Quote:
Originally Posted by sjastro
The strength of the field is a function of density rather than mass. A stellar black hole will always have a smaller mass than the progenitor star (assuming of course there is no excretion matter to increase black hole mass). Yet the field strength of the black hole is far greater than the progenitor star despite having a smaller mass.
It's the metric rather than the scalar curvature that one looks at that is an indicator of field strength.
The two defining metrics for black holes are Schwarzschild metric for non rotating black holes and the Kerr metric for rotating black holes.
The Schwarzchild metric when used for low gravity field objects such as the Earth breaks down into a simple spherical metric.
Regards
Steven
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Thanks Steven,
So, just comparing a non-rotating black hole and just your average star or massed body; what would be the governing factor which forces you to drop the Einstein Equation and adopt the Schwarzchild Metric, that is, where does GR break down...is it that the energy density (on the right side) goes to infinity and the Einstein Tensor (left side) cannot balance the whole equation or something?
The
Schwarzchild metric looks totally different from the
Einstein Equation...it looks like a polar coordinate system, which would explain the non-rotation part. Also, I can see how the
Kerr Metric came from he Schwarzchild Metric but it uses something I've never heard of, the
Oblate Spheroid Coordinate system.
Interesting that a Schwarzchild black hole can have any mass, but is limited only by the the conditions of its formation. SO, that means a grain of sand can become a black hole, but only if the conditions are favorable in its formation.
So who's right here??? Scientists at the LHC have been claiming that if in the unlikely event that a tiny black hole was created in a collision, it would instantly collapse, yet here we have a statement saying (subject to initial conditions for its creation) ANY size Schwarzchild black hole can exist. So I wonder how much system energy is required to sustain a Schwarzchild black hole.
"This suggests that there must be a lower limit for the mass of black holes. Theoretically this boundary is expected to lie around the Planck mass (~1019 GeV/c2 = ~2 × 10−8 kg), where quantum effects are expected to make the theory of general relativity break down completely.[citation needed] This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. Certain developments in quantum gravity however suggest that this bound could be much lower. Some braneworld scenarios for example put the Planck mass much lower, may be even as low as 1 TeV/c2.[49] This would make it possible for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the Earth's atmosphere, or possibly in the new Large Hadron Collider at CERN. These theories are however very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists."