# Presentation: 318179

## Acceleration of the Universe with Variable Gravitational Mass 

**       ****Nick Gorkavyi**  **1,2)**
**             ****1)**** ****Greenwich Institute of Science and Technology**
**               ****P.O. Box 797, Haymarket, VA 20168**
**                  ****2)**** Crimean Astrophysical Observatory**
**             **_[gistusa@aol.com](mailto:gistusa@aol.com)_
**             **_[gorkavyi@stars.gsfc.nasa.gov](mailto:gorkavyi@stars.gsfc.nasa.gov)_

**A Workshop on Studies of Dark Energy and Cosmology****from X-ray Cluster Surveys**
**January 15-16, 2004****at the Greenbelt Marriott****Greenbelt, MD**

## Important by-product of the Einstein-Eddington solution is the conclusion that gravitation waves can not be a source of stationary gravitational field (as laser beams don’t generate stationary electric fields). By other words, source of  gravitational fields is a matter only.

**Why gravitational energy is not a tensor?**

- A.Einstein and A.Eddington find the solution in framework of
- new (>1919) interpretation of classic Einstein equations (versus old interpretation by 1916).  See:
*1. Einstein, A. (1953), The Meaning of Relativity, 4th Edition, Princeton University Press, Princeton.** **(p.133, Appendix II, 4**th** Edition only!)*
*2.  Eddington, A.C. (1975), The Mathematical Theory of Relativity. Chelsea Publishing Company, New York, N.Y.** *

**Who cares about gravitational mass **
**of gravitational waves?**

**Important by-product of the Einstein-Eddington solution is the conclusion that gravitation waves can not be a source of stationary gravitational field (as laser beams don’t generate stationary electric fields). ****By other words, source of  gravitational fields is a matter only.**

## Gravitation radiation of merging black holes

**Initial**
**mass **
**= 1**

**Mass after **
**first merging**
**=0.8**

**=0.8x0.8**

**=0.8x0.8x0.8**

**Other 99.999992% **
**(or 1.0–0.8****73****)**
**of mass of the Universe **
**was transformed in the **
**gravitational radiation**

**      ****After a sequence of 73 mergers **
**      ****mass of matter in the Universe **
**      ****will 0.8****73****=0.000008%**

***Ergo****** *****the Universe has a variable total gravitational mass that close to zero on final stage of gravitational collapse.**

**Let us consider the Universe from 2****73**** (or 10****22****) black holes**.

##    We can not stop a gravitational collapse 

**100% of matter of the collapsing Universe from usual matter (stars etc.)**
**must be transformed into the gravitation radiation.**

**   *****We can not stop a gravitational collapse ***
**= We can not stop a gravitational instability** (or growth of fluctuations)
**= We can not stop a generation of gravitational waves**
**= ****The Universe near singularity will be a cloud of gravitational radiation with gravitational mass ~ 0.**

- The growth of fluctuations in collapsing Universe: E.M.Lifshitz, I.M.Khalatnikov,
- UFN, 80, 391,1963; origin of black holes from fluctuations during collapse:T.Banks, W.Fishler, Black Crunch,  hep-th/0212113, 12 Dec. 2002

## Gravitational force for variable gravitational mass.

**m = e** **–t/T****   **(2)

**r**

**φ**

- A

- B

- C

- D

**t = t - r/c       **(3)

-          **∂**** ****φ**          **∂**       Gm                                    Gm
- F = - —  =   - —  (  - —  )  (1) =  for m=const  =  - —
**  **         **∂ ****r        ∂ r       r                                       ****r ****2**

-         Gm      Gm
- F = - —   +  **——   **(4)
-         ** ****r****2 ****       rcT****     **

**for cT < r < ct,**
***repulsion***** is**
**stronger than**
**attraction**

**Attraction**

***Repulsion***

- Newton force :

_***Let us consider :***_
- -variable gravitational mass:

- - and finite speed of
- propagation of gravity:

- Gravity force for variable mass from (1)-(3) is *):

- Repulsion

- Attraction

- t=0

- t=1

- t=2

- t=3

***) Gorkavyi, N.N. Origin and Acceleration of the Universe without Singularities and Dark Energy. Bulletin of the American Astronomical Society,  2003, 35, #3.**

## Gravitational Potential for the Universe with variable gravitational mass. 

- Strong repulsive potential is responsible for BIG BANG and period of fast inflation.
- Any fluctuations or waves in such potential experienced strong blue shifts. Length of largest fluctuations in CMB was decreased in few times.

## Gravitational Potential for the Universe with variable gravitational mass. 

- Low repulsive potential is responsible for current acceleration of flat Universe

- You
- are
- here

## Conclusion

**Idea of fast decreasing gravitational mass of the Universe during **
**gravitational collapse (as result generation of gravitational radiation) **
**can help to solve next problems:**
**Elimination of singularities (as result of zeroing gravitational mass);**
**Origin of strong repulsive force for the Big Bang (and period fast inflation);**
**Nature of repulsive force for current acceleration of Universe;**
**Cause of low quadrupole in fluctuations in CMB (as result blue-shift of **
**fluctuations on the strong repulsive potential after the Big Bang).**
**5. “Kerrigan problem”**  **(** **attraction and repulsion are two sides of gravity **
**and this is good base for solution of the coincidence problems)**
**The idea is inside the Einstein relativistic theory but don’t contradict to **
**theorems by Penrose-Hawking about singularities (these theorems are **
**correct for the Universe with constant mass).**
**The idea keeps best parts of Big Bang theory (fireball, origin of elements) and **
**inflation theory (period of fast inflation, ** **flat Universe) without any unknown **
**physical fields, new dimensions etc.**

## P.S.      About c5/G  

**Huge constant c****5****/G in equations for gravitational radiation is**
**physically important. Misner, Thorne, Wheeler (Gravitation,**
**1973) consider this constant as maximal from possible value**
**for radiation of a single system. But inside of black hole or**
**during Big Crunch it is not true. Let consider variability of**
**radius of a black hole as function of variability mass:**
**          ****R=2GM/c****2  **** =>  dR/dt = 2G/c****2 ****dM/dt = 2G/c****4 ****dE/dt**
**If gravitational radiation is ****2dE/dt>c****5****/G ****then velocity of decreasing**
**radius of black hole is faster than speed of light: ****dR/dt>c**** **
***When gravitational radiation during collapse is larger than***
***the constant c******5******/2G, then radius of black hole must decreases ***
***faster than a speed of any falling observers. This is condition ***
***of opening black holes. For any outer observers black holes ***
***are black. For any falling observers black holes are exploded. ***
***We well know one such explosion:    ******Big Bang.***