Can we see super-Planckian domains?

1. Can we see super-Planckian domains? Ken-ichi Nakao (Osaka City Unviersity) In collaboration with Tomohiro Harada and Umpei Miyamoto (Rikkyo University) Hirotada Okawa and Masaru Shibata (YITP) Takehara Workshop June　6-8, 2011

2. §Introduction If GR correctly describes gravitational phenomena… Concentration of mass Collapse due to self-gravity Generation of spacetime singularities by Penrose(1965), Hawking & Penrose (1970)….. Near spacetime singularities Large spacetime curvature, large energy density, large stress All know theories of physics including GR are not available → New Physics (Superstring? Brane World? …..)

3. §Cosmic censorship hypothesis Are spacetime singularities observable? Cosmic censorship hypothesis by Penrose (1969) ？ Weak version: spacetime singularities generated by gravitational collapses are hiden behind event horizons Strong version：spacetime is globally hyperbolic × in 4-dim spaecetime.

4. “Domain of super-Planckian (SP) scale = Border of spacetime” Harada and Nakao, PRD70, 041501 (2004) Practical spacetime singularity = Domain in which GR is not available DomainA is called the border or SP domain, if where EP = fundamental Planck scale　　 a = a positive consitant of O(1) Visible super-Planckian domain ≈ Naked singularity

5. Large extra-dimension scenario Arkani-Hammed, Dimopoulos and Dvali 1998 Relation between D(>4)-dimensional Planck energy and 4-dimensional one: (R: length scale of extra-dimansions)

6. Collisions of high energy particles in large extra-dimension scenario Giddings & Thomas (2001), Dimopoulos and Landsberg (2001) Gravitational radius of the center of mass energy E Cross section of black hole production Production rate much larger than 4-dimansional theory

7. Visible SP Domains generated by collisions of high energy particles Nakao, Harada and Miyamoto (2010) Domain into which two particles can enter at once particle We call this the “collision domain”. particle If n≤1, a black hole forms. If n>1, no black hole forms.

8. Volume of the collision domain in (D-1)-dimensional space Volume in extra-dimensions Area of the base of the cylinder Height of the cylinder (VN : Volume of an N-dimsphere) Average energy density in the collision domain

9. Condition of visible SP domain formation from 00-component of Einstein’s equations where SN= Area of N dim sphere. 『Gravitational radius=Compton length, if M = EP. 』 =: nmax2 If nmax>1, then n >1is allowed. SP domain with no black hole can form !

10. The value of nmax Generation rate of visible SP domains Generation rate of black holes Generation rate of visible SP domain >> Generation rate of BH Practically, the weak version of cosmic censorship is not satisfied.

11. High speed scattering of two black holes by higher dimensional numerical relativity Numerical relativity Method to study various phenomena with strong gravity by numeically integrating Einsteinn’s equations Evolution of binary composed of compact objects (NS, BH) ＝ Main target of GW physics Scattering or merger of high speed BH’s （e.g., classical counterpart of high energy scattering of elementary particles） ＝ New target of numerical relativity New techniques are necessary

12. Scatter or merger of high speed BH’s Rg b BH BH

13. Scatter or merger of high speed BH’s For large impact parameter b After scattering, two BH’s go apart to infinity

14. Scatter or merger of high speed BH’s For small impact parameter b Formation of one larger BH BH horizon

15. Scattering of high speed BH’s in 5 dimensions (equal mass M） Initial data by Shibata, Okawa, Yamamoto (2008) If the distance between two BH’s is large enough, each BH and its neighborhood is very similar to Schwarzschild-Tangherlini spacetime Rg = EP (M/EP)1/2：　gravitational radius

16. Boost transformation translation

17. Extrinsic curvature of t = const. hypersurface Other components vanish.

18. Initial data for two BH’s approaching to each other with velocity v 4-dim. spatial metric ここで、 Extrinsic curvature Y anddKijare determined so that constraint equations are satidfied. However here, we have set Y = 0 = dKij . This is a good approximation for the case of large enough distance between the two BH’s. In this initial data, there is almost no junk radiation.

19. on the horizon of a spherically symmetric BH with M= EPin 5-dim spacetime. SP domain:

20. Scattering of high speed BH’s in 5 dimensions (equal mass M） by Okawa, Shibata & KN (2011) Example: b=3.38Rg,v=0.7 is shown in the unit of (EP/M)1/2. Visible SP domain BH’s

21. [EP /M]2 K2 After scattering, two BH’s will go apart to infinity

22. v [EP /M] K

23. The largest value of Kin our simulations is IfEP < M < 19EP , visible SP domain forms by the scattering of classical BH’s ! If finer simulations becomes possible, we may find largerK.

24. b [Rg] Scatter Simulations break down. (Naked singularity?) Merger bC bB v

25. Summary and discussion • We can see super-Planckian physics if the spacetime dimension is larger than four (Naked singularity might form). • It is unclear why visible super-Planckian domain forms by the scattering of 5-dim BH’s. • What is observed ?

26. 潮汐力による加速 Geodesic deviation equations 大雑把に m m X = 粒子間の距離 L =時空の曲率半径 重力源

27. m m 時空の曲率半径L がプランク長さlplより短いとき 粒子間の距離がコンプトン長でも、プランク時間内で プランクエネルギーまで加速される 量子論的粒子生成で生まれた粒子は、 高エネルギー衝突によりブラックホールを形成？