1. The Limiting Curvature hypothesis A new principle of physics Dr. Yacoub I. Anini

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3. Is there a limit to the strength of gravitational force? The surface gravity of the earth : 9.8 m/s² The surface gravity of the sun : 270 m/s² The surface gravity of a white dwarf : 5000,000 m/s² The surface gravity of a neutron star: 5,000,000,000,00 m/s² The surface gravity of a stellar black hole: 2,000,000,000,000 m/s² The surface gravity of a premordial black hole 7,000,000,000,000,000,000,000,000,000,000,0 m/s²

4. The limiting curvature hypothesis The curvature of spacetime (all curvature invariants) at any point have a maximum limiting value. Moreover, when the the curvature approaches its limiting value, The spacetime geometry approaches The perfectly regular de sitter geometry.

5. The Lagrangian It is possible to implement the limiting Curvature hypothesis by introducing the following lagrangian: L = (R + Λ/2 ) – (Λ/2)(√1 - R²/Λ²), where R is the Ricci scalar curvature and Λ is the limiting value of the curvature.

6. The contracted field equations -R -Λ (1 – U ) = -8 π G T, U = √(1- R²/Λ²) Introducing the following notation : Β =R/Λ γ = 8πG (T/Λ) The contracted field equations take the form 2β² + 2(1-γ)β + γ² - 2 γ = 0

7. Expressing β in terms of γ Β = - ½ (1 – γ ) ±½√1 - γ² + 2γ It is clear that if β is to be real then there will Be a limit on the allowed values of γ (1-√2 ) < γ < (1+ √2 )

8. By varying the gravitational action with respect to the metric we obtain the new field equations G μν - ¼ [1 - √(1- R²/Λ²)] gμν = - 8π G Tμν

9. Spaces of constant curvature Writing the field equation for A homogeneous and isotropic space The cosmological Case

10. The limiting geometry The limiting gravitational state The limiting value of curvature The limiting state of matter The limiting value of density

11. De sitter spacetime

12. Some Cosmological solutions The limiting de sitter geometry The radiation filled universe The matter filled universe The general case ( radiation + matter )

15. Spherically symmetric solutions Writing the field equations for spherically Symmetric solutions Non- singular black holes

16. Singular geometry

17. The numerical value of the limiting curvature Low curvature limiting value (effective gravity theory) Planck –scale limiting curvature (quantum Gravity scale)

18. Spherically Symmatric solutions Non- Singular Black Holes

19. The gravitational field lines inside a collapsing star

20. Accretion of matter into a black hole

26. References

32. references Collapse to a Black Hole (Movie)_files Falling to the Singularity of the Black Hole (Movie)_filesFalling to the Singularity of the Black Hole (Movie)_files Sphere collapsing to a black hole_files

33. White Holes and Wormholes.htm paper.pdf Falling to the Singularity of the Black Hole (Movie).htmFalling to the Singularity of the Black Hole (Movie).htm

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