Radius Of Black Hole Research Articles

Perry, Kelvin, and the age of the sun

Lord Kelvin argued that the Sun had to be between 20 and 100 million years old, based on the assumption that the Sun’s energy source was gravitational contraction. As everyone now knows, the Sun’s actual power source is the thermonuclear fusion of hydrogen into helium. But Kelvin’s number is based on a physical assumption for which he could give no justification: the Sun’s density is approximately constant. Had Kelvin assumed instead that the Sun had a small core near a black hole radius – an assumption allowed by the knowledge of physicists at the end of the nineteenth century – he would have obtained an age for the Sun as long as 10 trillion years, completely consistent with the long time scale required for evolution. Conversely, had Kelvin accepted the geologists’ time scale, he would have been forced to acknowledge the existence of very dense objects, making it easier for twentieth century astronomers to accept the existence of black holes and neutron stars.

A soliton and a black hole are in Gauss-Bonnet gravity: Who wins?

We study here the phase-transitional evolution between the Eguchi-Hanson soliton, the orbifolded Schwarzschild Anti de-Sitter black hole, and orbifolded thermal Anti de-Sitter space in Gauss-Bonnet gravity for a small Gauss-Bonnet coefficient $\alpha$. Novel phase structure is uncovered for both negative and positive $\alpha$ with spacetime configurations that are stable in Gauss-Bonnet gravity without being so in Einsteinian gravity. The evolutionary tracks taken towards such stable configurations are guided by quantum tunnelling and can be represented with a phase diagram constructed by comparing the Euclidean actions of each of our states as a function of $\alpha$ and the black hole radius $r_b$. According to the AdS/CFT correspondence dictionary, it is expected that some generalized version of closed-string tachyon condensation will exhibit the phase behaviour found here.

Enhancing the rate of tidal disruptions of stars by a self-gravitating disc around a massive central black hole

We further study the idea that a self-gravitating accretion disc around a supermassive black hole can increase the rate of gradual orbital decay of stellar trajectories (and hence tidal disruption events) by setting some stars on eccentric trajectories. Cooperation between the gravitational field of the disc and the dissipative environment can provide a mechanism explaining the origin of stars that become bound tightly to the central black hole. We examine this process as a function of the black hole mass and conclude that it is most efficient for intermediate central masses of the order of ∼ 10 4 M ʘ . Members of the cluster experience the stage of orbital decay via collisions with an accretion disc and by other dissipative processes, such as tidal effects, dynamical friction and the emission of gravitational waves. Our attention is concentrated on the region of gravitational dominance of the central body. Mutual interaction between stars and the surrounding environment establishes a non-spherical shape and anisotropy of the nuclear cluster. In some cases, the stellar sub-system acquires ring-type geometry. Stars of the nuclear cluster undergo a tidal disruption event as they plunge below the tidal radius of the supermassive black hole.

DYNAMICAL FRICTION AROUND SUPERMASSIVE BLACK HOLES

The density of stars in galactic bulges is often observed to be flat or slowly rising inside the influence radius of the supermassive black hole (SMBH). Attributing the dynamical friction force to stars moving more slowly than the test body, as is commonly done, is likely to be a poor approximation in such a core since there are no stars moving more slowly than the local circular velocity. We have tested this prediction using large-scale N-body experiments. The rate of orbital decay never drops precisely to zero, because stars moving faster than the test body also contribute to the frictional force. When the contribution from the fast-moving stars is included in the expression for the dynamical friction force, and the changes induced by the massive body on the stellar distribution are taken into account, Chandrasekhar's theory is found to reproduce the rate of orbital decay remarkably well. However, this rate is still substantially smaller than the rate predicted by Chandrasekhar's formula in its most widely-used forms, implying longer time scales for inspiral. Motivated by recent observations that suggest a parsec-scale core around the Galactic center SMBH, we investigate the evolution of a population of stellar-mass black holes (BHs) as they spiral in to the center of the Galaxy. After ~10Gyr, we find that the density of BHs can remain substantially less than the density in stars at all radii; we conclude that it would be unjustified to assume that the spatial distribution of BHs at the Galactic center is well described by steady-state models. One consequence is that rates of capture of BHs by the SMBH at the Galactic center (EMRIs) may be much lower than in standard models. We finally study the orbital decay of satellite galaxies into the central region of giant ellipticals and discuss the formation of multiple nuclei and multiplet of black holes in such systems.

A CORRELATION BETWEEN THE IONIZATION STATE OF THE INNER ACCRETION DISK AND THE EDDINGTON RATIO OF ACTIVE GALACTIC NUCLEI

X-ray reflection features observed from the innermost regions of accretion disks in Active Galactic Nuclei (AGNs) allow important tests of accretion theory. In recent years it has been possible to use the Fe K line and reflection continuum to parametrize the ionization state of the irradiated inner accretion disk. Here, we collect 10 measurements of xi, the disk ionization parameter, from 8 AGNs with strong evidence for reflection from the inner accretion disk and good black hole mass estimates. We find strong statistical evidence (98.56% confidence) for a nearly linear correlation between xi and the AGN Eddington ratio. Moreover, such a correlation is predicted by a simple application of alpha-disk accretion theory, albeit with a stronger dependence on the Eddington ratio. The theory shows that there will be intrinsic scatter to any correlation as a result of different black hole spins and radii of reflection. There are several possibilities to soften the predicted dependence on the Eddington ratio to allow a closer agreement with the observed correlation, but the current data does not allow for an unique explanation. The correlation can be used to estimate that MCG-6-30-15 should have a highly ionized inner accretion disk, which would imply a black hole spin of ~0.8. Additional measurements of xi from a larger sample of AGNs are needed to confirm the existence of this correlation, and will allow investigation of the accretion disk/corona interaction in the inner regions of accretion disks.

CHARGE-STARVED, RELATIVISTIC JETS AND BLAZAR VARIABILITY

High energy emission from blazars is thought to arise in a relativistic jet launched by a supermassive black hole. The emission site must be far from the hole and the jet relativistic, in order to avoid absorption of the photons. In extreme cases, rapid variability of the emission suggests that structures of length-scale smaller than the gravitational radius of the central black hole are imprinted on the jet as it is launched, and modulate the radiation released after it has been accelerated to high Lorentz factor. We propose a mechanism which can account for the acceleration of the jet, and for the rapid variability of the radiation, based on the propagation characteristics of large-amplitude waves in charge-starved, polar jets. Using a two-fluid (electron-positron) description, we find the outflows exhibit a delayed acceleration phase, that starts at roughly 1pc, where the inertia associated with the wave currents becomes important. The time-structure imprinted on the jet at launch modulates photons produced by the accelerating jet provided the pair multiplicity in the black-hole magnetosphere is sufficiently small, suggesting that very rapid variability is confined to sources in which the electromagnetic cascade in the black-hole magnetosphere is not prolific.

Small hairy black holes in global AdS spacetime

We study small charged black holes in global AdS spacetime in the presence of a charged massless minimally coupled scalar field. In a certain parameter range these black holes suffer from well known superradiant instabilities. We demonstrate that the end point of the resultant tachyon condensation process is a hairy black hole which we construct analytically in a perturbative expansion in the black hole radius. At leading order our solution is a small undeformed RNAdS black hole immersed into a charged scalar condensate that fills the AdS `box'. These hairy black hole solutions appear in a two parameter family labelled by their mass and charge. Their mass is bounded from below by a function of their charge; at the lower bound a hairy black hole reduces to a regular horizon free soliton which can also be thought of as a nonlinear Bose condensate. We compute the microcanonical phase diagram of our system at small mass, and demonstrate that it exhibits a second order `phase transition' between the RNAdS black hole and the hairy black hole phases.

Waves in Poynting-flux dominated jets

AbstractHigh-energy emission from blazars is thought to arise in a relativistic jet launched by a supermassive black hole. The rapid variability of the emission suggests that structure of length scale smaller than the gravitational radius of the central black hole is imprinted on the jet as it is launched, and modulates the radiation released after it has been accelerated to high Lorentz factor. We describe a mechanism which can account for the acceleration of the jet, and for the rapid variability of the radiation, based on the propagation characteristics of nonlinear waves in charge-starved, polar jets. These exhibit a delayed acceleration phase, that kicks-in when the inertia associated with the wave currents becomes important. The time structure imprinted on the jet at launch modulates the photons produced by the accelerating jet provided that the electromagnetic cascade in the black-hole magnetosphere is not prolific.

The stellar kinematic signature of massive black hole binaries

The stalling radius of a merging massive binary black hole (BBH) is expected to be below 0".1 even in nearby galaxies (Yu 2002), and thus BBHs are not expected to be spatially resolved in the near future. However, as we show below, a BBH may be detectable through the significantly anisotropic stellar velocity distribution it produces on scales 5-10 times larger than the binary separation. We calculate the velocity distribution of stable orbits near a BBH by solving the restricted three body problem for a BBH embedded in a bulge potential. We present high resolution maps of the projected velocity distribution moments, based on snapshots of ~ 10^8 stable orbits. The kinematic signature of a BBH in the average velocity maps is a counter rotating torus of stars outside the BBH Hill spheres. The velocity dispersion maps reveal a dip in the inner region, and an excess of 20-40% further out, compared to a single BH of the same total mass. More pronounced signatures are seen in the third and fourth Gauss-Hermite velocity moments maps. The detection of these signatures may indicate the presence of a BBH currently, or at some earlier time, which depends on the rate of velocity phase space mixing following the BBH merger.

Near-Eddington Luminosity Flares from Quiescent Supermassive Black Holes

AbstractA dormant supermassive black hole lurking in the center of a galaxy will be revealed when a star passes within its tidal disruption radius, is disrupted, and a flare of electromagnetic radiation is emitted when the bound stellar debris is accreted. Although the tidal disruption of a star is a rare event in a galaxy, ~ 10−4 yr−1, observational candidates have emerged in all-sky X-ray and deep UV surveys in the form of luminous UV/X-ray flares from otherwise quiescent galaxies. We present the light curves and broadband properties of three tidal disruption candidates discovered in the UV by GALEX, and find that (1) the light curves are well-fitted by the power-law decline expected for the fallback of debris from a tidally disrupted solar-type star, and (2) the UV/optical spectral energy distributions can be attributed to thermal emission from an envelope of debris located at ten times the tidal disruption radius of the central black hole. We use the observed peak absolute optical magnitudes of the flares to predict the detection capabilities of the next generation of wide-field optical synoptic surveys.

Orbital complexity in a time‐dependent potential

AbstractWe introduce a method to detect irregular or chaotic orbits in gravitational potentials based on a wavelet transform of stellar orbits. The method is based on a treatment of normalised frequency power‐spectrum coefficients, which we interpret as occupation probabilities (or, weights) of individual frequency modes. Each probability is fed to a Shannon informationentropy formula, before summing over the whole spectrum to compute the total entropy S. This entropy is then monitored in time as the wavelet coefficients change: each orbit is classi.ed as regular or not according to S and its dispersion. We find that diagrams of entropy versus entropy dispersion allow to identify orbits in a simple and efficient way, similarly to surface‐of‐section analysis but requiring less integration time. We apply the method to the case of a gravitational potential modulated by the periodic motion of a massive black hole and find that some 19% of stars are now shifted to highly irregular motion as a result of black hole orbital motion. This is the same fraction of stars that orbit within the black hole radius of influence. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shock waves in tidally compressed stars by massive black holes

We interest in the case of a main-sequence star deeply penetrating within the tidal radius of a massive black hole. We focus on the compression phase leading to a so-called pancake configuration of the star at the instant of maximal compression. The aim is to study the tidal compression process paying particular attention to the development of shock waves;to deduce reliable estimates of the thermodynamical quantities involved in the pancake star; and to solve a controversy about whether or not thermonuclear reactions can be triggered in the core of a tidally compressed star. We have set up a one-dimensional hydrodynamical model well-adapted to the geometry of the problem. Based on the high-resolution shock-capturing Godunov-type approach, it allows to study the compression phase undergone by the star in the direction orthogonal to its orbital plane. We show the existence of two regimes depending on whether shock waves develop before or after the instant of maximal core compression. In both cases we confirm high compression and heating factors in the stellar core able to trigger a thermonuclear explosion. Moreover, we show that the shock waves carry outwards a brief but very high peak of temperature from the centre to the surface of the star. We tentatively conclude that the phenomenon could give rise to hard electromagnetic radiation, to be compared to some X-ray flares already observed in some galactic nuclei harbouring massive black holes. Finally, we estimate that the rate of pancake stars should be about $10^{-5}$ per galaxy per year. If generated in hard X- or $\gamma$-ray band, several events of this kind per year should be detectable within the full observable universe.

SEMICLASSICAL (QUANTUM FIELD THEORY) AND QUANTUM (STRING) DE SITTER REGIMES: NEW RESULTS

We compute the quantum string entropy S s (m, H) from the microscopic string density of states ρ s (m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature T s = (1/2πk B )L cl c2/α', higher than the flat space (Hagedorn) temperature t s (L cl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). T s is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature T sem = ħ c/(2πk B L cl ). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low [Formula: see text] is the leading term, but for high H near c/ℓ Planck , a new phase transition operates and the whole entropy S sem (H) is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. We compute the string quantum emission cross-section σ string by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For T sem bhdS ℓ T s (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhdS (semiclassical regime). For T sem bhdS → T s , σ string exhibits a phase transition into a string de Sitter state of size [Formula: see text], [Formula: see text], and string de Sitter temperature T s . Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius r g emerge in the bhdS string regime: it can become r g = L s /2, or it can reach a more quantum value, r g = 0.365 ℓ s .

SEMICLASSICAL (QFT) AND QUANTUM (STRING) ANTI-DE SITTER REGIMES: NEW RESULTS

We compute the quantum string entropy Ss(m, H) from the microscopic string density of states ρs(m, H) of mass m in Anti-de Sitter space–time. For high m, (high Hm → c/α′), no phase transition occurs at the Anti-de Sitter string temperature Ts = (1/2πkB)L cl c2/α′, which is higher than the flat space (Hagedorn) temperature ts. (L cl = c/H, the Hubble constant H acts as producing a smaller string constant α′ and thus, a higher tension). Ts is the precise quantum dual of the semiclassical (QFT) Anti-de Sitter temperature scale T sem = ℏc/(2πkBL cl ). We compute the quantum string emission σ string by a black hole in Anti-de Sitter (or asymptotically Anti-de Sitter) space–time (bhAdS). For T sem bhAdS ≪ Ts (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhAdS (semiclassical regime). For T sem bhAdS → Ts, it exhibits a phase transition into a Anti-de Sitter string state of size [Formula: see text], and Anti-de Sitter string temperature Ts. New string bounds on the black hole emerge in the bhAdS string regime. The bhAdS string regime determines a maximal value for H : H max = 0.841c/ls. The minimal black hole radius in Anti-de Sitter space–time turns out to be rg min = 0.841ls, and is larger than the minimal black hole radius in de Sitter space–time by a numerical factor equal to 2.304. We find a new formula for the full AdS entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low H ≪ c/ℓ Planck , or classical regime, [Formula: see text] is the leading term with its logarithmic correction, but for high H ≥ c/ℓ Planck or quantum regime, no phase transition operates, in contrast to de Sitter space, and the entropy S sem (H) is very different from the Bekenstein–Hawking term [Formula: see text].

Black hole evaporation in a heat bath as a nonequilibrium process and its final fate

We consider a black hole in a heat bath, and the whole system which consists of the black hole and the heat bath is isolated from outside environments. When the black hole evaporates, the Hawking radiation causes an energy flow from the black hole to the heat bath. Therefore, since no energy flow arises in an equilibrium state, the thermodynamic state of the whole system is not in equilibrium. That is, in a region around the black hole, the matter field of Hawking radiation and that of heat bath should be in a nonequilibrium state due to the energy flow. Using a simple model which reflects the nonequilibrium nature of energy flow, we find the nonequilibrium effect on a black hole evaporation as follows: if the nonequilibrium region around a black hole is not so large, the evaporation time scale of a black hole in a heat bath becomes longer than that in an empty space (a situation without heat bath), because of the incoming energy flow from the heat bath to the black hole. However, if the nonequilibrium region around a black hole is sufficiently large, the evaporation time scale in a heat bath becomes shorter than that in an empty space, because a nonequilibrium effect of the temperature difference between the black hole and heat bath appears as a strong energy extraction from the black hole by the heat bath. Further, a specific nonequilibrium phenomenon is found: a quasi-equilibrium evaporation stage under the nonequilibrium effect proceeds abruptly to a quantum evaporation stage at a semi-classical level (at black hole radius Rg > Planck length) within a very short time scale with a strong burst of energy. (Contrarily, when the nonequilibrium effect is not taken into account, a quasi-equilibrium stage proceeds smoothly to a quantum stage at Rg < Planck length without so strong an energy burst.) That is, the nonequilibrium effect of energy flow tends to make a black hole evaporation process more dynamical and to accelerate that process. Finally, on the final fate of black hole evaporation, we find that, in order to make the total entropy of the whole system increase along an evaporation process, a remnant should remain after the evaporation of black hole without respect to the size of the nonequilibrium region around the black hole. This implies that the information loss problem may disappear due to the nonequilibrium effect of energy flow.

Fast Variability of Tera–Electron Volt γ Rays from the Radio Galaxy M87

The detection of fast variations of the tera-electron volt (TeV) (10(12) eV) gamma-ray flux, on time scales of days, from the nearby radio galaxy M87 is reported. These variations are about 10 times as fast as those observed in any other wave band and imply a very compact emission region with a dimension similar to the Schwarzschild radius of the central black hole. We thus can exclude several other sites and processes of the gamma-ray production. The observations confirm that TeV gamma rays are emitted by extragalactic sources other than blazars, where jets are not relativistically beamed toward the observer.

Capture rates of compact objects by supermassive black holes

Capture rates of compact objects were calculated by using a recent solution of the Fokker-Planck equation in energy space, including two-body resonant effects. The fraction of compact objects (white dwarfs, neutron stars, and stellar black holes) was estimated as a function of the luminosity of the galaxy from a new grid of evolutionary models. Stellar mass densities at the influence radius of central supermassive black holes were derived from brightness profiles obtained by Hubble Space Telescope observations. The present study indicates that the capture rates scale as $\ensuremath{\propto}{M}_{\mathrm{bh}}^{\ensuremath{-}1.048}$, a consequence of the fact that dwarf galaxies have denser central regions than luminous objects. If the mass distribution of supermassive black holes has a lower cutoff at $\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{6}{M}_{\ensuremath{\bigodot}}$ (corresponding to the lowest observed supermassive black hole mass, located in M32), then nine inspiral events are expected to be seen by the Laser Interferometer Space Antenna (7--8 corresponding to white dwarf captures and 1--2 to neutron star and stellar black hole captures) after 1 yr of operation. However, if the mass distribution extends down to $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{5}{M}_{\ensuremath{\bigodot}}$, then the total number of expected events increases up to 579 (corresponding to $\ensuremath{\sim}274$ stellar black hole captures, $\ensuremath{\sim}194$ neutron star captures, and $\ensuremath{\sim}111$ white dwarf captures).

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation $$P_{{\rm SH}} =\frac{{G\rho\, \hbar }}{{90}}$$ and other black hole radiated power is derived in terms of black hole density, ρ . Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy S bh∝ (kAc 3)/ℏ G. Variations of S bh can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius R H, p = $${\frac{3}{{2\pi }}})\frac{\hbar}{{R_{\rm H} }}$$ which is similar tothe Compton wavelength relation.

Variation in the luminosity of Kerr quasars due to an extra dimension in the braneRandall–Sundrum model

We propose an alternative theoretical approach showing how the existence of an extradimension in the Randall–Sundrum model can be used to estimate the correction in thehorizon of Schwarzschild and Kerr black holes, and consequently its measurability interms of the variation of quasar luminosity, which can be caused by an imprint ofan extra dimension endowing the geometry of the brane-world scenario to theAdS5 bulk. The rotation effects cause a more prominent correction in Kerr horizon radii than inthe Schwarzschild (static black hole) radius, via brane-world effects, and the consequentbigger variation in the luminosity in Kerr black hole quasars. This paper is intended toinvestigate the variation of luminosity due to the accretion of gas in Schwarzschild andKerr black holes (BHs) in the centres of quasars, besides also investigating the variationof luminosity in supermassive BHs arising from brane-world effects, using theRandall–Sundrum model.

NWO Awards Spinoza Prize

The Netherlands Organisation for Scientific Research (NWO) honored the winners of the NWO Spinoza Prize for 2004 at a ceremony this past November in The Hague. This prize is the Netherlands’ top award to researchers for their scientific work. Each winner received C1.5 million ($1.7 million) and a statuette of 17th-century Dutch philosopher and theologian Benedict de Spinoza. Ben Feringa, Jacobus van ’t Hoff Distinguished Professor of molecular sciences at the University of Groningen, was hailed by NWO for his “work on molecular motors and extremely selective catalysts.” He invented the first molecular motor powered by light, and his research group focuses on design and synthesis of complex molecules that can be used as molecular motors, switches, or catalysts.NWO cited Jaap Sinninghe Damsté for his “biological, geological, and chemical work on fossil molecules in sediments.” According to NWO, “his research into chemical fossils rewrote the theories about the carbon and sulphur cycles.” As a molecular biogeochemist, he analyzes specific organic compounds and uses the information to reconstruct the life and climate of earlier epochs. Sinninghe Damsté is head of marine biogeochemistry and toxicology at the Royal Netherlands Institute for Sea Research and a professor of molecular paleontology at Utrecht University. Astronomer Michiel van der Klis received the award for his “pioneering research into x-ray radiation from binary stars,” according to the citation. Van der Klis is a professor of astronomy at the University of Amsterdam’s astronomical institute. In the 1990s, his group discovered the first x-ray star that rotated at 400 times per second, the existence of which had been predicted 16 years previously but had not yet been proved. His studies provide data about the mass, radius, and rotational speed of neutron stars and black holes, as well as insights into the general theory of relativity. © 2005 American Institute of Physics.