Analytic solution to generalized Teukolsky equations in 5D ...

The 3rd IBS-KIAS Joint Workshop at High 1 2019.02.14. Exact Greybody Factors for Brane Scalar Field of Five-dimensional Rotating Black Holes Yoonbai Kim Sungkyunkwan University In collaboration with

Young-Hwan Hyun, Seong Chan Park arXiv:1901.10828 Myers-Perry Black Branes (4+n)D MP BH 5D Black hole: n=1 Single rotation parameter: dpsi=0 Charge is neglected.

What we are interested in among the high dimensional BHs In LHC, Colliding partons High gravitational effect in extradimension models Mini Black Holes production & Bolding phase

Spin-down Phase (Hawking radiation) & BH decay http://www.youtube.com/watch?v=cxqJHfTCzl0 Klein-Gordon equation Klein-Gordon equation in curved spacetime background Goal: exact solution Generalized Teukolsky equation Modes on the brane

Separation of variables Solution Generalized Teukolsky equation Generalized Teukolsky equation of the s=0 brane modes obtained by using the induced four-dimensional metric of the 5-dimensional rotating black hole Solution of Teukolsky equation

(4+1)D MP BH Generalized Teukolsky eq. for brane fields [Ida-Oda-SCP(2003)] Exact solution? Generalized Teukolsky equation The wave equation of the s=0 brane modes obtained by using the induced four-dimensional metric

of the (4+1)-dimensional rotating black hole Spin-weighted Spheroidal Harmonics[Teukolsky(1973),IOP(2003)] s=0, Spheroidal harmonics [Frolov (2003)] ???? Confluent Heun equation Confluent Heun Equation For s=0, Spheroidal eq.

Full Solution 5D, s=0 MP BH The Solution in terms of the radial 5D, s=0 spheroidal functions MP BH

Parameter range : Researches for Hawking radiation 4D Kerr BH (4+n)D MP BH Teukolsky eq.

[S. Teukolsky(1972,1973)] Sol. to Teukolsky eq. [Teukolsky-Press, Starobinsky, Unruh, Page (1973-1976)] [Leaver (1986), Sasaki(1994)] Hawking radiation [Hawking(1975), Page(1976)] Generalized Teukolsky

eq. for brane fields [Ida-Oda-SCP, PRD67(2003)] Sol. to Gen. Teu. eq. In the low energy limit ? [Ida-Oda-SCP, PRD67(2003)] Hawking radiation Numerical methods

[Ida-Oda-SCP (low ,analyticanalytic)PRD67(2003) (s=0)PRD71(2005), (s>0) PRD73(2006)] [Duffy et al. (s=0) JHEP0509(2005)] [Casals, et al (s=1)JHEP0602(2006) (s=1/2)JHEP0703(2007) (s=0)JHEP0806(2008)] ? Analytical trials in the low-frequency limit

High freq. limit h [Ida-Oda-SCP PRD67(2003)] Matching method works Near horizon solution

Low freq. limit Ingoing boundary condition () Far field solution

Analytical trials To 5D Radial Teu. Eq. High freq. limit Full Solution h

() Far field solution Near horizon solution Ingoing boundary condition Asymptotic solutions and ingoing boundary condition

Ingoing boundary condition Greybody factor for brane scalar fields (4+n)D, s=0 MP BH Ingoing boundary condition The absorption probability

of the incoming wave Correction to black body radiation (not black) Greybody factor for brane scalar fields MP BH Consistent check with analytic results (In low frequency limit) MP BH

Confirmed! Consistent check with analytic results (In low frequency limit) Consistent check with numerical results (In low frequency limit) Conclusion We found the full solution to the five-dimensional rad ial Teukolsky equation for brane scalar fields.

We derived the analytic form of the greybody factor fo r brane scalar fields in terms of the spheroidal joining factors. We check the results with known analytic results in th e low frequency limit. We also check the results with numerical results.