Cosmological Black Holes Research Articles

Einstein gravity with Gauss-Bonnet entropic corrections

A toy model of Einstein gravity with a Gauss-Bonnet classically ``entropic'' term mimicking a quantum correction is considered. The static black hole solution due to Tomozawa is found and generalized with the inclusion of nontrivial horizon topology, and its entropy is evaluated, deriving the first law by equations of motion. As a result the Bekenstein-Hawking area law turns out to be corrected by a logarithmic area term. A Misner-Sharp expression for the mass of a black hole is found. Within a Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological setting, the model is used in order to derive modified Friedmann equations. Such new equations are shown to reproduce the first law with the same formal entropy and quasilocal energy of the static case, but here within a Friedmann-Lema\^{\i}tre-Robertson-Walker space-time interpreted as a dynamical cosmological black hole. A detailed analysis of cosmological solutions is presented, and it is shown that the presence of the correction term provides regular solutions and interesting phases of acceleration and deceleration, as well as, with negligible matter, exact de Sitter solutions.

Bondi accretion onto cosmological black holes

In this paper we investigate a steady accretion within the Einstein-Straus vacuole, in the presence of the cosmological constant. The dark energy damps the mass accretion rate and --- above certain limit --- completely stops the steady accretion onto black holes, which in particular is prohibited in the inflation era and after (roughly) $10^{12}$ years from Big Bang (assuming the presently known value of the cosmological constant). Steady accretion would not exist in the late phases of the Penrose's scenario - known as the Weyl curvature hypothesis - of the evolution of the Universe.

Vaidya Solution in Non-Stationary de Sitter Background: Hawking’s Temperature

In this paper we propose a class of non-stationary solutions of Einstein’s field equations describing an embedded Vaidya-de Sitter solution with a cosmological variable function Λ(u). Vaidya-de Sitter solution is interpreted as the radiating Vaidya black hole which is embedded into the non-stationary de Sitter space with variable Λ(u). The energymomentum tensor of the Vaidya-de Sitter black hole may be expressed as the sum of the energy-momentum tensor of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We also find that the equation of state parameter w= p/ρ = -1 of the non-stationary de Sitter solution holds true in the embedded Vaidya-de Sitter solution. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is type D in the Petrov classification of space-times. The surface gravity, temperature and entropy of the space-time on the cosmological black hole horizon are discussed.

THE SPHERICAL SYMMETRY BLACK HOLE COLLAPSE IN EXPANDING UNIVERSE

The spherical symmetry black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions whether dynamical horizon forms for these cosmological black holes. We also discuss about the cosmological constant effect on these black hole and the redshift of the light which comes from the marginally trapped tube surface.

Do we know the mass of a black hole? Mass of some cosmological black hole models

Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or different they are. It has been shown that the mass within the horizon follows the familiar Brown-York behavior. It increases, however, outside the horizon again after a short decrease, in contrast to the Schwarzschild case. Further away, near the void, outside the collapsed region, and where the density reaches the background minimum, all the mass definitions roughly coincide. They differ, however, substantially far from it. Generically, we are faced with three different Brown-York mass maxima: near the horizon, around the void between the overdensity region and the background, and another at cosmological distances corresponding to the cosmological horizon. While the latter two maxima are always present, the horizon mass maxima is absent before the onset of the central singularity.

Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant: 8πGTμν = Λδμν as r → 0, 8πGTμν = λδμν as r → ∞ with λ < Λ. It represents an anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. In the range of the mass parameter Mcr1 ≤ M ≤ Mcr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon rc, a black hole horizon rb < rc, and an internal horizon ra < rb, which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. We present the basicfeatures of space-time geometry and the detailed analysis of thermodynamics of horizons using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. We find that in a certain range of parameters M and q =√Λ/λ there exist a global temperature for an observer in the R-region between the black hole horizon rb and cosmological horizon rc. We show that a second-order phase transition occurs in the course of evaporation, where a specific heat is broken and a temperature achieves its maximal value. Thermodynamical preference for a final point of evaporation is thermodynamically stable double-horizon (ra = rb) remnant with the positive specific heat and zero temperature.

Horizons, singularities and causal structure of the generalized McVittie space-times

The generalized McVittie space-times, which are the natural extensions of a class of metrics introduced by McVittie in 1933 to model the space-time outside a spherical object embedded in an expanding universe, have recently been proposed by Faraoni and Jacques as candidate space-times for cosmological black holes. In this paper I analyze the singularities and horizon structure of the generalized McVittie space-times, and show that any expanding space-time of this type that satisfies the null energy condition and develops apparent horizons must asymptote to a standard McVittie solution. Furthermore, if the scale factor is asymptotically exponential then the space-time is future-incomplete and can be joined smoothly to an eternally-inflating Kottler (Schwarzschild-de Sitter) solution. I argue that no generalized McVittie space-time, apart from the Schwarzschild solution, can adequately represent a black hole, because all singular points are surrounded by anti-trapped regions rather than trapped regions.

Thermodynamics of regular cosmological black holes with de Sitter interior

We address the question of thermodynamics of a regular spherically symmetric cosmological black hole. The spacetime is asymptotically de Sitter as r → 0 and as r →∞ . A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of the cosmological constant and corresponds to an anisotropic vacuum fluid defined by the symmetry of its stress-energy tensor, invariance under radial boosts. In the range of the mass parameter Mcrit1 ≤ M ≤ Mcrit2 it describes a regular cosmological black hole.

Implications of a Multiverse String Cosmology

Vafa’s (11+1) F theory is extended by means of Bars’ 2T holographic theory to yield a 14d Multiverse theory that permeates the brane of a 12d Universe in which both the Universe and the Multiverse have (3+1) spacetimes. Given the 2d toroidal compactification of F theory, we conjecture that the Multiverse has a 4d Cartesian compactification that is filled with 3D+T spacetime via the standard 6d elliptic Calabi-Yau compactification, as in both M and F theory. The result is exemplified using supermassive black hole cosmology. Implications of the existence of a Multiverse and at the Planck scale, two Compact Manifolds, one for the Multiverse and one for our Universe, are explored. In particular, the Multiverse is proposed to be the pre-spacetime for which gravity is nonlocal and instantaneous, and which allows quantum entanglement to achieve unity of mind.

Regular black hole remnants in de Sitter space

We address the question of thermodynamical evolution of regular spherically symmetric cosmological black holes with de Sitter center. Space–time is asymptotically de Sitter as r→0 and as r→∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress–energy tensor. In the range of masses Mcr1⩽M⩽Mcr2 it describes a regular cosmological black hole with three horizons, an internal horizon ra, a black hole horizon rb>ra, and a cosmological horizon rc>rb. Thermodynamical preference for a final product of evaporation is a double-horizon (ra=rb) black hole remnant with the positive specific heat.

Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class

This is the second of two papers in which we study the asymptotics of the generalized Nariai solutions and its relation to the cosmic no-hair conjecture. In the first paper, the author suggested that, according to the cosmic no-hair conjecture, the Nariai solutions are non-generic among general solutions of Einstein's field equations in vacuum with a positive cosmological constant. We explained that this is true within the class of spatially homogeneous solutions. In this current paper, we continue these investigations within the spatially inhomogeneous Gowdy case. On the one hand, we are motivated to understand the fundamental question of cosmic no-hair and its dynamical realization in more general classes than the spatially homogeneous case. On the other hand, the results of the first paper suggest that the instability of the Nariai solutions can be exploited to construct and analyze physically interesting cosmological black hole solutions in the Gowdy class, consistent with certain claims by Bousso in the spherically symmetric case. However, in contrast to that, we find that it is not possible to construct cosmological black hole solutions by means of small Gowdy symmetric perturbations of the Nariai solutions and that the dynamics shows a certain new critical behavior. For our investigations, we use the numerical techniques based on spectral methods which we introduced in a previous publication.

Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations

This is the first of two papers in which we study the asymptotics of the generalized Nariai solutions and its relation to the cosmic no-hair conjecture. According to the cosmic no-hair conjecture, generic expanding solutions of Einstein's field equations in vacuum with a positive cosmological constant isotropize and approach the de-Sitter solution asymptotically. The family of solutions which we introduce as ‘generalized Nariai solutions’, however, shows quite unusual asymptotics and hence should be non-generic in some sense. In this paper, we list basic facts for the Nariai solutions and characterize their asymptotic behavior geometrically. One particular result is a rigorous proof of the fact that the Nariai solutions do not possess smooth conformal boundaries. We proceed by explaining the non-genericity within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild–de-Sitter solutions. A motivation for our work here is to prepare the second paper devoted to the study of the instability of the Nariai solutions for Gowdy symmetry. We will be particularly interested in the construction of new and in principle arbitrarily complicated cosmological black hole solutions.

Analysis of the Sultana-Dyer cosmological black hole solution of the Einstein equations

The Sultana-Dyer solution of general relativity representing a black hole embedded in a special cosmological background is analyzed. We find an expanding (weak) spacetime singularity instead of the reported conformal Killing horizon, which is covered by an expanding black hole apparent horizon (internal to a cosmological apparent horizon) for most of the history of the Universe. This singularity was naked early on. The global structure of the solution is studied as well.

Cosmological solutions from fakeN= 2 EYM supergravity

We characterise the (fake) supersymmetric solutions of Wick-rotated N=2 d=4 gauged supergravity coupled to non-Abelian vector multiplets. In the time-like case we obtain generalisations of Kastor & Traschen's cosmological black holes: they have a specific time-dependence and the base-space must be 3-dimensional hyperCR/Gauduchon-Tod space. In the null-case, we find that the metric has a holonomy contained in Sim(2), give a general characterisation of the solutions, and give some examples. Finally, we point out that in some cases the solutions we found are non-BPS solutions to N=2 d=4 supergravity coupled to vector multiplets.

Artificial contradiction between cosmology and particle physics: the Λ problem

It is shown that the usual choice of units obtained by taking G=c=ℏ=1, giving the Planck’s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ℏ. We note that the choice of ℏ=1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ℏ≈1/10122, while the choice of ℏ=1 corresponds to the cosmological scale. This is due to the scale factor of 1061 that converts the Planck scale to the cosmological scale. By choosing the ratio G/c 3=constant=1, which includes the choice G=c=1, and the momentum conservation mc=constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c 2=r g , the gravitational radius of m, is constant. For a quantum black hole we prove that ℏ≈r 2 ≈(mc)2. We also prove that the product Λℏ is a general constant of order one, for any scale. The cosmological scale implies Λ≈ℏ≈1, while the Planck scale gives Λ≈1/ℏ≈10122. This explains the Λ problem. We get two scales: the cosmological quantum black hole (QBH), size ∼1028 cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size ∼10−13 cm, as well as the Planck’ scale, size ∼10−33 cm.

Zel’dovich Λ and Weinberg’s relation: an explanation for the cosmological coincidences

In 1937 Dirac proposed the large number hypothesis (LNH). The idea was to explain that these numbers were large because the Universe is old. A time variation of certain constants was assumed. So far, no experimental evidence has significantly supported this time variation. Here we present a simplified cosmological model. We propose a new cosmological system of units, including a cosmological Planck constant that absorbs the well known large number 10120. With this new Planck constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zeldovich formula, for the cosmological constant, is equivalent to the Weinberg relation. The immediate conclusion is that the speed of light c must be proportional to the Hubble parameter H, and therefore decrease with time. We find that the gravitational radius of the Universe and its size are one and the same constant (Mach principle). The usual cosmological omega parameters for mass, lambda and curvature turn out to be all constants of order one. The anthropic principle is not necessary in this theory. It is shown that a factor of 1061converts in this theory a Planck fluctuation (a quantum black hole) into a cosmological quantum black hole: the Universe today. General relativity and quantum mechanics give the same local solution of an expanding Universe with the law const. t. This constant is just the speed of light today. Then the Hubble parameter is exactly H = 1/t.

Cosmological Black Hole Spin Evolution by Mergers and Accretion

Using recent results from numerical relativity simulations of black hole mergers, we revisit previous studies of cosmological black hole spin evolution. We show that mergers are very unlikely to yield large spins, unless alignment of the spins of the merging holes with the orbital angular momentum is very efficient. We analyze the spin evolution in three specific scenarios: (1) spin evolves only through mergers, (2) spin evolves through mergers and prolonged accretion episodes, and (3) spin evolves through mergers and short-lived (chaotic) accretion episodes. We study how different diagnostics can distinguish between these evolutionary scenarios, assessing the discriminating power of gravitational-wave measurements and X-ray spectroscopy. Gravitational radiation can produce three different types of spin measurements, yielding, respectively, the spins of the two black holes in a binary inspiral prior to merger, the spin of the merger remnant (as encoded in the ring-down waves), and the spin of "single" black holes during the extreme mass-ratio inspiral (EMRI) of compact objects. The latter spin population is also accessible to iron-line measurements. We compute and compare the spin distributions relevant for these different observations. If iron-line measurements and gravitational-wave observations of EMRIs only yield dimensionless spins j = J/M2 > 0.9, then prolonged accretion should be responsible for spin-up, and chaotic accretion scenarios would be very unlikely. If only a fraction of the whole population of low-redshift black holes spins rapidly, spin-alignment during binary mergers (rather than prolonged accretion) could be responsible for spin-ups.

Nonisolated dynamic black holes and white holes

Modifying the Kerr-Schild transformation used to generate black and white hole spacetimes, new dynamic black and white holes are obtained using a time-dependent Kerr-Schild scalar field. Physical solutions are found for black holes that shrink with time and for white holes that expand with time. The black hole spacetimes are physical only in the vicinity of the black hole, with the physical region increasing in radius with time. The white hole spacetimes are physical throughout. Unlike the standard Schwarzschild solution the singularities are nonisolated, since the time dependence introduces a mass-energy distribution. The surfaces in the metrics where g{sub tt}=g{sup rr}=0 are dynamic, moving inward with time for the black holes and outward for the white holes, which leads to a question of whether these spacetimes truly have event horizons--a problem shared with Vaidya's cosmological black hole spacetimes. By finding a surface that shrinks or expands at the same rate as the null geodesics move, and within which null geodesics move inward or outward faster than the surfaces shrink or expand, respectively, it is verified that these do in fact behave like black and white holes.

Jet-enhanced accretion growth of supermassive black holes

We investigate the effect of a disc-driven jet on the accretion growth of cosmological supermassive black holes (SMBHs). The presence of a jet enhances the mass growth rate because for a given luminosity, the mass accretion rate, is higher (or equivalently, the radiative efficiency e_r is lower for a fixed mass accretion rate) than that predicted by standard accretion disc theory. As jets carry away very little of the accreting matter, a larger proportion of the rest mass can reach the black hole during episodes of jet activity. We show quantitatively that the conditions required to grow a rapidly spinning black hole to a mass ~ 10^9 solar masses by redshift z ~ 6, whilst satisfying the observational constraint e_r > 0.1, are considerably less restrictive for jet-enhanced disc accretion than for standard disc accretion, which requires implausibly high super-Eddington accretion rates. Furthermore, jet-enhanced accretion growth offers a viable explanation for the observed correlation between black hole mass and radio-loudness of quasars.

Hawking temperature of expanding cosmological black holes

In the context of a debate on the correct expression of the Hawking temperature of a cosmological black hole, we show that the correct expression in terms of the Hawking-Hayward quasilocal energy ${m}_{H}$ of the hole is $T=(8\ensuremath{\pi}{m}_{H}(t){)}^{\ensuremath{-}1}$. This expression holds for comoving black holes and agrees with a recent proposal by Saida, Harada, and Maeda.