There is no special "GR dynamics", because time isn't special, it's part of space-time.

http://www.amazon.com/General-Relativity-Introduction-Theory-Gravitational/dp/0521370663/ref=dp_ob_title_bk    

http://www.amazon.com/General-Relativity-Robert-M-Wald/dp/0226870332/ref=sr_1_1?s=books&ie=UTF8&qid=1463838152&sr=1-1&keywords=robert+wald

 This is the most comprehensive book on Cauchy problem in general relativity

http://www.amazon.com/Relativity-Einstein-Equations-Mathematical-Monographs/dp/0199230722/ref=pd_sim_14_5?ie=UTF8&dpID=41nUN1wz%2BzL&dpSrc=sims&preST=_AC_UL320_SR212%2C320_&refRID=19GC3E54GR3EWSYMVAXC

@Larry

Unfortunately the whole situation is steeped with mathematical difficulty.

This can be partially obviated by the higher level of approximation that Einstein used, with a modification to get easy to use formulae which technically give exactly the same answers as GTR

These formulae also solve some of the more difficult problem that beset GTR

The force of gravity in General relativity  (GTR) is thought to come form the curvature of space-time.

Unfortunately the maths of GTR implies infinite curvature and zero time passage at the black hole event horizon  and the black hole becomes a singularity- and yet the black hole has a radius.

The Misner Wheeler Thorne modification partially resolved this in  that the singularity rests inside the event horizon.

But yet another paradox arises if time stops at the event horizon (frozen star) no matter would fall in hence  black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon, hence the firewall.

The solution is to reinterpret  the maths of GR.

Additionally GR falls down in a number of areas, so any new maths should also resolve these problems

Yes GR works in the weak fields of the the solar system, and Intermediate

fields of neutron stars. 

1). It produces infinite density singularities in the very strong fields

such as in black holes.

2).It does not necessarily explain dark matter in galaxy cores where we

know super-massive black holes exist and the galactic dark matter

therein,

3). It does not explain dark mater present in galactic halo's,and galactic

clusters such as the bullet cluster,

4).It does not explain the presence of cosmological dark matter as a whole.

5). It has not yet been fully corroborated by the studies of neutron stars

and in black holes.

6). It does not easily explain the presence of dark energy and cannot be

translated in quantum gravity.

7). It predicts that time stops at the event horizon

Here I enclose a number of publications which explain all of these

phenomena, whilst agreeing with the results of GR where it has been

thoroughly tested.

1).First to obviate the infinite density singularities.

1a)

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)

https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the

galaxy.

2a)

https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the

galactic halo.

3a)

https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation

damping ) and is corroborated by black hole studies.

5a)

https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).

https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

7). It does not offer infinite time dilation at the event horizon

https://www.researchgate.net/publication/287213872_Finite_Gravitational_Time_Dilation_In_Black_Holes_Using_Dynamic_Newtonian_Advanced_Gravity_DNAg

Article An advanced dynamic adaptation of Newtonian equations of gravity

Article The formulation of Dynamic Newtonian advanced gravity, DNAg

Article Advances in Black Hole Gravitational Physics and Cold Dark M...

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

Article An advanced modification of dynamic gravitation

Article Corroboration of Dynamic Black Hole Gravitational Physics fr...

Article String quintessence and the formulation of advanced quantum gravity

Article Finite Gravitational Time Dilation In Black Holes Using Dyna...

If you intend also to read an innovative and alternative treatment of gravity dynamics, I could propose the following paper

https://www.researchgate.net/publication/277648714_Dynamics_of_Motion_in_Gravitational_Fields_of_First_Type

Article Dynamics of Motion in Gravitational Fields of First Type

@Daniele.

I like you work on graviation

There really is little point in trying to promote original published scientific work on this website

Unless you give the  conventional response you seem to get a negative response.

Andrew,

thanks for your sincere appreciation with regard to my paper. It is true, I agree with you, "unless you give the conventional response you seem to get a negative response". It happens on this website but happens also more on other websites and above all on scientific journals. Sometimes I ask me if those people understand what research means. We are living a hard time for research, but perhaps for innovative research every time was hard, because who decides promotion of original research is castled on obsolete and defensive positions. But in spite of this I am optimist for the future of research untill there will be open people as you.

Larry:

Please forgive that people may interpret this response as promoting 'personal work,' but the work may be of interest regarding your question.

The work develops (somewhat as a sidelight) the possibility that 'quantum gravity in a flat space-time' may be a basis for reproducing useful results that people produce via general relativity. (The main features of the work are [a] a math-based meta-model that correlates with each known and some possible elementary particles and [b] applications {of [1] models based on the meta-model and [2] the possibly broader list of particles} to various topics in elementary-particle physics and cosmology and various related topics such as dark matter and dark energy.)

Work most related to your question occurs in Chapters 2, 3, and 4 of the Springer-published book for which I attach an introduction. You might want to see especially Sections 3.2, 3.3, and 4.6. And, you might want to see Sections 6.3. and 6.4.

The extent one 'stays with' traditional applications of general relativity, it is possible that remarks in Section 4.8 (about the 'spacecraft flyby anomaly) and other remarks about a possible gravitational analog to electromagnetism's magnetic field point to opportunities to improve some modeling that is based on general relativity.

Ferent Gravitation theory

It is important there are many new theories of gravitation. It would be suitable and necessary to compare all old and new gravitation theories.

German petition on the LIGO scientific fraud:

https://www.change.org/p/prof-karsten-danzmann-beantworten-sie-bitte-3-fragen-%C3%BCber-das-ligo-experiment

Scientists have detected gravitational waves for the second time?

http://www.theverge.com/2016/6/15/11932652/ligo-gravitational-waves-second-detection-two-black-holes

LIGO like LISA is another scientific fraud, large sums of public money involved.

Einstein Gravitation theory: Gravitation is a distortion of space-time, limited to the speed of light.

Ferent Gravitation theory: Gravitation is a force mediated by gravitons, not limited to the speed of light.

In Einstein Gravitation theory the gravitational waves have the speed of light, detected by LIGO.

In Ferent Gravitation theory the gravitational waves have the speed of the gravitons 10^17 m/s, not detected by LIGO!

Why the Graviton smaller 10^42 times than a Photon, can not travel faster than the speed of light?

Because you were brainwashed by your professors for 100 years, that nothing can travel faster than light!

In the last 100 years physicists did not understand Gravitation, the space pushes them into their chairs, like Dr. Kaku said, following Einstein gravitation theory!

 “I am the first who understood and explained Gravitation with high speed gravitons v = 1.001762 × 10^17 m/s, with Negative Momentum, Negative Mass and Negative Energy” Adrian Ferent

https://www.academia.edu/23507496/Ferent_Gravitation_theory

There is no dynamic solution for the Einstein equation in general relativity.