Dirac dynamical resonance states around Schwarzschild black holes

Abstract

Recently, a novel kind of scalar wigs around Schwarzschild black holes-scalar dynamical resonance states were introduced in [Phys. Rev. D 84, 083008 (2011)] and [Phys. Rev. Lett. 109, 081102 (2012)]. In this paper, we investigate the existence and evolution of Dirac dynamical resonance states. First we look for stationary resonance states of a Dirac field around a Schwarzchild black hole by using the Schrödinger-like equations reduced from the Dirac equation in Schwarzschild spacetime. Then Dirac pseudo-stationary configurations are constructed from the stationary resonance states. We use these configurations as initial data and investigate their numerical evolutions and energy decay. These dynamical solutions are the so-called "Dirac dynamical resonance states".It is found that the energy of the Dirac dynamical resonance states shows an exponential decay.The decay rate of energy is affected by the resonant frequency, the mass of Dirac field, the total angular momentum, and the spin-orbit interaction. In particular, for ultra-light Dirac field, the corresponding particles can stay around a Schwarzschild black hole for a very long time, even for cosmological time-scales.

Quasibound states of charged dilatonic black holes

“…This means that ultralight scalar field can be very long-lived around the GMGHS black hole. Similar results have been found for massive scalar and Dirac fields around a Schwarzschild or a Reissner-Nordström black hole [17,22,23].…”

“…Quasibound states of a black hole have been studied under several different conditions [13][14][15][16][17][18][19][20][21][22][23]. The minimal extension of general relativity, i.e., the dilatonic gravity or called scalar tensor theory, can be traced back to Kluza-Klein compactification and Dirac's large number hypothesis, in which only one new degree is introduced.…”

Massive charged Dirac fields around Reissner-Nordström black holes: Quasibound states and long-lived modes

“…[3,4], Barranco et al studied the evolution of massive scalar fields around a Schwarzschild BH and found configurations that can survive for a very long time, even for cosmological time scales. Zhou et al further showed that such long-lived nontrivial distributions can be extended to Dirac fields [5]. These dynamical resonance solutions are basically described by the so-called quasibound states of massive fields in the BH spacetimes, which have attracted much attention in recent years [6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…A common feature of the results in Refs. [3][4][5] is that the long-lived modes are obtained in the limit of smallmass coupling M µ ≪ 1, where M and µ are the masses of the BH and field, respectively. There is a simple physical explanation for this: smaller value of M µ corresponds to weaker gravitational attraction between the external field and BH, which implies that it takes a longer time for the BH to absorb the external fields around it.…”

Schwarzschild scalar wigs: Spectral analysis and late time behavior

“…Motivated by the possibility of describing the dark matter in the galactic halo by the coherent excitation of an ultra-light scalar field [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], including the supermasive black hole [51][52][53][54], in previous work we analyzed the time scale for the quasi-bound states on a supermassive, nonrotating black hole background [32,33]; see [55] for a recent generalization to the Dirac field. In particular, we showed in Ref.…”