I am relearning gravity and acceleration this summer and preparing for teaching next semester. I was trying to calculate the orbital of Earth in the solar system and pull out the energy, momentum, and angular momentum of the system.
It becomes clear to me that in order for Earth to get closer to the Sun, a push is needed in the transverse of its radial direction. Such that Earth can accelerate and gain extra angular momentum to get closer to the Sun. The gravitational pulling is always in the radial direction and cannot contribute to the angular momentum.
Specifically, the momentum at the transverse direction is m*v_trans = L/r where L is the angular momentum of the Earth and r is the orbit radius. L = m*sqrt(G*M*r), where G is the gravitational constant and M is the mass of the Sun. Thus the speed in the transverse direction is v_trans = sqrt(G*M/r). i.e. faster when closer. This relation holds slightly differently if the orbit is elliptical. I think this relation should maintain in the General Relative theory.
(PDF) From Particle-in-a-Box Thought Experiment to a Complete Quantum Theory? -Version 19 (researchgate.net)
If the Sun is a black hole, then the maximum speed the Earth can reach before reaching the horizon is the speed of light. If the limit in the universe is the speed of light, then nothing can penetrate the horizon but rather stay at the horizon forever because there is no mechanism to push when the speed of light is reached. In order to gain this push within the solar system and not from out of the solar system, half of the materials have to evaporate into photons and escape the solar system in order to conserve energy and momentum.
However, this violates our hypothesis that black hole forms from a star and that the center should have materials left from the formation. So either these materials are pushed out to the horizon or materials have a way to speed up passing the speed of light limit such that they can get closer to the center of the black hole. Either argument removes the need for a singularity point because no material can achieve infinite energy at the singularity.
Thus, the question is, what is the speed of light inside a black hole?
Jixin Chen , the speed of light is always constant relative to the local reference frame. In the case of a Black Hole, you have a phenomenon called "frame dragging", which means that the local reference frame is "dragged" around the BH so that the speed of light is always locally constant.
JES
Inside the "boundary" of a black hole exists the electric part (field) of the electromagnetic field and the Higgs field (reduced scalars). The magnetic field is not present (no evidence of its existence).
The speed of light is the velocity of the linear propagation of 1 quantum of energy (Planck's constant) within the structure of the electromagnetic field.
The electric field is a 3D field - thus its stucture still exists inside the black hole - so there is no reason to propose that the speed of light within the boundary of a black hole has changed its velocity. However, we only observe the propagation of quanta with the speed of light as an electromagnetic wave. Thus without the magnetic field there are no electromagnetic waves inside a black hole.
A black hole has a rotation (like every local concentration of energy). Because of the size of a black hole there must exist microscopic and macroscopic loops and concentric shells of quanta transfer inside the black hole. Because the propagation of just 1 quantum of energy within the structure of the electromagnetic field is generated by the electromagnetic field itself.
So I have to conclude that the speed of light still exists within the boundary of a black hole but only as the propagation of a topological change (1 h) within the structure.
With kind regards, Sydney
“…It becomes clear to me that in order for Earth to get closer to the Sun, a push is needed in the transverse of its radial direction. Such that Earth can accelerate and gain extra angular momentum to get closer to the Sun. The gravitational pulling is always in the radial direction and cannot contribute to the angular momentum. …”, etc.
- that looks as rather vague passage, which is in framework of the standard mechanics, so here, if Gravity field is weak, it is enough to use what is written in textbooks. Including, say, in closed gravitational systems, say, when a comet is on its orbit, it is on quite different distances from Sun, while the angular momentum conservation law acts and this momentum is constant.
However, again, that is correct only in weak fields. If a filed is strong, the mainstream mechanics really isn’t adequate to the reality, since in this mechanics equations [Lagrangian, Hamiltonian, the GR, etc.] the energy conservation law is violated.
If a field is extremely strong, the point above becomes critically important – and evident; and though, say, that
“…If the Sun is a black hole, then the maximum speed the Earth can reach before reaching the horizon is the speed of light….”
- is in complete accordance with the GR [and mainstream mechanics] – the “event horizon surface” radius is just defined as that is a surface where escape velocity - and so falling body’s velocity at reaching of the surface - are equal to the speed of light,
- however it is evidently wrong – if a body’s speed is equal to speed of light, its energy is equal to infinity; what is evident nonsense in accordance with the energy conservation law.
Though yeah, in mainstream physics there exist innumerous publication about “black”, “white”, “worm”, “holes in the spacetime” etc.; despite that from the fact that all such fantastic and evidently unreal mental constructions completely directly and rigorously follow from the GR quite evidently completely directly and rigorously it follows that the GR is rather strange theory.
What really happens in Gravity, which, of course, is nothing else than some fundamental Nature force, and which – as all other [Weak, Electric, Strong/Nuclear] Forces acts in the Matter’s fundamentally flat, and fundamentally “Cartesian”, [4+4+1]4D spacetime with metrics (cτ,X,Y,Z,g,w,e,s,ct),
- which fundamentally by no means can be impacted by anything in Matter, and fundamentally by no means can impact on anything in Matter, see the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
Cheers
If we are inside of a blackhole then it will make sense that according to the shell theorem, all matter inside will fell no gravity yet the universe is separated with external environment by the event horizon.
The rigorous scientific answer to the thread question “What is the speed of light inside the black hole?” is given in the SS posts above – the speed of light is equal to the observed/measured on Earth the speed of light in any situation in Matter, if light – more correctly a flow of particles “photons”,
- since photons move only in 3D space of Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE],
- and so also in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), where the lattice is placed,
- since speeds of everything in Matter is determined only by main the lattice’s FLEs parameters: FLE “size” and “FLE binary flip time” that are Planck length, lP, and Planck time, tP, c= lP/tP.
Besides the SS&VT Planck scale initial Gravity model that is linked in the SS post July 28 above, more about what “black holes” are see section “Cosmology” in https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics , to read two reDzennn comments (4 and 3 passages) in https://phys.org/news/2023-11-black-hole-paradox.html it is useful as well.
Cheers
If we assume the speed of light inside a black hole is the same c measured near Earth, then almost all mass of a black hole should be at its surface. Mass from outside or the event horizon will accelerate to speed of light and join the surface with a fixed angular momentum but cannot get further inside the black hole because there is no mechanism to further increase its angular momentum. This is because it has reached speed of light and no push or pull can accelerate it when we use the center of the black hole as the reference frame(Einstein).
Conservation of angular momentum holds in both Newton’s and Einstein’s theories of gravity because when pulling or curving space there is no magnetic sideway pulling in gravity, so angular momentum maintains from basic geometric argument. i.e, average distance of an outside mass from the center of the black hole is only defined by the angular momentum.
Mass inside the black hole will feel no gravity according to the shell theorem(Newton). It could have attracted the mass on the shell but cannot change its orbit to get across the event horizon. So it can be zero speed related to the center thus singularity does not exist. If there is a mechanism (Hawking) for mass on the shell to evaporate outside, then it is possible it can also evaporate inside which will balance the mass joining the surface from inside and forming a stable universe inside the black hole.