Virtual Black Holes Research Articles

Black hole entropy: a spacetime foam approach

I introduce the spacetime foam structure by briefly reviewing the ideas of Wheeler, topological fluctuations and the possibility of virtual black holes. The contribution of Jacobson (the equation of state of the foam) is recalled. In the second part, I introduce a model of spacetime foam at the surface of the event horizon of a black hole. I apply these ideas to the calculus of the number of states of a black hole, of its entropy and of other thermodynamical properties. A formula for the number of micro-holes on the surface of the event horizon is derived. Subsequently, I extend the thermodynamical properties of the event horizon to thermodynamical properties of the space. Here I face the problem of the maximum entropy contained in a space region of a given volume. Finally, on the basis of the results obtained previously, I briefly treat the possibility of micro-black-hole creation by the Unruh effect.

Virtual black holes.

One would expect spacetime to have a foam-like structure on the Planck scale with a very high topology. If spacetime is simply connected (which is assumed in this paper), the non-trivial homology occurs in dimension two, and spacetime can be regarded as being essentially the topological sum of $S^2\times S^2$ and $K3$ bubbles. Comparison with the instantons for pair creation of black holes shows that the $S^2\times S^2$ bubbles can be interpreted as closed loops of virtual black holes. It is shown that scattering in such topological fluctuations leads to loss of quantum coherence, or in other words, to a superscattering matrix $\$ $ that does not factorise into an $S$ matrix and its adjoint. This loss of quantum coherence is very small at low energies for everything except scalar fields, leading to the prediction that we may never observe the Higgs particle. Another possible observational consequence may be that the $\theta $ angle of QCD is zero without having to invoke the problematical existence of a light axion. The picture of virtual black holes given here also suggests that macroscopic black holes will evaporate down to the Planck size and then disappear in the sea of virtual black holes.

Planckian-energy scattering, colliding plane gravitational waves and black hole creation

In a series of papers Amati, Ciafaloni and Veneziano and 't Hooft conjectured that black holes occur in the collision of two light particles at Planckian energies. In this paper we discuss a possible scenario for such a process by using the Chandrasekhar-Ferrari-Xanthopoulos duality between the Kerr black hole solution and colliding plane gravitational waves. We clarify issues arising in the definition of transition amplitude from a quantum state containing only usual matter without black holes to a state containing black holes. Collision of two plane gravitational waves producing a space-time region that is locally isometric to an interior of black hole solution is considered. The phase of the transition amplitude from plane waves to white and black holes is calculated by using the Fabbrichesi, Pettorino, Veneziano and Vilkovisky approach. An alternative extension beyond the horizon in which the space-time again splits into two separating gravitational waves is also discussed. Such a process is interpreted as the scattering of plane gravitational waves through the creation of virtual black and white holes.

The string universe. High Tc superconductor or quantum Hall conductor?

Our answer is the latter. Space-time singularities, including the initial one, are described by world-sheet topological abelian gauge theories with a Chern-Simons term. Their effective N = 2 supersymmetry provides an initial fixed point where the Bogomolny bound is saturated on the world-sheet, corresponding to an extreme Reissner-Nordstrom solution in space-time. Away from the singularity the gauge theory has world-sheet matter fields, bosons and fermions, associated with the generation of target space-time. Because the fermions are complex (cf. the quantum Hall effect) rather than real (cf. high- T c superconductors) the energetically-preferred vacuum is not parity or time-reversal invariant, and the associated renormalization group flow explains the cosmological arrow of time, as well as the decay of real or virtual black holes, with a monotonic increase in entropy.

T-symmetry violation as a result of virtual gravitational interaction

T-symmetry violation observed in the weak K-decays is interpreted as a result of an influence of the virtual black holes, inside which the space and time coordinates change places. When this decay happens inside the black hole theP-symmetry violation inherent to (V−A)-type of weak Lagrangian is accepted by the observer asT-symmetry violation.CP-symmetry conservation corresponds toCT-symmetry conservation.

"It's Money That Matters": Campaign Expenditures and State Legislative Primaries

This paper develops and tests an empirical model of state legislative primary outcomes that focuses on campaign expenditures. The analysis of primary elections indicates that candidates in six of the seven states analyzed are able to increase their share of the primary vote by increasing their level of campaign spending. By increasing their own level of campaign spending, candidates are also able to affect negatively the opponent's share of the primary vote. As in state legislative general elections, incumbency status in state legislative primaries affords candidates a clear advantage. If the general elections to state legislatures are still largely a mystery to political scientists, the primary elections are a virtual black hole. Direct primaries were instituted to make elections more democratic, and they have existed for most of this century. Yet we know little about how they operate at the state legislative level. How competitive are state legislative primaries? How democratic are they? What factors shape the outcome of primary elections? How important is incumbency? What role does money play in primary elections? This paper looks at these questions by developing and testing a model of state legislative primary elections that focuses on campaign expenditures. The role of money in state legislative primary elections has important implications for how those elections are viewed. The direct primary was created to take control of nominations away from the party elite. Because of the power of incumbency, however, direct primaries may merely have shifted control between elites-from party organization elites to party-in-government elites (Sorauf and Beck 1988). If money is also an important factor in shaping the outcome of legislative primaries, then we must question the extent to which primaries have made state legislative elections more democratic.

Is it necessary to abandon the ? function in quantum gravitation?

Hawking's conclusion that a pure state of an elementary particle converts into a mixed state as a result of a coupling with real and virtual black holes and that it is necessary to abandon the description of elementary particles by means of aψ function in quantum gravitation is subjected to a critical analysis. An examination of a specific example — the motion of particles of nonzero mass and of photons in the field of a charged black hole — does not support Hawking's conclusion. Ellis's estimates of a lower (energy) limit on the applicability of quantum mechanics has been improved by 40 orders of magnitude.

Quantum correlations, non-locality and the EPR paradox

An experiment measuring the relative polarisations of paired 511 keV photons from s-state e+e- annihilation has shown that within the errors of measurement quantum correlations do not fall off with increasing detector-detector separation up to a separation of 24 m. An important aspect of the measurement has been that the resolving time of the electronic equipment could be made as small as 100 ps. This gave the largest spacelike geometry of any such measurement so far. An attempt has been made to explain any possible fall-off of the correlation within the error of the measurement in terms of scattering produced by hypothetical virtual quantum black holes.

Renormalization of general relativity on a background of spacetime foam

We show that a distribution of virtual black holes in the vacuum at shorter than Planck scales can have a profound effect on the perturbative high-energy behavior of a quantum field theory. This follows if we make the assumption that only perturbations which vanish inside the apparent horizons of virtual black holes can make a coherent contribution to scattering amplitudes. As a result there is a cutoff-dependent contribution to the density of states which comes from the scale dependence of the density of virtual black holes in the vacuum. This results in a modification in the divergence-structure of perturbation theory on a background of spacetime foam. The divergence structure then depends on how fast the volume of a typical spacelike surface fills up with virtual black holes as the cutoff scale is decreased to zero. If the distribution of virtual black holes is scale invariant then the result is to decrease the spectral dimension of spacetime to a nonintegral value less than four. In this case general relativity becomes renormalizable in a 1 N expansion without additional dimension-four counterterms. This case can also be understood in terms of recent work on density of states functions on fractals, because the set of points which are not contained within a scale-invariant distribution of black holes will be fractal. If the distribution of virtual black holes fills up faster, asymptotically, than the scale-invariant distribution, all sums over virtual states are cut off by exponential factors and are finite. In both cases, as the dynamics is generated by the hamiltonian of general relativity, the energy is bounded from below and the theory will be stable.

Space-time foam as the universal regulator

A distribution of virtual black holes in the vacuum will induce modifications in the density of states for small perturbations of gravitational and matter fields. If the virtual black holes fill the volume of a typical spacelike surface then perturbation theory becomes more convergent and may even be finite, depending on how fast the number of virtual black holes increases as their size decreases. For distributions of virtual black holes which are scale invariant the effective dimension of space-time is lowered to a noninteger value less than 4, leading to an interpretation in terms of fractal geometry. In this case general relativity is renormalizable in the 1/N expansion without higher derivative terms. As the Hamiltonian is not modified the theory is stable.

Quantum gravity and path integrals

The path-integral method seems to be the most suitable for the quantization of gravity. One would expect the dominant contribution to the path integral to come from metrics which are near background metrics that are solutions of classical Einstein equations. The action of these background metrics gives rise to a new phenomenon in field theory, intrinsic quantum entropy. This is shown to be related to the scaling behavior of the gravitational action and to the topology of the gravitational field. The quadratic terms in the Taylor series of the action about the background metrics give the one-loop corrections. In a supersymmetric theory the quartic and quadratic but not the so-called logarithmic divergences cancel to give a one-loop term that is finite without regularization. From the one-loop term one can obtain the effective energy-momentum tensor on the background metric. In the case of an evaporating black hole, the energy-momentum tensor will be regular on the future horizon. The usual perturbation expansion breaks down for quantum gravity because the higher (interaction) terms in the Taylor series are not bounded by the quadratic (free) ones. To overcome this I suggest that one might replace the path integrals over the terms in the Taylor series by a discrete sum of the exponentials of the actions of all complex solutions of the Einstein equations, each solution being weighted by its one-loop term. This approach seems to give a picture of the gravitational vacuum as a sea of virtual Planck-mass black holes.