Tendex-Vortex visualization of curvature tensor, and Brane-world scenario

1. Tendex-Vortex visualization of curvature tensor, and Brane-world scenario Tarique Monsoor

2. several facts in hand… • The Ranque-Hilsch Effect3,4 Ranque reported the phenomenon of noticeable temperature distribution (fig.3) in confined steady rotating gas flows in 1933. • Superfluid Vortex: Experiments performed by Hall and Vinen established the existence of quantized vortexlines in superfluid helium. Experiments performed by Rayfield and Reif established the existence of quantized vortex rings. Packard has observed the intersection of vortex lines with the free surface of the fluid.

3. several facts in hand… • Violation of the zeroth law of thermodynamics in Black Hole, which is one the most fundamental assumptions concerning macroscopic systems in equilibrium. A. Ramirez-Hernandez, H. Larralde, and F. Leyvraz showed1 that systems with negative specific heat can violate the zeroth law of thermodynamics. • Negative Specific Heat of Black-hole: from the works of W. Thirring2 we are informed of the fact that if radiation energy is extracted from a star whose nuclear fuel is exhausted, the star will contract and heat up. Thus a star acts like a system with negative specific heat.

4. Several recent paradigms… • The paradigm of foliating spacetime into spacelike hypersurfaces; introduction of tools for visualizing curvature tensor e.g. frame-drag vortex lines, tidal tendex lines, vorticity, tendicity, vortexes and tendexes are several recent developments.5 • Brane-world scenario, the other recent developments, the spacetime itself is a foliate/ brane. 6,7 • Holographic Duality

5. Splitting of Weyl curvature tensor Here, represents Kronecker delta and the square bracket represents antisymmetrization. Denoting the 4-veocity of the observers who move orthogonal to foliation’s space-slices by and the induced spatial three metric by . Using the projection operator, , we can split the Weyl tensor covariantly into two irreducible parts… which are symmetric and trace-free. The even parity field is called “electric” part and the odd parity field is called “magnetic” part of .

6. Fig.1: the ‘red’ lines have negative tendicity the ‘blue’ lines have positive tendicity Fig.2: the ‘red’ lines have negative vorticity the ‘blue’ lines have positive vorticity

7. Black-hole: 5-D vortex or not? From this Ranque-Hilsch effect we find that vortex and turbulent fluid motion generates cooling effect. Since it is a 4-dimensional phenomena, it also has manifested opposite effect, the heating effect. This nature of vortex motion persuades me to think black hole as vortex and which is the probable source of negative specific heat of black hole. Now, there are two options; first one is that black hole and white hole exists in pair; the second and the most imaginative one is that black-hole actually is a higher dimensional object whose 4-dimensional cross-section or projection is our astronomical black-holes and resides in the brane, which is our universe.

8. References [1] A. Ramirez-Hernandez, H. Larralde, and F. Leyvraz arXiv:0802.1748v2 [cond-mat.stat-mech] 26 Apr 2008 [2] W. Thirring, Z. Physik 235 339 (1970); “Systems with negative specific heat” [3] Vlad Bezprozvannykh and Hank Mottl; “The Ranque-Hilsch Effect: CFD Modeling” [4] G J Ranque. .Experiments on Expansion in a Vortex with Simultaneous Exhaust of Hot and Cold Air.. Le Journal De Physique, et le Radium (Paris), vol 4, June 1933, pp 1125-1130. [5]David A. Nichols, Robert Owen, Fan Zhang, Aaron Zimmerman, Jeandrew Brink, Yanbei Chen, Jeffrey D. Kaplan, Geoffrey Lovelace, Keith D. Matthews, Mark A. Scheel, and Kip S. Thorne “Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications” [6] Zurab Kakushadze and S.H. Henry tye; “Brane world” hep-th/9809147 v3 [7] A. Chamblin, S.W. Hawking and H.S. Reall; “Brane-World Black Holes” hep-th/9909205 v2

9. Fig.3: the temperature distribution in a vortex tube

10. Thank you