A non-linear resonance model for the black hole and neutron star QPOs: theory supported by observations

Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two modes of accreting disk oscillation. This hypothesis implies certain very general predictions, several of which have been borne out by observations. Some of these follow from properties of non-linear oscillators, while the others are specific to oscillations of fluid in strong gravity. A 3:2 resonant ratio of frequencies can be clearly recognized in the black-hole as well as in the neutron-star QPO data.Comment: 8 pages, 8 figures, to appear in Proceedings of the Albert Einstein Century International Conferenc

A causal Schwarzschild-de Sitter interior solution by gravitational decoupling

We employ the minimal geometric deformation approach to gravitational decoupling (MGD- decoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object.Comment: 15 pages, 6 figure

Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a<0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a>0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a~0.7 to a~0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a<0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a~1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).Comment: 6 pages, 4 figures, accepted by Astronomy & Astrophysic

Isotropization and change of complexity by gravitational decoupling

We employ the gravitational decoupling appro- ach for static and spherically symmetric systems to develop a simple and powerful method in order to (a) continuously isotropize any anisotropic solution of the Einstein field equa- tions, and (b) generate new solutions for self-gravitating dis- tributions with the same or vanishing complexity factor. A few working examples are given for illustrative purposes

Einstein-Klein-Gordon by gravitational decoupling

We investigate how a spherically symmetric scalar field can modify the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the scalar field and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling by Minimal Geometric Deformation (MGD-decoupling), which allows us to show that, under the MGD paradigm, the Schwarzschild solution is modified in such a way that a naked singularity appears.Comment: 16 pages, 2 figures. arXiv admin note: text overlap with arXiv:1804.0346

Black holes by gravitational decoupling

We investigate how a spherically symmetric fluid modifies the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the fluid and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling realised via the minimal geometric deformation approach, which allows us to prove that the fluid must be anisotropic. Several cases are then explicitly shownComment: New section with a regular hairy black hole solution; references adde