The Limiting Curvature hypothesis

1. The Limiting Curvaturehypothesis 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 ) = -8π 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 obtainthe new field equations • Gμν - 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)_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).htm

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