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a1call
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- If a neutron star can be seen dense enough in some inertial frames of reference (due to relativistic length contraction) to form a Black-Hole, but not in others, how could the two realities coexist?
Ibix said:If you want to know what's going on deeper in the gravitational field then you'll have to solve Einstein's field equations. As far as I'm aware there's a known solution when the mass is stationary (the Schwarzschild solution) and one where it's moving at near lightspeed (the Aichelberg-Sexl ultraboost), but only numerical solutions for masses moving at less extreme speeds.
The whole framework of this question is not valid. Consider a much more mundane question in pure special relativity. Consider that a gas at some temperature becomes a liquid if compressed. Consider a cannister of such gas moving at near c relative to you. Do you think it is liquid per you while being gas per an observer in the cannister? If that seems nonsensical, it is. To make the silliness apparent: no matter how fast you fly be the cannister, its state is not affected by your choice of motion.a1call said:Trying to understand as much as I can. So let's go one step at a time.
Let's define volumetric mass density as mass/volume
https://en.m.wikipedia.org/wiki/Density
Would the volumetric mass density of a body such as our sun be higher than that measured in our frame of reference, than one measured in an inertial frame of reference where the sun would be observed as contracted in length?
Another way of asking the same question is, is relativistic length contraction associated with reduced volume our not?
Thanks in advance.
Yes, it is a coordinate dependent formula. Since one is referring to gravity, with high speeds, one needs GR. In GR, frames are strictly local quantities. The equivalent question in GR is whether the formula is coordinate dependent, and it is. Alternatively, you could make it invariant by defining a precise procedure for measuring the variables which would, for example, involve deriving the radius from the circumference measured by an observer on the planet. However, if construed it as invariant in this way, then none of the quantities in it are affected by motion of the planet relative to some observer.a1call said:Is the escape velocity formula linked above a frame dependent formula or not?
Thanks in advance.
The Schwarzschild formula also assumes that spacetime has spherical symmetry. A moving neutron star would not. The result does not applya1call said:Schwarzschild radius formula gives a radius For any given mass below which the escape velocity would be greater than the speed of light
Actually, it would, as long as it is isolated. The symmetry would not be apparent in coordinates in which it is moving, but could be recovered by analyzing the killing vector fields.Dale said:The Schwarzschild formula also assumes that spacetime has spherical symmetry. A moving neutron star would not. The result does not apply
Oops, yes you are right. The killing vector fields are invariant.PAllen said:Actually, it would, as long as it is isolated. The symmetry would not be apparent in coordinates in which it is moving, but could be recovered by analyzing the killing vector fields.
I am trying to think of a way to make this statement make sense in terms of GR. The problem is that GR is formulated in terms of invariant quantities, and in terms of invariant quantities the gravity is the same at all points on the spheroidal surface.a1call said:another spot on the non-spherical spheroidal planet where the gravity is different
But the mass of the fuel is invariant. Could one argue that this mass is converted into proper acceleration of a rocket such that escape velocity is achieved?Dale said:The energy would not be the same in all frames. Energy is a frame variant quantity, even in Newtonian physics. Energy is conserved, but not invariant.
Yes, that is the type of argument one would need to make. Everything in terms of invariants like invariant mass and proper accelerationtimmdeeg said:But the mass of the fuel is invariant. Could one argue that this mass is converted into proper acceleration of a rocket such that escape velocity is achieved?
Sure, but to do the calculation properly you'll have to account for all the energies involved, including the kinetic and potential energy of the rocket exhaust which does not escape and the rocket which does escape. These energies are all frame dependent, but when you add them all up you'll find that the difference between the pre-launch energy and the post-launch energy is frame-independent and what you'd expect from burning the invariant amount of fuel consumed.timmdeeg said:But the mass of the fuel is invariant. Could one argue that this mass is converted into proper acceleration of a rocket such that escape velocity is achieved?
Thanks for pointing this out to me. The more I think about it the more powerful a concept this becomes.PAllen said:Actually, it would, as long as it is isolated. The symmetry would not be apparent in coordinates in which it is moving, but could be recovered by analyzing the killing vector fields.
I had the idealized assumption to neglect the mass of the rocket in my mind but should have mentioned that.Nugatory said:Sure, but to do the calculation properly you'll have to account for all the energies involved, including the kinetic and potential energy of the rocket exhaust which does not escape and the rocket which does escape. These energies are all frame dependent, but when you add them all up you'll find that the difference between the pre-launch energy and the post-launch energy is frame-independent and what you'd expect from burning the invariant amount of fuel consumed.
A neutron star is the densest and smallest type of star, formed when a massive star explodes in a supernova. It is made up of tightly packed neutrons and has an extremely strong gravitational pull. When a neutron star reaches a certain mass, it can collapse under its own gravity and become a black hole.
In the scenario of a neutron star becoming a black hole, both objects exist in the same space but have different properties. The neutron star still retains its original mass and density, while the black hole has a much stronger gravitational pull due to its smaller size and higher mass.
No, a supernova is necessary for a neutron star to form in the first place. The explosion of a massive star provides the energy and pressure needed for the remaining core to collapse into a neutron star. Without this process, a neutron star cannot form and therefore cannot become a black hole.
When a neutron star collapses into a black hole, the matter is compressed to an infinitely small point known as a singularity. This is where the gravitational pull is so strong that not even light can escape, making it impossible to observe the matter inside the black hole.
Scientists have observed the process of a neutron star collapsing into a black hole through the detection of gravitational waves. These ripples in space-time are created by the intense gravitational pull of the black hole. Additionally, theoretical models and simulations support the idea that a neutron star can turn into a black hole under certain conditions.