Rotating BHs at future colliders: Greybody factors for brane fields Kin-ya Oda Kin-ya Oda, Tech. Univ. Munich Why Study BHs at Collider? BH at Collider (Basic Facts) Production arelarge angular momenta BHs are produced with large angular momenta. (Black ring formation) Evaporation separable Brane-field eqs. are separable in any dim. Greybody factors Greybody factors for 5-d BH Power spectra Power spectra from 5-d BH Summary hep-th/ with S. Park and D. Ida hep-th/ , to appear in PRD

Why study BHs at collider? In ADD/RS1 scenario, hierarchy problem is solved to result in the fundamental gravitational scale ~ O(TeV). Experimentally accessible quantum gravity!! There is no complete description at this non-perturbative region. E, M Correspondence principle in string theory S, T, σ g -2 M s Another point of view Truly QG effects will be observed as the deviation from the asymptotic behavior (in BH picture). as precisely as possible! It is essential to predict BH behavior as precisely as possible! BH picture String picture NOT general consequence BH production is NOT mere a model but the general consequence of the theory if nature realizes ADD/RS1 scenario. (Voloshin ’ s criticisms are already answered.) Giddings 01 Eardley, Giddings 02; Yoshino, Naumbu 02 Dimopoulos, Emparan 02 …

BH at collider (basic facts) 1. Balding Phase Dynamical production phase BH loses its “ hair ”. 2. Spin Down Phase. BH loses its mass and angular momentum. 3. Schwartzschild Phase Angular momentum is small. BH loses its mass. 4. Planck Phase Truly QG, highly unpredictable A few quanta would be emitted. Temperature gets higher and higher. We consider the region where the produced BH is: largesemi-classcially large enough to be treated semi-classcially and small “ spherical ” small enough to be “ spherical ” in the bulk. on the brane. BH radiates mainly on the brane. (Both are typically satisfied in LHC energy range.)

Rotating BH formation must finite angular momentum. It must be produced with finite angular momentum. Initial angular momentum: neglect balding phase When we neglect balding phase, gives condition for BH formation. There is maximum b allowed for BH formation. The BH formation process is non- perturbative but classical. b parton Banks, Fischler 99; Giddings, Thomas 01; Dimopoulos, Landsberg 01 Naively, BH forms when b <r S. ~ RHS is decreasing function of J (or b). rescaled angular momentum This is obtained by neglecting balding phase. How good is this approximation? (typical LHC energy)

nicely Our formula nicely fits numerical result with full GR Closed trapped surface Closed trapped surface forms when b < b max. cf) Numerical result utilizes the Aichelburg-Sexl solution (Eardley, Giddings 02) Yoshino, Nambu 02 Setup: two Schwarzschild BHs with boost→∞, mass→0, energy: fixed. t z b A few % for n =1 and ~1% for n >1. There are two direct consequences. So what?

larger 1. Production cross section becomes larger larger angular momentum Production cross section becomes larger when one take angular momentum into account.

large angular momenta 2. BHs are produced with large angular momenta increases Differential cross section increases linearly with J. large angular momenta BHs are really produced with large angular momenta!! Initial angular momentum:

Radiation from rotating BH large angular momentawhich signal would result Once we have established that BHs are produced with large angular momenta,we want to find out which signal would result.

Radiations from rotating BH brane fieldsHawking radiation BH radiates mainly into the brane fields via Hawking radiation. Greybody factorsbrane field equations Greybody factors are obtained by solving the brane field equations. What we have found: Brane field equationseparable any spin sany dimensions n Brane field equation is separable into angular and radial parts for any spin s and in any dimensions n. any spin s5 dim. greybody factorslow frequency expansion We have analytically solved this equation for any spin s in 5 dim. and found greybody factors in low frequency expansion. anisotropic We show that radiations are highly anisotropic (initially). g.o. limit Conventionally one has simply assumed g.o. limit: Greybody factorsdetermine Greybody factors for Brane fields determine the evolution of BH (up to Planck phase).

Higher dim. Kerr metric (just to show how it looks) vanishes on the brane

Newman Penrose formalism (just to show how it looks) We set null tetrad as follows: Spinor: Vector: Scalar:

Brane field equations Same as 4-dim. Can be treated in a standard manner. This term vanishes for n=1 (5-d). For this case, we can find greybody factors analytically. angular part: radial part: absent Cvetic-Larsen equation vanishes (in 4-d) Note: This term is absent in Kanti, March- Russell 02 (appeared after our work) because they utilized Cvetic-Larsen equation which essentially relies on the fact that this term vanishes (in 4-d). Gives the greybody factor. Decomposition:

Greybody factors in 5-d (just to show how it looks) Analytic solution in 5-d Greybody factors in low frequency expansion.

Scalar power spectrum

Spinor power spectra

Vector power spectrum

Scalar ang. power spectrum

Spinor ang. power spectrum

Vector ang. power spectrum

Summary  What we have done –Production of rotating BH large aungular momenta.  BHs are produced with large aungular momenta. larger  Production cross section of BH becomes larger when one takes angular momentum into account. –Evaporation of rotating BH separable  Brane field equation is separable for any spin and in any dimensions.  Analytic expression of greybody factors for n=1 different from g.o. limit  Power spectrum is substantially different from g.o. limit. anisotropic  Especially spinor and vector are highly anisotropic.  Works in progress –Greybody factor in any dimensions without low frequency limit time integrated power and angular spectrum –Complete determination of time integrated power and angular spectrum which can be observed in real experiment Usable by experimentalists!!