**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;