is the same as the time taken for a particle at the edge of the cloud to fall to the centre.
You can only have a gravitational collapse if the gas cloud continuously loses energy through inelastic collisions (which is then radiated off). Otherwise the collapse would soon come to a halt as the lost potential energy would be turned into kinetic energy and a steady state would be reached once the kinetic energy is -1/2 x the potential ...
It still has the same center of gravity. Now, when the radiation and shock waves arrive lots of stuff starts happening, including the effect mass around which the planets are orbiting dropping as material propagates outside of the planetary radius. "at the instant of gravitational collapse". Remember that gravitation propagates at the speed of ...
As given in the answer you link to, the collapse time for a homogeneous sphere of gas where we neglect pressure reads. t = 3π 32Gρ0− −−−−−√ t = 3 π 32 G ρ 0. Now we know that the gas has a certain constant number density n0 n 0 and atomic mass mA m A. Then we simply substitute ρ0 =mAn0 ρ 0 = m A n 0. If the gas has more than ...
Gravitational trajectories are a prime example of almost perfectly reversible, frictionless physics. Of course, gravity could deflect an electron wave to a detector, but we'd attribute the collapse to the irreversible detection process. Edit: Apparently, "gravitational decoherence" is the subject of theoretical study (thanks, @Connor Behan).
2. The "hair" is lost via gravitational radiation. This is also known as quasi-normal ringdown, as the BH vibrates at different frequencies much like a drum (maybe a "gong" is better analogy). Any charge on the black hole will simple get shorted out by free charges in the surrounding plasma, on a very short time scale.
In chapter 11, section 9 of Weinberg's Gravitation and Cosmology, the metric of a collapsing pressureless star of uniform density $\\rho(t)$ is derived. In comoving coordinates, it essentially looks...