Particle creation by black holes

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 10¹⁵ g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.     

Synchrotron peak luminosity,black hole mass and Eddington ratio for SDSS flat-spectrum radio quasars

For a sample of 185 flat-spectrum radio quasars (FSRQs) constructed from the SDSS DR3 quasar catalog, we found a significant correlation between the synchrotron peak luminosity and both the black hole mass and Eddington ratio. This implies that the physics of its jet formation is not only tightly related with the black hole mass, but also with the accretion rate. We verify that the synchrotron peak luminosity can be a better indicator of jet emission than 5 GHz luminosity, through comparing the relationships between each of these two parameters and both black hole mass and Eddington ratio. The fundamental plane of black hole activity for our FSRQs is established as L _r ∝ L ^0.80±0.06_x M ^{−0.04±0.09}_bh with a weak dependence on black hole mass, however, the scatter is significant.

     

Pregalactic black holes: A new constraint

Pregalactic black holes accrete matter in the early universe and produce copious amounts of x radiation. By using observations of the background radiation in the x and wavebands we have been able to impose a strong new constraint upon their possible abundance. If pregalactic black holes are actually present, several outstanding problems of cosmogony can be resolved with typical pregalactic black hole masses of 100M. Significantly more massive holes cannot constitute an appreciable mass fraction of the universe and are limited by _PGBH(M)<10(M JM)^–1.This essay received an honorable mention (1978) from the Gravity Research Foundation.     

Hierarchical scales and “family” of black holes

An attempt to unify the scales of physical quantities is presented within the framework of a hypothesis about the existence of a family of black holes. There exists a scale characterized by parametersm _x 4×10¹⁴ GeV and _GUM 1/25 which may be identified with a scale for the grand unification.     

Black holes associated with galaxies

A small and a large black hole are naturally associated with a galaxy of total massM and spherical halo radiusR. Also of massM, the large black hole is a spatial contraction of the galaxy down to its Schwarzschild radius,r r, with=2GM/c ²R, whereG/c ²=4.78×10^–17 kpc/M is Newton's gravitational constant divided by the speed of light squared. The small black hole is ther r contraction of the large hole, i.e., the iterated double contraction of the galaxy itself, with the resulting massm=M=2GM ²/c²R. In the case of the Milky Way (M=7.0×10¹¹ M andR=15 kpc) the latter equation for the small black hole mass yieldsm=3.1×10⁶ M , which is close to the observed value for the mass of the black hole at the center of the Milky Way. Black holes of the small type may evolve to the large by mass accretion, perhaps during a quasar phase. Vast regions of the universe may in fact be populated by large black holes—missing mass—which validates the cosmological principle and effects the closure of the universe.     

Motion of primordial black holes in the early universe and their likely distribution today

We look in detail at those effects which slow down black holes of mass 10¹⁵ g and affect their spatial distribution today. In particular we treat effects caused by the charge fluctuations of the hole which result from quantum-mechanical processes. The dominant energyloss mechanism for the holes is the expansion of the universe, which leaves them virtually at rest at the time of galaxy formation. The resultant violent relaxation should concentrate roughly half of them in present-day galaxies and their halos.     

Shear Hell Holes and anisotropic universes

If the early universe was highly anisotropic, primordial black holes may have formed prolifically (despite previous claims to the contrary) even if the initial density fluctuations were small. However, the holes would initially be endowed with an immense amount of shear, so it is not obvious that they would evolve into the conventional type ofstationary black hole envisaged by the no hair theorem. If they do settle down to a stationary state, it may only be on a considerable time scale; and in principle there might exist soliton-type solutions which represent holes with shear which persists indefinitely. Such shear hell holes, as we term them, could have even more dramatic properties than the usual stationary holes: in particular, they might be prolific generators of gravitational radiation and they could be associated with interesting quantum effects.This essay received the fifth award from the Gravity Research Foundation for the year 1979-Ed.     

Evolution of Dimensionless Angular Momentum of Central Black Holes of Accretion Disks

The effects of the Blandford-Znajek (BZ) process on the evolution of the central black holes of accretion disks are investigated. It is proved that the dimensionless angular momentum a_* of the central black hole will evolve to a stable value in the case of thin disks, while it will evolve to a stable value in the case of thick disks. These results imply that the central black holes of accretion disks will never evolve to extreme Kerr black holes.     

Possible effects of a cosmological constant on black hole evolution

We explore possible effects of vacuum energy on the evolution of black holes. If the universe contains a cosmological constant, and if black holes can absorb energy from the vacuum, then black hole evaporation could be greatly suppressed. For the magnitude of the cosmological constant suggested by current observations, black holes larger than 4×10²⁴ g would accrete energy rather than evaporate. In this scenario, all stellar and supermassive black holes would grow with time until they reach a maximum mass scale of 6×10⁵⁵ g, comparable to the mass contained within the present day cosmological horizon.     

f(R) Black Holes as Heat Engines

With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS f(R) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS f(R) black holes. It is found that when ΔV ? ΔP, the efficiency of isobar-isochore cycles running between high temperature T_H and low temperature T_C will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.     

Black Hole Radiation and Volume Statistical Entropy

The simplest possible equation for Hawking radiation 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 = which is similar tothe Compton wavelength relation.     

Supermassive Black Holes May Be Limited by the Holographic Bound

Supermassive Black Holes are the most entropic objects found in the universe. The Holographic Bound (HB) to the entropy is used to constrain their formation time with initial masses 10^6–8 M , as inferred from observations. We find that the entropy considerations are more limiting than causality for this direct formation. Later we analyze the possibility of SMBHs growing from seed black holes. The growth of the initial mass is studied in the case of accretion of pure radiation and quintessence fields, and we find that there is a class of models that may allow this metamorphosis. Our analysis generalizes recent work for some models of quintessence capable of producing a substantial growth in a short time, while simultaneously obeying the causal and Holographic Bound limits.     

Mining a charged black hole and the third law of black hole thermodynamics

We consider the rate at which energy can be extracted from a charged black hole using the mining process developed by Unruh and Wald. It is shown that for a Reissner-Nordström black hole the mining rate depends on the mass of the hole (unlike in the Schwarzschild case) and goes to zero asT ^BH 0. We also argue that it is impossible to achieveT _BH=0 in a finite time by mining.     

Implications of a viscosity bound on black hole accretion

Motivated by the viscosity bound in gauge/gravity duality, we consider the ratio of shear viscosity (η) to entropy density (s  ) in black hole accretion flows. We use both an ideal gas equation of state and the QCD equation of state obtained from lattice for the fluid accreting onto a Kerr black hole. The QCD equation of state is considered since the temperature of accreting matter is expected to approach ¹⁰¹² K${10}^{12}\text{K}$ in certain hot flows. We find that in both the cases η/s$\eta /s$ is small only for primordial black holes and several orders of magnitude larger than any known fluid for stellar and supermassive black holes. We show that a lower bound on the mass of primordial black holes leads to a lower bound on η/s$\eta /s$ and vice versa. Finally we speculate that the Shakura–Sunyaev viscosity parameter should decrease with increasing density and/or temperatures.     

Thermodynamics,phase transitions and Ruppeiner geometry for Einstein–dilaton–Lifshitz black holes in the presence of Maxwell and Born–Infeld electrodynamics

In this paper, we first obtain the higher-dimen-sional dilaton–Lifshitz black hole solutions in the presence of Born–Infeld (BI) electrodynamics. We find that there are two different solutions for the cases of \(z=n+1\) and \(z\ne n+1\) where z is the dynamical critical exponent and n is the number of spatial dimensions. Calculating the conserved and thermodynamical quantities, we show that the first law of thermodynamics is satisfied for both cases. Then we turn to the study of different phase transitions for our Lifshitz black holes. We start with the Hawking–Page phase transition and explore the effects of different parameters of our model on it for both linearly and BI charged cases. After that, we discuss the phase transitions inside the black holes. We present the improved Davies quantities and prove that the phase transition points shown by them are coincident with the Ruppeiner ones. We show that the zero temperature phase transitions are transitions in the radiance properties of black holes by using the Landau–Lifshitz theory of thermodynamic fluctuations. Next, we turn to the study of the Ruppeiner geometry (thermodynamic geometry) for our solutions. We investigate thermal stability, interaction type of possible black hole molecules and phase transitions of our solutions for linearly and BI charged cases separately. For the linearly charged case, we show that there are no phase transitions at finite temperature for the case \( z\ge 2\). For \(z<2\), it is found that the number of finite temperature phase transition points depends on the value of the black hole charge and there are not more than two. When we have two finite temperature phase transition points, there is no thermally stable black hole between these two points and we have discontinuous small/large black hole phase transitions. As expected, for small black holes, we observe finite magnitude for the Ruppeiner invariant, which shows the finite correlation between possible black hole molecules, while for large black holes, the correlation is very small. Finally, we study the Ruppeiner geometry and thermal stability of BI charged Lifshtiz black holes for different values of z. We observe that small black holes are thermally unstable in some situations. Also, the behavior of the correlation between possible black hole molecules for large black holes is the same as for the linearly charged case. In both the linearly and the BI charged cases, for some choices of the parameters, the black hole system behaves like a Van der Waals gas near the transition point.     

On the equilibrium of a black hole in a radiation-filled cavity

By using the horizon entropy, Hawking showed that a stable black hole will form inside a radiation cavity of finite energyE and small enough volume,VV _h(E). But two heuristic considerations seem to contradict this. First, a spontaneous fluctuation large enough to form a hole is so improbable that the chance of one developing even in 10¹⁰ years is negligible. Second, any such hole should not be in equilibrium, let alone stable; it should evaporate away again because the radiation, with typical wavelength 16 times larger than the hole, can hardly be accreted. Study of the combined accretion and evaporation resolves this difficulty. It confirms the prediction of stability and it does so without appeal to the concept of horizon entropy. A state of pure radiation is actually favored over one including a hole when 1V/V _h>0.2556, but the reverse holds for smaller cavity volumes. The horizon entropy of a black hole plays a natural role; it helps determine the system's evolution and equilibria through the condition that the total entropy of hole plus radiation always tends to increase. Using the known temperature of the hole and the fact (deduced from the accretion formula) that energy flows from the hot body to the cold, one easily inverts the reasoning to derive a unique value for the black-hole entropy.     

General tachyon absorption by Kerr-Newman black holes: Thermodynamic consequences

Following the analyses of B. Carter and J. V. Narlikar, the nature of the incomplete, spacelike trajectories about a charged, rotating black hole is described. The study concentrates on those paths which a charged tachyon would follow, incident from off the equatorial plane (on which=/2). The effect of the absorption upon the black hole is calculated and it is concluded that for _i /2 only certain charged tachyons will reduce its entropy. However, a sustained bombardment by such particles could cause the singularity to be exposed.     

Effective two-dimensional description from critical phenomena in black holes

We study the occurrence of critical phenomena in four-dimensional, rotating and charged black holes, derive the critical exponents and show that they fulfill the scaling laws. Correlation function critical exponents and Renormalization Group considerations assign an effective (spatial) dimension,d=2, to the system. The two-dimensional Gaussian approximation to critical systems is shown to reproduce all the black hole's critical exponents. Higher order corrections (which are always relevant) are discussed. Identifying the two-dimensional surface with the event horizon and noting that generalization of scaling leads to conformal invariance and then to string theory, we arrive at 't Hooft's string interpretation of black holes. From this, a model for dealing with a coarse grained black hole quantization is proposed. We also give simple arguments that lead to a rough quantization of the black hole mass in units of the Planck mass, i.e.M(1/2)M _Pll with anl positive integer and then, from this result, to the proportionality between quantum entropy and area.This essay received the fifth award from the Gravity Research Foundation, 1994—Ed.     

The total space-time of a point charge and its consequences for black holes

Singularities associated with an incomplete space-timeS are not uniquely defined until a boundaryB is attached to it. [The resulting space-time-with-boundary, ¯S S B, will be termed a total space-time (TST).] Since an incomplete spacetime is compatible with a variety of boundaries, it follows thatS does not represent a unique universe, but instead corresponds to a family of universes, one for each of its distinct TSTs. It is shown here that the boundary attached to the Reissner-Nordström space-time for a point charge is invalid forq ²<m ². When the correct boundary is used, the resulting TST is inextendible. This implies that the Graves-Brill black hole cannot be produced by gravitational collapse. The same is true of the Kruskal-Fronsdal black hole for the point mass, and for those black holes which reduce to the latter for special values of their parameters.     

Spin and mass of the supermassive black hole in the Galactic Center

A new method for exact determination of the masses and spins of black holes from the observations of quasi-periodic oscillations is discussed. The detected signal from the hot clumps in the accretion plasma must contain modulations with two characteristic frequencies: the frequency of rotation of the black hole event horizon and the frequency of the latitudinal precession of the clump’s orbit. Application of the method of two characteristic frequencies for interpretation of the observed quasi-periodic oscillations from the supermassive black hole in the Galactic center in the X-rays and in the near IR region yields the most exact, for the present, values of the mass and the spin (Kerr parameter) of the Sgr A* black hole: M = (4.2 ± 0.2) × 10⁶ M _⊙ and a = 0.65 ± 0.05. The observed quasi-periodic oscillations with a period of about 11.5 min are identified as the black hole event horizon rotation period and those with a period of about 19 min are identified as the latitudinal oscillation period of the hot spot orbits in the accretion disk.