1. The Structures of Accretion Objects of Compact Objects

What are the blackhole accretion objects? What are the blackhole accretion objects structures? The blackhole accretion object is usually understood as the disc-like structure(s) of macroscopic matter which is in the vicinity of the blackhole; its properties of swirling and its gravitational ones allow one to prescribed the emissions. A cusp is described in accordance with the photon ring; more in detail, it is due to the gravitational forces causing the geodesics close to the blackhole (which are orbited by the photons): this way, the gravitational properties of the phenomenology of the neighbourhood of the blackhole are observed. The phenomenon of gravitational lensing is taken into account.

The aspects of the accretion objects which lead to the classification of the qualities of the cusp(s) of the accretion objects can now be classified as follows from the work of Abramowicz et al. ^[1].

The existence of cusps in blackhole accretion objects was traced from the work of Abramowicz et al. ^[2] as far the delineation of an axisymmetric configuration of Relativistic macroscopic non-self-gravitating gas with non-vanishing thermo-dynamical pressure is hypothesized; the related qualities are developed up to the description of the torus accretion objects, from which the geometric bowl-shaped objects are developped.

From the work of Abramowicz et al. ^[1], the accretion discs theory is recalled after the previous guidelines as far as the structure of the objects is concerned from the event horizon, from the innermost stable circular orbit, and from the ergosphere.

The disc modes are ibidem classified as Polish doughnut thick discs, - Shakura-Sunyaev thin discs, slim discs, and advection-dominated accretion flows, for which the thermodynamical paradigm is taken into account.

The features of stability, those of oscillations and those of jets are studied. The theoretical aspects and the numerical ones are studied from blackhole objects with respect to those which qualify those ,i.e., from neutron stars, from ^[1].

The study of stability is recommended for blackhole accretion objects due to the description of differential rotation; oscillations are needed to be described when the study of the matter (fluid) distribution is concerned, and also as related with the presence of jets as the latter ones induce energy transport and angular momentum transfer. The disc types are specified after the number and the structures of the cusps.

2. About Blackhole Cusps

From ^[3], a cusp spacetime can be obtained for a self-gravitating object with accretion object as the occurrence of the angular-momentum isoclynes on the equatorial plane, for which

being l_K the Keplerian angular momentum, when a gravitational potential is taken into account.

2.1. The Keplerian Aspects and the General-Relativistic Ones of Accretion Objects

As discussed from ^[3], the cusps are classified; more in detail, Type 1 (Shakura-Sunyaev) discs are further classified according to the features of the two or more cusps:

- a: the potential surface corresponding to the inner cups is opened towards the blackhole, while the potentiality surface(s) of the outer cusp(s) can be described as semi-closed;

- b: The equipotential surface of the inner cusp is fully enclosed in the disc center and the equipotential surface of the outer cusp is opened towards the blackhole;

- c: the effective potential of the inner cusp and that evaluated at the outer cusp are the same: the corresponding equipotential surfaces has two intersections.

In the 1d case, the cusp outshines the supermassive blackhole in the regime of low-luminosity of an AGN.

The features of gas accretion models are revised after ^[2] and afterwards: the outer cusps are calculated to be places after a radial distance of 3rg, being rg the gravitational radius of th compact object, while the hydrodynamical inner forms are evaluated after the analysis of the magneto-Rotational Instabilities (MRI’s). A comparison with the instabilities arising in the slender torus ^[4] is therefore in order.

3. Experimental Methods of Disc Cusps

The setting of a Schwarzschild blackhole in a swirling background is considered from ^[5], after which the instabilities of the circular geodesics are predicted. As a result, the appearance of one outer cusp due to the rotation is described.

From ^[6], the kinematic viscosity coefficient  v= l₀v₀, being l₀ the Keplerian angular momentum and v₀ the shear speed of turbulence, is specified for the experimental evidence as with l0 being the correlation length of the turbulence bounded, and being v₀ the speed of the turbulence being bounded from above as the speed of sound c_b: the advection dimensional coefficient ∝ is therefore specified as  

being

the Keplerian angular momentum, after which the available discs height H is correlated as

.The shear stress is this way described.

The new configurations of spacetimes of Kerr blackholes on a rotating background ar described starting from ^[7]. In this case, the spacetimes are characterized after the rotAs a consequence of the swirling rotation, one outer marginally stable orbits is described from ibidem to appear further than the inner cusp according to which the different disc types are further classified.

It is my duty to stress that the isoclyne surfaces of the gravitational potential of the disc are to be calculated analytically after including the gravitational-pressure contribution in the differential of the pressure.

From ^[7], the geometric thick discs are described as a bowl-shaped configuration.

The effective vonZeipel angular velocity is written as a function of the specific angular momentum L which allows one to encode the thermodynamics paradigm into the polytropic equation of state. The corresponding pressure is written after which the General-Relativistic Euler equations are integrable.

As introduced from the properties of the angular momentum from ^[8], the angular momentum realizations from galactic structures are achieved.

From ^[7], after integration of the Relativistic Euler equations in the vonZeipel regime, of the angular momentum, the distribution of the rest mass density as equilibrium tori is possible. From fig.4 from ^[7], the isoclynes of the rest mass density of the disc at the variation of the swirling parameter with fixed angular momentum of the compact object are studied.

The here-collected experimental methods are therefore implemented in order to align the frameworks of the observers as from the relative velocities of the Zero-angular-velocity observer (ZAVO) and of the Zero-angular-momentum observer (ZAMO) as the ratios of the pertinent components of the metric tensor. Such distributions are similar after the study of radiation to the method of the effective potential.

4. Experimental Selection of Blackholes

A comparison with the realisation coming from remnants near galactic centers is performed after ^[9]. Ibidem, stellar-mass remnants are recalled to form a high-concentration cusp- the thermodynamical mechanisms and the fluid-dynamics ones are to be implemented. The gas-capture rates onto the cusp of stellar remnants are here then constrained. Stellar-mass remnants are assumed the total mass of the stellar mass black holes as 5% of the mass of the central Stellar-mass blackhole.

4.1. The Experimental Techniques to Observe Blackhole-discs Cusps?

The properties of the blackholes originating the Astrophysical systems from which the experimental evidence can be issued in order for the cusps to be analyzed in the corresponding blackhole accretion objects are now juxtaposed.

From ^[10], the characteristics of gravitational waves from binary blackhole space-times are reviewed to be experimentally constrained for the blackhole mass to be as where the power radiated is one corresponding to the energy of The sum of the Schwarzschild radii of the binary components is this way constrained. The binary system of two neutron stars is this way not selected as the appropriate source as the deduced chirp mass would not have required mass. The waveforms are calculated according to the resulting source parameters.

The experimental results of misalignment of the schematized model of an accretion disc with respect to the spin of the blackhole was introduced after the Bardeen-Petterson 1975 description. The geometry of tilted accretion discs was recapitulated in ^[11]; within this framework, the role of General-Relativistic Magneto-Hydro-Dynamics (GRMHD) simulations was tested.

5. Accretion Objects in Generalized Theories of Gravity

Examples of accretion objects from generalized Theories of gravity are presented in order for the experimental techniques to be developped.

The features of the blackhole shadows are studied from ^[12] as those which are taken after the three regimes of optical thickness of the disc- i.e., as those from ^[12], where the reference frames of the observers are schematized; in this respect, the structure of the blackhole horizons is implied in the position of the Rankine-Hugoniot initial boundary conditions of the cusp, where the presence of a gravitational torque has to be imposed. The corresponding photons rings are described and the experimental results can be brought. The example of the Sagittarius A* cusp in the accretion object has in this framework to be evaluated within the strictest analysis of the structure of the horizon ^[13].

In de Rham-Gabadadze-Tolley (dRGT) massive gravity ^[14], nonlinear Lorentz-invariant models are used, as the graviton is attributed a mass in the absence of the Boulware–Deser (BD) ghost mechanism, from which the previous Stueck-elberg description and the Fridman-Robertson-Walker metric(s) can be reconducted. In dRGT theories, the qualities of the accretion objects are written from ^[15]; more in detail, the gravitational potential is written as one which encodes the features descending from a massive graviton after which the new equations of the 3 horizons can be calculated: the locations of the stable orbits are spelled out where attention is paid to the comparison with the Schwarzschild case.

The limit to a vanishing graviton mass is here recalled to be fixed. The specific energy is studied at varying constant parameters of the gravitational action with fixed anti-DeSittter properties.

The description of the jets pointing the observer are scrutinized in order for the mechanisms underlying the r-ray bursts (GRB’s) to be revealed.

The Weyl distorted blackholes ^[16] can therefore be predicted within the analysis of the Bondi accretion. More in detail, the Weyl metric is used to calculate the qualities of the accretion rates. As a prospective study, one finds in the simple model of a Bondi accretion the accretion rate is modified if and only if (iff) the asymptotic flatness is discarded in the modified version.

More in detail, the sonic behaviour of the accretion object has to be retained at large distances for the new blackhole models to find comparison with the Schwarzschild one.

6. Congruences of Timelike Geodesics

The techniques which are used to investigated the geodesics structure of blackholes, and, in particular, those of the cusp(s) region(s) close to a blackhole are the studies of congruences of timelike-geodesics (i.e., with respect to a time-affine parameter).

The blackhole spacetimes are compared according to congruences of timelike geodesics; as an example, from ^[17], the geodesics structures are analyzed of Schwarzschild blackholes; the investigation is completed to discover that genealized Schwarzschild blackholes are not uniquely defined, as the Cauchy maxi-mal completion, after which the Cauchy maximal extensions are calculated, is unique- the technique introduced is the study of the null geodesics to compare diverse Generalized-Schwarzschild blackholes.

6.1. Geodesics Close to the Blackhole

As introduced in ^[18], blackhole-image experiments are aimed at observing the phenomena due to the geodesics followed by particles and by the light in GR spacetime: the blackhole shadows are this way resolved; ibidem, the methodology is illustrated, according to which it is possible to select the photon trajectories at different order: the observer solves the different images of the geodesics when the radiation regime has to be singled out.

In particular, the shadow of blackholes is studied as it provides with information from the structure of the spacetimes to the optical image.

Non-linear contributions are appreciated i.e. in the case of a Reissner-Nordstrom (RN) blackhole spacetime and in that of the RN-anti-deSitter as a correction quadrupole term. More in detail, there exits the circular orbit. From ^[19], a comparison with alternative Theories of gravity is this way possible.

From the Randall-Sundrum scenarioes, one is issued in ^[20] where the shadows of a Relativistic blackhole can be analytically depicted after not only the metric in the region near the blackhole, but also after the linearized of the faraway region; this way, the comparison with the experimental data allows one to constrain the parameter space of the braneword scenario: the example of M87* is there taken.

6.2. Some of the Consequences of External Fields

In ^[21], the occurrence of magnetic fields above he equatorial plane of blackhole accretion objects is studied as due to the non-vanishing curl of the disc radiation field.

The pertinent MHD description is this way enhanced; among the possible mechanisms which are apt to induce magnetic fields in the Relativistic macroscopic matter, the mechanisms are to be chosen, according to which the poloidal magnetic field and the toroidal one are in good agreement within the analysis of the experimental data from X-ray binaries.

The qualities of the radiation flux attribute the properties of the macroscopic matter around the blackhole ^[22][23].

In the work of Franzin et al. ^[24], the superradiance of electro-magnetic test fields is studied in Kerr-blackhole spacetimes and in Kerr-like-blackhole space-times in the strong-gravity regime; the test is aimed at distinguishing the GR blackholes from those described in further Theories of gravity: the main aspects of the issue are demonstrated in the region close to the Physical horizon as far as the emission of gravitational waves is concerned.

6.3. Further Consequences of the Presence of External Fields

The geodesics structures of electric stringy blackholes and those of magnetic stringy ones are revealed in ^[25]; for these purposes, the congruences of timelike geodesics are investigated ibidem: as a result, the time affine parameter and the spelling of the kinematic variables are chosen as indicators.

As a proposed methodology, the Raydachury equations are written for the components of the shear and of the rotation; however, the geodesics equations on the equatorial section are shown to be written as from first integrals.