DimaMazin

Energy, created by potential energy, can exist only in gravitational field. Let's consider annihilation of matter and anti-matter. They have energy after falling to each other mc2+mc2+so called potential energy of fall . After the annihilation, created photons have energy = 2mc2 +so called potential energy . There is no gravitational field but energy, created by potential energy , exists because the energy arrived from space.

Mass does not lose energy for acceleratiom of objects. Then it use energy of space expansion. Why I can not say that mass uses cosmological force for a fall of objects?

Yes. But bigger gravitational field creates bigger acceleration and longer space to BB. All run to big masses and to own masses, changing velosities ,redusing and increasing distances. So gravitational force is stronger cosmological force on local level.

I don't consider your central point. Acceleration direction is from visible BB to bigger distance to it.

The direction is from BB ,exacter, to farther distance , which exists in gravitational field. Increase of distance from BB proves the accelerating relative to it. Farther distance from BB to earlier accelerated objects is gravitational deepening.

Gravitational field does not attract objects , it accelerates them relative to BB. Therefore free objects run to farther space, which is in gravitational deepening.

Let's consider unit circle with central point x=0 ;y=0 a is an angle in rad x is cosine of angle a y is sine of angle a Area of tryangle is At=y*x/2 Area of segment a = a/2 Area of half of sector 2a =area of segment of a - area of tryangle = a/2 - yx/2= a - y(1-y2)1/2 Can area of half of sector 2a be calculated by integration if x=31/2/2 then x2=1 (3^1/2)/2f1 (1 - x2)1/2 dx How to calculate the integral?

Let's consider acceleration of two spaceships wich are rigidly connected on distance. In frame S backward spaceship is earlier accelerating. In S' frame backward spaceship is later stoping, therefore backward spaceship is attracting forward spaceship . Also backward spaceship is more traveling in S and in S' therefore it is younger . By the analogy a center of the Earth is backward spaceship and a surface is forward spaceship in frame of BB, in frame of center and in frame of surface. Escape velocity is caused by the non-simultaneity.

Thank you very much. Now it is clear.

What about slowing of time? Is it there : t0=tf( 1- 3GM/2Rc2)1/2 ?

Swansont said that gravitational potential should be divided by c2 -3GM/2Rc2 it has no unit therefore it would be a factor of slowing of time, but haw should I use negative factor for time dilation definition? what is 3/2 ?

Potential energy doesn't slow time. Did you mean "g" slows time? Do you think there is no gravitational slowing of time? How do you define gravitational slowing of time in the center of a massive body mathematicaly?

Can we use the formula: to= tf(1- 2GM/rc2)1/2 r is midle radius of all points of the massive body R is radius of the body (4Pi R3/3)/(4Pi r3/3)=2 r = R/21/3 to=tf(1 - 2 * 21/3GM/Rc2)1/2 so?

Thanks for your answers.

Can spacetime exist without gravitational particles? Does mass lose itself for support of spacetime (or gravitational field) ?

Density of space around of mass isn't caused by gravitational radiation?

If gravitational radiation is traveling, then in space is more and more the meetting gravitational radiation. Does it increase quantity of meters of the space?

They do measure distances and times in S'. But we can define results of the measurements in S, using velosity of the spaceships as v which is 0 in S' . And I made it.

tf = l /(gamma(c+v))+l/(gamma(c-v))=2lc/(gamma(c2-v2))=2 l /(c2-v2)1/2 tb = l/(gamma(c-v)+l/(gamma(c+v))=2 l/(c2-v2)!/2 The measurements are made in S. Clock indication of event without distance is the same in both frames. The clocks indications of receptions and emissions of light are measured in S , but they are the same in S'.

Distance beetween the spaceships is the same before and after the accelerations in S and is l . In S' before the events of accelerations the distance = l/gamma. And after the events of accelerations of both spaceships a distance between the spaceships is gamma * l . If velosity =0 in S then it is v in S'. If vlosity =v in S then it is 0 in S'. t is time between events of acelerations of spaceships in S. t' is time between events of negative acceleration of spaceships in S' . What koncretely is unclear?

In the experiment t=0 not t'.

Zero is point of observer. x0=0 then x= l or -l if x=l then v is negative if x= -l then v is pozitive

In center of the Earth or in center of any planet or star.

https://en.wikipedia.org/wiki/Relativity_of_simultaneity - l isn't -1 . Use glasses. l is distace between the spaceships.