Paralleltransport and geodesic deviation in static spherically symmetric space-times

Tetrads which are parallelpropagated along time-like geodesics in static spherically symmetric spce-times are constructed. Its connection with the geodesic precession is explained. Moreover, we express the solution of the equations of geodesic deviation in terms of the Killing vectors and the fourvelocity.     

Physical properties of charged Kaluza-Klein black holes

In this paper, we consider an exact vacuum solution of the Kaluza-Klein (KK) theory, which describes nonrotating KK black holes. We investigate general properties of geodesic motion in the space-time and calculate the effective potential for null geodesics. The thermodynamical quantities as well as the gravitational lensing of the solution is calculated. We illustrate that the Carter-Penrose diagram for different parameter values resembles the Schwarzschild-like, naked and charged solutions.     

Extremal charged black holes,dark matter and dark energy

Formation of black holes may be constrained by intrinsic parameters characterizing them such as electric charge. Here we discuss the effects of a relatively minute excess of charge on extremal black hole formation and the horizon. We extend the implications of this argument to the formation of primordial black holes (PBH) in the early universe which gives a possible reason for the lack of detection of Hawking radiation. These charge limits also apply to dark matter (DM) particles that may form PHBs in the early universe. The constraint thus obtained on the electric charge of DM particles could also account for the required magnitude of the repulsive dark energy (DE) currently causing an accelerated universe which provides a possible unified picture of DM and DE.     

Thermodynamics of 4-dimensional charged black holes in Brans-Dicke-Born-Infeld gravity theory

In this work, the charged black hole solution to the Brans-Dicke gravity theory in the presence of the nonlinear electrodynamics has been investigated. To simplify the field equations, a suitable conformal transformation has been used which transforms the Brans-Dicke-Born-Infeld Lagrangian to that of Einstein-dilaton theory with new nonlinear electrodynamics field. A new class of 4-dimensional black hole solution has been constructed out as the exact solution to the Brans-Dicke theory in the presence of the Born-Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. The black hole charge and temperature have been calculated making use of the Gauss’s law and the concept of surface gravity, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Through a Smarr-type mass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as the intensive parameters conjugate to the black hole entropy and charge, have been calculated.     

Spherical accretion of matter by charged black holes on $$ Gravity

We studied the spherical accretion of matter by charged black holes on \(f(T)\) Gravity. Considering the accretion model of a isentropic perfect fluid we obtain the general form of the Hamiltonian and the dynamic system for the fluid. We have analysed the movements of an isothermal fluid model with \(p=\omega e\) and where \(p\) is the pressure and \(e\) the total energy density. The analysis of the cases shows the possibility of spherical accretion of fluid by black holes, revealing new phenomena as cyclical movement inside the event horizon.     

Gravitationless black holes

A gravitationless black hole model is proposed in accord with a five-dimensional fully covariant Kaluza-Klein (K-K) theory with a scalar field, which unifies the four-dimensional Einsteinian general theory of relativity and Maxwellian electromagnetic theory. It is shown that a dense compact core of a star, when it collapses to a critical density, suddenly turns off or shields its gravitational field. The core, if its mass exceeds an upper limit, directly collapses into a black hole. Otherwise, the extremely large pressure, as the gravity is turned off, immediately stops the collapse and drives the mantle material of supernova moving outward, which leads to an impulsive explosion and forms a neutron star as a remnant. A neutron star can further evolve into a black hole when it accretes enough matter from a companion star such that the total mass exceeds a lower limit. The black hole in the K-K theory is gravitationless at the surface because the scalar field is infinitely strong, which varies the equivalent gravitational constant to zero. In general, a star, at the end of its evolution, is relatively harder to collapse into a gravitationless K-K black hole than a strong gravitational Schwarzschild black hole. This is consistent with the observation of some very massive stars to form neutron stars rather than expected black holes. In addition, the gravitationless K-K black hole should be easier to generate jets than a Schwarzschild black hole.     

Primordial black holes

Primordial black holes(PBHs) are a profound signature of primordial cosmological structures and provide a theoretical tool to study nontrivial physics of the early Universe.The mechanisms of PBH formation are discussed and observational constraints on the PBH spectrum,or effects of PBH evaporation,are shown to restrict a wide range of particle physics models,predicting an enhancement of the ultraviolet part of the spectrum of density perturbations,early dust-like stages,first order phase transitions and stages of superheavy metastable particle dominance in the early Universe.The mechanism of closed wall contraction can lead,in the inflationary Universe,to a new approach to galaxy formation,involving primordial clouds of massive BHs created around the intermediate mass or supermassive BH and playing the role of galactic seeds.     

Primordial black holes

Primordial black holes (PBHs) are a profound signature of primordial cos-mological structures and provide a theoretical tool to study nontrivial physics of the early Universe. The mechanisms of PBH formation are discussed and observational constraints on the PBH spectrum, or effects of PBH evaporation, are shown to re-strict a wide range of particle physics models, predicting an enhancement of the ul-traviolet part of the spectrum of density perturbations, early dust-like stages, first or-der phase transitions and stages of superheavy metastable particle dominance in the early Universe. The mechanism of closed wall contraction can lead, in the inflation-ary Universe, to a new approach to galaxy formation, involving primordial clouds of massive BHs created around the intermediate mass or supermassive BH and playing the role of galactic seeds.     

Intermediate-mass black holes in globular clusters

The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (10²–10⁴ M _⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.     

Supermassive black holes and their environments

We make use of the first high-resolution hydrodynamic simulations of structure formation which self-consistently follows the build-up of supermassive black holes (BHs) introduced in Di Matteo et al. to investigate the relation between BHs, host halo and large-scale environment. There are well-defined relations between halo and BH masses and between the activities of galactic nuclei and halo masses at low redshifts. A large fraction of BHs forms anti-hierarchically, with a higher ratio of BH to halo mass at high than at low redshifts. At   z = 1  , we predict group environments (regions of enhanced local density) to contain the highest mass and most active (albeit with a large scatter) BHs while the rest of the BH population to be spread over all densities from groups to filaments and voids. Density dependencies are more pronounced at high rather than low redshift. These results are consistent with the idea that gas rich mergers are likely the main regulator of quasar activity. We find star formation to be a somewhat stronger and tighter function of local density than BH activity, indicating some difference in the triggering of the latter versus the former. There exist a large number of low-mass BHs, growing slowly predominantly through accretion, which extends all the way into the most underdense regions, that is, in voids.     

Nearby young single black holes

We consider nearby young black holes formed after supernova explosions in close binaries whose secondary components are currently observed as the so-called runaway stars. Using data on runaway stars and making reasonable assumptions about the mechanisms of supernova explosion and binary breakup, we estimate the present positions of nearbyyoung black holes. For two objects, we obtained relatively small error regions (～50–100 deg²). The possibility of detecting these nearby young black holes is discussed.     

Evolution of evaporating black holes

Dynamical behaviour of an evaporating black hole is investigated for a Vaidya-type metric. The Raychaudhuri equation is examined with including terms up to the second order in the luminosity near the event horizon. Such a solution is found that the luminosity increases as the mass decreases during the evaporation.     

Gravitational collapse without black holes

The contemporary notion of black hole originates in Oppenheimer and Snyder’s 1939 article “On Continued Gravitational Contraction” (Phys. Rev. 56:455, 1939). In particular, Penrose (Phys. Rev. Lett. 14:57, 1965) showed that their metric gave rise to trapped surfaces, that is regions of space from which no light rays can escape, and proved that within such surfaces black-hole formation is inevitable. Section “No trapped surfaces” of this article shows that a simple modification of the Oppenheimer-Snyder metric, fully consistent with General Relativity, may be made, so that all radial light rays originating in the interior escape to the exterior. There is no trapped surface and no black hole; on the contrary there is a stable end state with finite density, contained within a sphere of Schwarzschild radius. Implications for the interpretation of General Relativity, and also for experimental observation of supermassive objects and the Event Horizon Telescope project, are discussed in the concluding section.     

Mini-discs around spinning black holes

Accretion on to black holes in wind-fed binaries and in collapsars forms small rotating discs with peculiar properties. Such 'mini-discs' accrete on the free-fall time without the help of viscosity and nevertheless can have a high radiative efficiency. The inviscid mini-disc model was previously constructed for a non-rotating black hole. We extend the model to the case of a spinning black hole, calculate the structure and radiative efficiency of the disc and find their dependence on the black hole spin. If the angular momenta of the disc and the black hole are anti-aligned, a hydrodynamic analogue of Penrose process takes place.     

Formation of supermassive black holes

Evidence shows that massive black holes reside in most local galaxies. Studies have also established a number of relations between the MBH mass and properties of the host galaxy such as bulge mass and velocity dispersion. These results suggest that central MBHs, while much less massive than the host (~0.1%), are linked to the evolution of galactic structure. In hierarchical cosmologies, a single big galaxy today can be traced back to the stage when it was split up in hundreds of smaller components. Did MBH seeds form with the same efficiency in small proto-galaxies, or did their formation had to await the buildup of substantial galaxies with deeper potential wells? I briefly review here some of the physical processes that are conducive to the evolution of the massive black hole population. I will discuss black hole formation processes for ‘seed’ black holes that are likely to place at early cosmic epochs, and possible observational tests of these scenarios.     

Formation of intermediate-mass black holes as primordial black holes in the inflationary cosmology with running spectral index

Formation of primordial black holes (PBHs) on astrophysical mass scales is a natural consequence of inflationary cosmology, if the primordial perturbation spectrum has a large and negative running of the spectral index as observationally suggested today because double inflation is required to explain it and fluctuations on some astrophysical scales are enhanced in the field-oscillation regime in between. It is argued that PBHs thus produced can serve as intermediate-mass black holes (IMBHs), which act as the observed ultraluminous X-ray sources (ULXs) by choosing appropriate values of the model parameters in their natural ranges. Our scenario can be observationally tested in near future because the mass of PBHs is uniquely determined once we specify the values of the amplitude of the curvature perturbation, spectral index and its running on large scales.     

Implications of primordial black holes on the first stars and the origin of the super-massive black holes

If the cosmological dark matter has a component made of small primordial black holes (BHs), they may have a significant impact on the physics of the first stars and on the subsequent formation of massive BHs. Primordial BHs would be adiabatically contracted into these stars and then would sink to the stellar centre by dynamical friction, creating a larger BH which may quickly swallow the whole star. If these primordial BHs are heavier than  ∼10²² g  , the first stars would likely live only for a very short time and would not contribute much to the reionization of the Universe. They would instead become  10–10³ M_⊙  BHs which (depending on subsequent accretion) could serve as seeds for the super-massive BHs seen at high redshifts as well as those inside galaxies today.     

Wave and stability properties of black holes

In this paper we transform the wave equation governing gravitational perturbations of a Schwarzschild black hole from its standard Schrödinger or Regge-Wheeler form to a Klein-Gordon type wave equation. This latter form reveals immediately that incoming waves with frequencies () _cml , a critical frequency, are completely reflected (transmitted). This process is entirely due to the radial variation of the cut-off frequency inherent in the dispersive nature of the wave propagation properties of gravitational perturbations of the Schwarzschild metric. Moreover, those high-frequency waves ( _cml) which penetrate through the region near the Schwarzschild radiusr _sare, on crossing this event horizon, attenuated by a factor exp (–r _s/c), thereby dumping most of their energy and momentum into the black hole. It is shown that in the vicinity ofr _sthe metric is locally unstable. This feature and the wave absorption process indicate that the neighbourhood aroundr _sis dynamically active, and, as well as acting like a Hawking-type particle creator, will behave as a wave emitter in order to relax the stresses on the metric.