**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;