Mordred

Roflmao

The rubber sheet analogy is useful if you think of the observer being on the sheet itself. In this regard it doesn't do a bad job of mapping light paths. The problem is when you think in terms of Mass and orbits there is the tendency to ignore observer affects. It tends to lead to a more Newtonian way of drawing conclusions. This is fine if you remember to include relativity effects. For example some of the furmulas used for gravity waves are fairly Newtonian like. Those work fine but you have to be careful what conclusions you draw from them. This formula for example is a good one. [latex] P=\frac{de}{dt}=-\frac{32}{5}\frac{G^4}{c^5}\frac{(m_1m_2)^2(m_1+m_2)}{r^5}[/latex] In essence it's a Newtonian formula. The problem with formula comes into play is the measured mass of M_1 and M_2. Do you use the rest mass or do you also include the inertial mass?

Forget the term mass. Just think of the curvature the term mass isn't particularly well defined in GR. Yes mass causes curvature but this doesn't strictly mean rest mass, or inertial mass, Komar mass, Bondi mass, ADM mass etc etc etc. How we measure mass or energy is also subjective to the observer.

Yes and no if you think about observer limitation. An outside observer would never see the event horizon change. At one time blackholes were called "frozen stars" that terminology dropped out of literature.

Can you see an event horizon? We can only measure the gravitational influence. We never never see the EH. The gravitational influence is the curvature outside the EH. That curvature changes regardless of whether or not we can see it's change. For example on Earth we are a static observer. We wouldn't see the change. However if your an infalling observer you can record the change. For example if a BH is removed from any other object. Outside of gravitational influence, to any other object and has no unfailing material. You would have no means of even knowing it's there. The surrounding curvature would still be affected. The curvature will change regardless of the observer. However we may or may not be able to directly measure that change depending on observer limits. We can get around this by observing how other objects react to the curvature. This is why it's correct to state the information of the BH's mass is contained in the spacetime region outside the event horizon. Gravity being curvature and the rate of curvature change being maximum c.

That's the other question lol. I lost track of the number of theories of what lies beyond an EH. Infinite density, Wormhole tunnels to new universe Wormhole tunnels joining multiple Bhs Solid core, The list goes on and on.

Yes but we can't measure any change to the singularity mass. That information can only be inferred via the radius of the event horizon. At the time the event horizon first formed. Though during a merger the radius of the EH would change this allows a more recent estimate of the singularity mass

In theory...I haven't yet seen any papers that suggest a measured analysis describing beyond the EH. Have you?

Simply because the Event horizons could already be merged before the singularities merge. In this case you have no idea when the singularities merge. Due to the time dilation this event under this description would always be a future event. Also the effects of the singularity merger behind an event horizon wouldn't escape the EH for us to record in the first place.

Accretion jets and the reasons for them is a rather tricky subject. The leading theory for their cause afaik is the interaction with the BH,s magnetic field. Particularly in the ergosphere region. Much like the vorticity of plasma in our sun creates magnetic fields so can infalling material from an accretion disk. The process model usually involve Kerr rotating blackholes. The various models is discussed in the accretion disk article I posted earlier this thread. One of the processes is the Penrose process or mechanism, the other is the Blandford-Znajek process. (Hopefully I got the last process name correct lol) Here is a non technical pop media coverage. http://www.space.com/5285-powerful-black-hole-jet-explained.html Part of the problem is that also theories that suggest part of the energy powering the jet isn't just from the disk itself, but may include the rotational energy of the BH. Subject is still highly debated on that score. Part of the latter also suggests an accretion disk via this angular momentum interaction can cause a rotating BH to lose some rotation.

"A well-known feature of radial fall towards the event horizon is that the coordinate time (the time that would be measured by a static distant observer) taken to reach the event horizon by a freely falling object is infinite(see e.g. [2]). This feature is accompanied by unlimited redshift:" http://cosmology101.wikidot.com/local--files/main/touching_ghosts.pdf They occur outside the event horizon.

No one will ever know. You can never measure beyond the event horizon. No information escapes. An outside observer cannot even see an object fall past the event horizon due to the amount of redshift.

Ok I see what your getting at. This follows the convention that gravity potential energy is negative. This is really just a consequence of coordinate choice. Or rather the vector direction. In the next formula working from M to m. By the classical Newtonian formula [latex]U=-\frac{GMm}{r^3}[/latex] However SR, or rather the Minkowskii looks at the vector change from at rest. With the equivalence principle. M_i=m_g. The first equation I posted includes a term that specifies the coordinate choice. [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex] [latex]\eta^{\mu\nu}[/latex] specifies Euclidean flat geometry. Your covariant and contravarient terms specify your vector direction. or more accurately the Minkoswkii form. (Raised or lowered indices) [latex]\mu\nu[/latex] being your tensor matrix coordinates Essentially were both stating the same thing just under a different reference frame. Were both right as their is no preferred coordinate frame of reference. In Newtonian physics the relations are from center of mass outward. In Minkowskii form it's at rest or Euclidean flat geometry as your coordinate baseline. Now the other problem here is you you know mass has energy. You also know that when a particle gains kinetic energy it gains inertial mass. So lets say you have 100 moles, of particles at a given volume lets use m^3. Those particles have the same rest mass. Closer to the BH they gain inertial mass. Relative to reference frame M. By this vector convention gravitational energy is negative. The gravitational binding energy is also negative. so yes you have negative energy in a gravity well. By Newtonian convention. (Thankfully GR uses the four momentum four velocity, and doesn't require potential energy). Not that Newtonian theory works with gravity waves lol

I have no idea why you would have difficulty in understanding that the tensors involve scalar and vector field strength at each coordinate. A vector field has both direction and magnitude. How do you define a magnitude without an energy value. Why would you have a problem with a gravitational potential energy at a given location on a spacetime curvature as having an energy/density relation? Does the term gravitational potential energy not mean a specific type of energy ? At a given radius from a mass the force of gravity has a field strength. That field strength can be calculated via f=ma. Those equations above equate this to the curvature and stress/energy momentum

The Higgs mass is important for setting the vacuum expectation value. Particles of the details you need is to understand how thermal equilibrium works with the coupling constants of each of the four forces. Without going into the gritty details I'll give a brief description. As you increase temperature via volume change. Ie smaller volume of the Universe in the past. The coupling constants start to become the same strength. For example you can no longer distinquish the strength of coupling constant for the strong or weak force. As you can no longer distinguish them they have symmetry. at temperature above the vacuum expectation value, the strong, weak and electromagnetic force all become indistinct. The Higgs field itself has 4 components those four components all have symmetry. The particles that are normally distinguished by their interactions with the Higgs field and the three forces also become indistinct from one another. Here is a quick lecture showing the components of the Higgs field. There is a brief correlation to the above. http://www.google.ca/url?q=http://www2.ph.ed.ac.uk/~playfer/PPlect17.pdf&sa=U&ved=0ahUKEwju3dGVxPDLAhWKk4MKHYH1CoUQFggVMAE&usg=AFQjCNG5MOS24Ts73nVxWc6fMdaqRcnrmQ http://arxiv.org/abs/0810.3328 A Simple Introduction to Particle Physics http://arxiv.org/abs/0908.1395 part 2 GUT theories http://arxiv.org/pdf/0904.1556.pdf The Algebra of Grand Unified Theories John Baez and John Huerta http://pdg.lbl.gov/2011/reviews/rpp2011-rev-guts.pdf GRAND UNIFIED THEORIES These articles will help. Keep in mind there are alternative particle physics models. Ie SO(10) MSSM super symmetry as opposed to SO(10) MSM minimal standard model S0(5) an older standard model the first GuT model. That should give you plenty of study material.

I don't recall ever stating that energy is being created. Other than that your explanation is good. However you can see from the curvature statement I quoted from the wikilink that the curvature changes occur. If you look at the curvature to stress/tensor relations. You can see the curvature equates to energy momentum... Via the stress/energy tensor. The formulas involved are posted in this thread. You can see the first equation equates gravitational potential energy to the energy/density and pressure relations. The second equation relates those relations to the curvature. That's the part I think your missing.

Why would you think that? Does the change in angular momentum of the BINARY system somehow elude you? It is the changes in angular momentum that causes the changes in the spacetime curvature. "certain circumstances, accelerating objects generate changes in this curvature, which propagate outwards at the speed of light in a wave-like manner. These propagating phenomena are known as gravitational waves. https://en.m.wikipedia.org/wiki/Gravitational_wave you must have looked at this wiki page 100s of times. Did the quoted section somehow elude you? It specifically states changes to the curvature. It does not state change to the mass of the rotating objects. Here is another appropriate line. "In theory, the loss of energy through gravitational radiation could eventually drop the Earth into the Sun. However, the total energy of the Earth orbiting the Sun (kinetic energy + gravitational potential energy) is about 1.14×1036 joules of which only 200 joules per second is lost through gravitational radiation, leading to a decay in the orbit" In other words the Earth Sun system is technically emitting gravity waves. They are simply too weak for us to detect. The Earth and Sun certainly aren't touching each other. Lol. Take a look at the equation for radiated power of a gravitational wave. [latex] P=\frac{de}{dt}=-\frac{32}{5}\frac{G^4}{c^5}\frac{(m_1m_2)^2(m_1+m_2)}{r^5}[/latex] You can keep the mass m1 and m2 constant but just change the radius and you emit a gravity wave. (PS I wish I had remembered this formula dozens of posts ago. Would have saved a lot of effort)

That doesn't particularly make much sense. Space being a volume. However if your referring to the thermodynamic conditions of the Universe. Then it has undergone several stages. Example particles dropping out of thermal equilibrium, which affect the dynamics

The dark simply revers to something we don't completely understand. Each of the three has its own history. They are rather unrelated to the other.

Not bad, a good way to understand it in more detail is to Google Higgs metastability. http://www.google.ca/url?q=http://arxiv.org/pdf/1210.6987&sa=U&ved=0ahUKEwimkrGn4O7LAhVQxWMKHSF_ABEQFggRMAA&usg=AFQjCNFs4oyWK_egHU-PrVlPeJGr_hWRvg Little secret add pdf at the end of a search. Ie "Higgs metastability pdf" It will help avoid pop media hype style articles.

Don't read too much into that paper. Lol at least not in your stage of understanding. The paper is theoretical. Ie has plausible mathematics. Yer it states it doesn't conform to GR. Let's stick to how GR describes a BH until evidence shows it is wrong. (Which hasn't happened yet) The reason I posted that article in your other thread was to show you the ringdown formula itself.

That would be accurate.

Any particles that cross the event horizon for whatever reason is essentially lost to the blackhole. We cannot get them back ever. That's pretty straightforward. A point of no return is just that. We cannot ever get any information beyond the event horizon. That's why I stated the mass or energy that causes gravity waves do not emit from inside the event horizon. The energy for gravity waves originate from the spacetime geometry outside the event horizon. Not from within.

Particles with mass will always move slower than the speed of light. Particles moving in and out of the EH is kind of nonsense. We're talking geometry change. It's the geometry that's changing. The event horizon is a specific geometry condition. Once a particle crosses the event horizon it's never going to exit. The event horizon is a point of no return. It doesn't matter if the EH moves or not. There is no spacetime path for a particle to ever exit an event horizon. Doesn't matter if the EH gets warped, stretched etc. It still represents the boundary of point of no return.

We are modelling changes in geometry. Think of the particles as attached to the geometry. Curvature means a higher energy/density. When your modelling changes in spacetime or gravity waves your modelling the changes in geometry. Granted you need a change in energy/density to change the geometry. Ie change in angular momentum or acceleration etc. Remember the equivalence principle inertia mass is the same as gravitational mass. Energy is simply the ability to do work. Mass is resistance to inertia.