[Alex Dullius Siqueira]

" a 45 degree angle with respect to the (ground)."
  From local perspective, I believe the answer to be yes.
 When considering it from "space", the example seems to have no real application.
  The existence of the very ground itself changed the rules by offering a point of reference for the arrow.
 Without that reference (earth) no angle is possible to be achieved.

 As for the question itself the way it is, I believe the answer to be yes...

[jeffreyH (OP)]

The problem with the gravity of gravity arise because of increasing relativistic mass. If a test particle approaches a black hole from infinity and its instantaneous velocity gets very near to light speed then its relativistic mass tends towards infinite. This means that it surpasses the strength of the central mass. In this situation even a single particle could generate a field capable of canceling that of the black hole and effectively move the black hole. If mass were in falling from all directions this should destroy the black hole by negating its field.

[jeffreyH (OP)]

There is, however, a solution to the above problem 

[Alex Dullius Siqueira]

There is, however, a solution to the above problem 

BH firewall. A frozen frame (not solid) of sppinging +C that's now diverging the particle trajectory from towards the virtual center into a straing line towards "still" infinite trajectory "Around" the firewall(horizon) and by doing so all it's relativistic mass of the very particle is now being atributed to the BH by "gravity" but I sugest that the horizon is reducing gravity at the center and not increasing it, which for its turn is converting the knetic energy into motion?

[timey]

The problem with the gravity of gravity arise because of increasing relativistic mass. If a test particle approaches a black hole from infinity and its instantaneous velocity gets very near to light speed then its relativistic mass tends towards infinite. This means that it surpasses the strength of the central mass. In this situation even a single particle could generate a field capable of canceling that of the black hole and effectively move the black hole. If mass were in falling from all directions this should destroy the black hole by negating its field.

This is why physicists such as Wheeler use 4 momentum where kinetic energy isn't considered as part of the mechanics of the mass itself and the concept of relativistic mass is not changing the properties of mass, but you may suit yourself.

Under the remit of the vector energy space that I suggest no body of mass could ever obtain the speed of light under any circumstance of gravitational acceleration because the speed of light would be being held relative to the g-field coordinate 3rd time dilation, the 3rd time dilation being the physical cause of the acceleration

However as said before, you may suit yourself about relativistic mass, and I will respectfully leave you to it.

[jeffreyH (OP)]

I'm afraid it contains gamma and therefore relativistic mass.
https://en.m.wikipedia.org/wiki/Four-momentum

[nilak]

I'm afraid it contains gamma and therefore relativistic mass.
https://en.m.wikipedia.org/wiki/Four-momentum

Relativistic mass is not so used anymore. You could simply say the particle aquires kinetic energy and because it has more energy the gravity force increases. I suppose you can explain better.

There is also another thing you need to take into account I guess. Can a particle  accelerate from infinity towards the massive body? Gravitational field of the massive body doesn't act instantaneously at infinity. You need an infinite amount of time for the field to reach infinity.

[jeffreyH (OP)]

The use of infinity is to establish some limit. It is not meant to represent a physical location.
@Thebox You are beginning to think more clearly.

[timey]

I'm afraid it contains gamma and therefore relativistic mass.
https://en.m.wikipedia.org/wiki/Four-momentum

https://en.m.wikipedia.org/wiki/Mass_in_special_relativity

: Wiki
Many contemporary authors such as Taylor and Wheeler avoid using the concept of relativistic mass altogether:

"The concept of "relativistic mass" is subject to misunderstanding. That's why we don't use it. First, it applies the name mass - belonging to the magnitude of a 4-vector - to a very different concept, the time component of a 4-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of spacetime itself."

***In reality the increase of energy with velocity originates not in the object but in the geometric properties of spacetime itself***

Which, if you think about it Jeff, is exactly the approach that my suggested energy vector space is employing within its attributing a physical cause for the acceleration.

If you read the link through it will tell you that relativistic mass is not a derivation of GR.  That Einstein himself disapproved of the convention, and that there are already differing interpretations as to 'where' the 'value of' the gamma is held relevant.

[jeffreyH (OP)]

The inertia of the object increases. Therefore the force required to move it increases. This normally means an increase in mass. I don't know how you can get around that by ignoring it.

[timey]

By doing exactly as Taylor and Wheeler suggest:
Instead of stating the force as a property of the mass the force is exerted upon, one states the force as a property of the spacetime the mass is located in.

[jeffreyH (OP)]

That is a cop out. Gravity is a force which acts upon mass.

[jeffreyH (OP)]

http://spiff.rit.edu/classes/phys150/lectures/ke_rel/ke_rel.html

[timey]

That is a cop out. Gravity is a force which acts upon mass.

I could understand your stance if I were not giving a physical cause for this force that is a property of spacetime, but I am.

And given that no-one has ever managed to give the force of gravity a physical cause, the premise I suggest is hardly a cop out.
It's actually a radical improvement on current physics that describes space curvature and the path light takes through space within Newtonian geometry without the necessity for SR.

It results in the fact that when you ask:
"Is there a linear vector space that can be used with gravitational fields?"
I can answer:
"Yes there is, and this vector space will be compatible with Einstein's laws of gravity, and Newtonian gravity, and will also be compatible with electrodynamics."

As to to the KE link...  There are many ways to skin a cat Jeff, but the means of doing so in that link does not give the gravitational force that results in the KE a physical cause.

[jeffreyH (OP)]

It is adequate to describe what is going on in particle accelerators. So does everyone at CERN need a lesson from timey?

[jeffreyH (OP)]

Here are the guys doing practical physics and not just piddling around on a forum.
https://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/lhc-machine-outreach-faq.htm

[timey]

Why do you have to be sarcastic?

The people at CERN are looking for truths about physics.
Most physicists are quite openly stating that new ideas are required.

What I suggest is describing exactly what SR describes, it just gets there by differing means.

CERN are investigating particle physics...
The Standard Model has so far not been united with gravity.

[jeffreyH (OP)]

Ok let's take you at face value. How does your vector space operate with respect to the gravitational field? Even simple equations will do.

[timey]

The force of gravity is caused by the length of the second causing a in the g-field at r from M.
And the g-field is caused by M.

This being why, despite the equation of F=ma, all value m is accelerated at same rate towards M.

[jeffreyH (OP)]

The force of gravity is caused by the length of the second causing a in the g-field at r from M.

That doesn't make sense to me.

And the g-field is caused by M.

This being why, despite the equation of F=ma, all value m is accelerated at same rate towards M.