Late-time behavior of massive scalars in Kerr spacetime. Gaurav Khanna UMass - Dartmouth February 24th, 2005

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1 Late-time behavior of massive scalars in Kerr spacetime Gaurav Khanna UMass - Dartmouth February 24th, 2005

2 Radiative tails of massless fields in black hole spacetimes have been studied for decades. In contrast, late-time behavior of massive fields has been studied much less. This talk is about a time-domain based study of massive scalars in Kerr spacetime using linear perturbation theory (Teukolsky Eq.) Collaboration with Lior Burko and Matt Strafuss Phys.Rev.D70 (2004) (gr-qc/ ); Phys.Rev.D71 (2005) (gr-qc/ )

3 Massive scalars in flat spacetime Tails already exist in flat spacetime! (massive scalar fields disperse..) t l 3/2 sin(µt) µ scalar field mass l multipole moment

4 Massive scalars in Schwarzschild spacetime Frequency domain, analytic calculation yields: Koyama et.al. Phys.Rev.D 64, (2001) t 5/6 sin(ω(t) t) ω(t) = µ[1 3/2(2πM/t) 2/3 + O(1/t)] Note: It is independent of multipole moment. The decay rate is slower than the massless case.

5 Massive scalars in Kerr spacetime No known results. Analytic calculations too complex for Kerr. But, what do we expect? As seen in the Schwarzchild case, the tail is independent of the field multipole moment.. Intuitively, we expect the same tail (there will be mode-mixing but all modes decay at the same rate!).

6 Numerical computation in the time-domain (axisymmetric) We use the PTC (Penetrating Teukolsky Code) with a mass term added in.. Time scale of evolutions 4000M Inner boundary at r=r+ ( ingoing ); Outer at 4000M ( outgoing ) Grid size X 32 (radial X polar-angle) µ 0<a/M<0.995, M = 1 ID: Gaussian centered at 50M, width 2M and various multipoles were tried.

7 Results (axisymmetric) Convergence? Nice second order..

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9 Results (axisymmetric) Period of the late-time oscillations ω(t) = µ[1 3/2(2πM/t) 2/3 + O(1/t)]

10 Non-axisymmetric? Super-radiance, Black hole bombs (Teukolsky Press bomb), Instability.. ω ω + If frequency of a massless field < then rotational energy is extracted from the hole. This is the super-radiance condition. Now, surround the hole with mirrors and let the amplified massless field bounce successively. You have a bomb! Instead of using artificial mirrors, use a natural mirror like a non-zero mass of the field. Thus, massive fields should be unstable in Kerr spacetime ( < ). ω µ

11 Numerical Simulation of a Black hole bomb Time-domain Teukolsky Code NTC for massless scalar field with spherical mirror a=0.9999m; l =m=1 ID: almost monocromatic wave-packet, centered at 80M, width 50M modulated with frequency w=0.25/m Outer boundary mirror 160M (fields zero); Inner -40M ( ingoing )

12 Numerical Simulation of a Black hole bomb

13 Numerical simulation of a massive scalar instability Time-domain Teukolsky Code NTC for massive scalar field l µ a=0.9999m; =m=1; =0.25/M ID: almost monocromatic wave-packet, centered at 120M, width 50M modulated with frequency w=0.25/m Outer boundary 1460M ( outgoing ); Inner -40M ( ingoing )

14 Numerical simulation of a massive scalar instability

15 Numerical simulation of a massive scalar with superradiance condition violated

16 Growth estimates e-folding time from frequency domain computations (Detweiler, Phys.Rev.D (1980)): Works out to parameters (a/m) 1 24(µM) 8 µ M for our choice of From our numerical data M; the growth is two orders of magnitude higher! Could it simply be because of the approximation µ M << 1 used in Detweiler s formula? More work needed