Narrow Results

For the massless Dirac equation outside a slow Kerr black hole, we prove asymptotic completeness. We introduce a new Newman–Penrose tetrad in which the expression of the equation contains no artificial long-range perturbations. The main technique used is then a Mourre estimate. The geometry near the horizon requires us to apply a unitary transformation before we find ourselves in a situation where the generator of dilations is a good conjugate operator. The results are eventually re-interpreted geometrically to provide the solution to a Goursat problem on the Penrose compactified exterior.

It is shown that the geodesics with negative energy for rotating black holes cannot originate or terminate inside the ergosphere. Their length is always finite and this leads to conclusion that they must originate and terminate inside the gravitational radius of the ergosphere.

We reconsider the classical Schwarzschild solution in the context of a Janus cosmological model. We show that the central singularity can be eliminated through a simple coordinate change and that the subsequent transit from one fold to the other is accompanied by mass inversion. In such scenario matter swallowed by black holes could be ejected as invisible negative mass and dispersed in space.

Three mechanisms of getting high energies in particle collisions in the ergosphere of the rotating black holes are considered. The consequences of these mechanisms for observation of ultra high energy cosmic rays particles on the Earth as result of conversion of superheavy dark matter particles into ordinary particles are discussed.

A new paradigm for black holes is introduced. It is known as the External Energy Paradigm. The paradigm asserts that all energies of a black hole are external quantities; they are absent inside the horizon. These energies include constituent mass, gravitational energy, electrostatic energy, rotational energy, heat energy, etc. As a result, quantum particles with charges and spins cannot exist inside the black hole. To validate the conclusion, we derive the moment of inertia of a Schwarzschild black hole and find that it is exactly equal to mass $\times$ (Schwarzschild radius)², indicating that all mass of the black hole is located at the horizon. This remarkable result can resolve several long-standing paradoxes in black hole theory; such as why entropy is proportional to area and not to volume, the singularity problem, the information loss problem and the perplexing firewall controversy.

The coordinate transformations are proposed to transform Gödel and Kerr metrics to a nonrotating form by the uniform way.

We investigate the Carter-like constant in the case of a particle moving in a nonrelativistic dipolar potential. This special case is a missing link between the Carter constant in stationary and axially symmetric spacetimes (SASS) such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from the Newtonian mechanics to the relativistic SASS.

In this paper, we study some features of the Kerr metric both from an analytic and a visual point of view by performing accurate raytracing in various situations. We focus on features that are unique to the maximal analytic extension of the Kerr metric as compared to that of the Schwarzschild or even the Reissner–Nordström one. A large number of new, yet underexplored phenomena appear, especially regarding the structure of bounded null geodesics and the aspect of the negative gravity regions whose visual characteristics are shown both from outside and inside it.

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking.

• (1)The Horizon Mass Theorem states that the mass at the event horizon of any black hole — neutral, charged, or rotating — is always twice its irreducible mass observed at infinity.
• (2)The External Energy Theorem asserts that the rotational energy of a Kerr black hole exists completely outside the horizon. This is due to the fact that the irreducible mass does not contain rotational energy.
• (3)The Moment of Inertia Theorem shows that every black hole has a moment of inertia. When the rotation stops, the irreducible mass of a Kerr black hole becomes the moment of inertia of a Schwarzschild black hole. This is recognized as the rotational equivalent of the rest mass of a moving body in relativity.

Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it a limiting value in rotation, it determines black hole dynamics and structure. What is believed to be a black hole is a mechanical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

In this paper, we study spin effects in the neutrino gravitational scattering by a supermassive black hole with a magnetized accretion disk having a finite thickness. We exactly describe the propagation of ultrarelativistic neutrinos on null geodesics and solve the spin precession equation along each neutrino trajectory. The interaction of neutrinos with the magnetic field is due to the nonzero diagonal magnetic moment. Additionally, neutrinos interact with plasma of the accretion disk electroweakly within the Fermi approximation. These interactions are obtained to change the polarization of incoming neutrinos, which are left particles. The fluxes of scattered neutrinos, proportional to the survival probability of spin oscillations, are derived for various parameters of the system. In particular, we are focused on the matter influence on the outgoing neutrinos flux. The possibility to observe the predicted effects for astrophysical neutrinos is briefly discussed.

In this paper, we derive the exact form of effective potential in Kerr geometry from the general relativistic radial momentum equation. The effective potential accurately mimics the general relativistic features, over the entire range of the spin parameter $-1<a<1$. We obtain the exact expression of the rate of dragging of inertial frames that can be used to study the relativistic precession of twisted accretion disks that are formed when the disk outskirts are tilted relative to the equatorial plane of the black hole. We then present an effective potential that provides a simplistic approach to study particle dynamics using physical concepts analogous to the Newtonian physics. We compare the equatorial as well as off-equatorial particle trajectories obtained using our potential with the general relativistic solutions. We find that our approach can capture the salient features of Kerr geometry and is applicable to studies of accretion processes around Kerr black holes.

In the paper the work of the tidal forces that arise when the relative deviation of the protons on distance of the order of the Compton wavelength near the horizon of Kerr black hole is considered. For ease of calculation the assumption is made that the proton has only a radial component of the velocity. It is shown that the work of the tidal forces at speeds close to the speed of light sharply increases with Lorentz factor and it can obtain very high energy of the Grand Unification order.

We reveal three new discoveries in black hole physics previously unexplored in the Hawking era. These results are based on the remarkable 1971 discovery of the irreducible mass of the black hole by Christodoulou and Ruffini, and subsequently confirmed by Hawking.

1. The Horizon Mass Theorem shows that the mass at the event horizon of any black hole: neutral, charged, or rotating, depends only on twice its irreducible mass observed at infinity.

2. The External Energy Conjecture proposes that the electrostatic and rotational energy of a general black hole exist completely outside the horizon due to the nature of the irreducible mass.

3. The Moment of Inertia Property shows that every Kerr black hole has a moment of inertia. When the rotation stops, there is an irreducible moment of inertia as a result of the irreducible mass.

Thus after 50 years, the irreducible mass has gained a new and profound significance. No longer is it just a limiting value in energy extraction, it can also determine black hole dynamics and structure. What is believed to be a black hole is a physical body with an extended structure. Astrophysical black holes are likely to be massive compact objects from which light cannot escape.

Gravitational waveforms radiated during the inspiral, plunge and merger stages of a small body moving in the equatorial plane of a Kerr black hole can be exploited to get unique, physical information on the strong-field regime. Such waveforms are constructed by numerically solving the Teukolsky equation in the time domain. When building the source term for the gravitational perturbations, one models the dissipation of orbital energy using the Teukolsky frequency-domain gravitational-wave flux for circular, equatorial orbits, down to the light-ring. The merger features of the Teukolsky waveforms have proven to be instrumental to extending the effective-one-body model of spinning, nonprecessing black-hole binaries, from the comparable-mass to the test-particle limit.

In the paper the dependence of the tidal forces for the two protons at a distance of the order of the Compton wavelength from the polar angle in the Kerr spacetime is considered. It is shown that in approach to the equatorial plane the tidal forces are increase.