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The Limiting Curvature hypothesis

The Limiting Curvature hypothesis. A new principle of physics Dr. Yacoub I. Anini. Shortcut (2) to Presentation.dvi.lnk. 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

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The Limiting Curvature hypothesis

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

  2. Shortcut (2) to Presentation.dvi.lnk

  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 )

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

  14. Singular geometry

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

  16. Spherically Symmatric solutions • Non- Singular Black Holes

  17. The gravitational field lines inside a collapsing star

  18. Accretion of matter into a black hole

  19. References

  20. 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

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

  22. Want to know what's going on? Continue the step-by-step tour at Falling to the Singularity of the Black Hole.

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