Gravitational waves from plunges into Gargantua

Abstract

We analytically compute time domain gravitational waveforms produced in the final stages of extreme mass ratio inspirals of non-spinning compact objects into supermassive nearly extremal Kerr black holes. Conformal symmetry relates all corotating equatorial orbits in the geodesic approximation to circular orbits through complex conformal transformations. We use this to obtain the time domain Teukolsky perturbations for generic equatorial corotating plunges in closed form. The resulting gravitational waveforms consist of an intermediate polynomial ringdown phase in which the decay rate depends on the impact parameters, followed by an exponential quasi-normal mode decay. The waveform amplitude exhibits critical behavior when the orbital angular momentum tends to a minimal value determined by the innermost stable circular orbit. We show that either near-critical or large angular momentum leads to a significant extension of the LISA observable volume of gravitational wave sources of this kind.

Near-horizon geodesics of high spin black holes

“…Partial classifications were performed in [16] and [17]. In [16], equatorial timelike prograde incoming (i.e. that originate from the Kerr exterior geometry) geodesics were classified.…”

“…Proposition 3. For a given normalization κ, the radial integrals t As in NHEK, the radial taxonomy of [16] is easily extended to bounded, outward and/or retrograde orbits by studying the roots and the sign of v R;κ (R). This leads to the classification displayed in Table 5 and Figure 7.…”

“…The equivalence classes of equatorial critical and supercritical prograde timelike geodesics under the action of SL(2, R) × U (1)× ↑↓ symmetry were derived in [16] following earlier work [36][37][38]40]. In this section, we will perform the decomposition of arbitrary geodesics into equivalence classes under the action of SL(2, R) × U (1)× ↑↓ × × .…”

“…As outlined in [16], this mapping can be viewed as the action on Poincaré NHEK coordinates of a shift of the global NHEK time τ → τ − ζ. The energy of the final orbit isĒ = √ −C(sin ζ + T 0 (cos ζ − 1)).…”

“…The study of timelike and null geodesics of the Kerr metric has a long history which is still ongoing [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There are at least two motivations for studying Kerr geodesics.…”