Publication date: Jun 2009
Abstract:
Rotating black holes in the brany universe of the Randall-Sundrum type
with infinite additional dimension are described by the Kerr geometry
with a tidal charge b representing the interaction of the brany black
hole and the bulk spacetime. For b < 0 rotating black holes with
dimensionless spin a > 1 are allowed. We investigate the role of the
tidal charge in the orbital resonance model of quasiperiodic
oscillations (QPOs) in black hole systems. The orbital Keplerian
frequency v K and the radial and vertical epicyclic
frequencies v r, v θ of the equatorial,
quasicircular geodetical motion are given. Their radial profiles related
to Keplerian accretion discs are discussed, assuming the inner edge of
the disc located at the innermost stable circular geodesic. For
completeness, naked singularity spacetimes are considered too. The
resonant conditions are given in three astrophysically relevant
situations: for direct (parametric) resonances of the oscillations with
the radial and vertical epicyclic frequencies, for the relativistic
precession model, and for some trapped oscillations of the warped discs,
with resonant combinational frequencies involving the Keplerian and
radial epicyclic frequencies. It is shown, how the tidal charge could
influence matching of the observational data indicating the 3 : 2
frequency ratio observed in GRS 1915 + 105 microquasar with prediction
of the orbital resonance model; limits on allowed range of the black
hole parameters a and b are established. The “magic” dimensionless black
hole spin enabling presence of strong resonant phenomena at the radius,
where v K: v θ : v r = 3 : 2 : 1, is
determined in dependence on the tidal charge. Such strong resonances
could be relevant even in sources with highly scattered resonant
frequencies, as those expected in Sgr A*. The specific values of the
spin and tidal charge are given also for existence of specific radius
where v K : v θ : v r = s : t : u
with 5≥ s > t > u being small natural numbers. It is shown that
for some ratios such situation is impossible in the field of black
holes. We can conclude that analysing the microquasars high-frequency
QPOs in the framework of orbital resonance models, we can put relevant
limits on the tidal charge of brany Kerr black holes.
Authors:
Stuchlík, Zdeněk; Kotrlová, Andrea;