Pair Production Of Black Holes Research Articles

Black hole pair production on cosmic strings in the presence of a background magnetic field

We investigate the pair creation of magnetically charged black holes on a cosmic string in the presence of a background magnetic field. The string may either break or fray to produce a pair of accelerating black holes described by Ernst metric. By using the instanton action we obtain the rate of such production. For large values of background magnetic field the production of large black holes is probable. Comparing our results with the case of black hole pair creation in magnetic field with no string, we show that fraying/breaking of the cosmic string can substantially enhance the production rate. We also obtain the result of monopole-antimonopole pair production on cosmic string in an external magnetic field, using the WKB approximation and compare it with the black hole results. We also provide a heuristic study of black hole pair creation on cosmic string in the presence of a magnetic field in the de Sitter background, although the analog of Ernst metric with a cosmological constant is lacking. Like a cosmic string and/or a background magnetic field, a positive cosmological constant increases the production rate.

Cosmological production of noncommutative black holes

We investigate the pair creation of noncommutative black holes in a background with a positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild--de Sitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive-mass spacetimes admit one cosmological horizon and two, one, or no black hole horizons, while negative-mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the nonsingular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the de Sitter background is quantum mechanically stable according to experience. However, positive-mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the Universe, Planck size black holes production would have been largely disfavored. We also find a potential instability for production of negative-mass solitons.

The instability of vacua in Gauss-Bonnet gravity

Owing to the quadratic nature of the theory, Einstein-Gauss-Bonnet gravity generically permits two distinct vacuum solutions. One solution (the "Einstein" vacuum) has a well defined limit as the Gauss-Bonnet coupling goes to zero, whereas the other solution (the "stringy" vacuum) does not. There has been some debate regarding the stability of these vacua, most recently from Deser and Tekin who have argued that the corresponding black hole solutions have positive mass and as such both vacua are stable. Whilst the statement about the mass is correct, we argue that the stringy vacuum is still perturbatively unstable. Simply put, the stringy vacuum suffers from a ghost-like instability that is not excited by the spherically symmetric black hole, but would be excited by any source likely to emit gravitational waves, such as a binary system. This result is reliable except in the strongly coupled regime close to the Chern-Simons limit, when the two vacua are almost degenerate. In this regime, we study instanton transitions between branches via bubble nucleation, and calculate the nucleation probability. This demonstrates that there is large mixing between the vacua, so that neither of them can accurately describe the true quantum vacuum. We also present a new gravitational instanton describing black hole pair production in de Sitter space on the Einstein branch, which is preferred to the usual Nariai instantons and is not present in pure Einstein gravity.

The symplictic vacuum, exotic quasi particles and gravitational instanton

Abstract Various experimental studies conducted in the eighties indicated the existence of certain anomalous positron production which could not be accounted for within the generally accepted framework of the standard model. Subsequently several theories were advanced by different investigators notably in Darmstadt, Frankfurt and Cairo to explain the new phenomenon and a neutral meson with a mass equal to 1.8 MeV was predicted by a German group around Greiner and his associates. Concurrently to this development, and seemingly independent of it, some fundamental work by `t Hooft in Utrecht and subsequent studies by Peccei and Quinn in Stanford led Weinberg in Austin to postulate the existence of a new particle which was christened by Wilczek and him the axion. We note that the connection between the Darmstadt–Frankfurt–Cairo–Bristol neutral boson and the axion was not immediately recognized although even a fleeting glance would have revealed the similarity, particularly because the neutral boson was estimated to have a mass of about m =1.8 MeV while the mass of the axion was also conjectured to be m a =1.8 MeV. The present work draws attention to the possibility of relating the said anomalous positron production to certain types of topological defects in the so-called symplictic vacuum of E Infinity theory. These defects, which could be interpreted physically as exotic quasi particles or mini black holes pair production, are created via the instanton mechanism rather than the usual classical gravitational collapse. In turn these “mini” black holes and or exotic particles are perceived experimentally, as an increased rate in the positron production which is not entirely surprising when we note that electrons may be modelled using some forms of mini black hole. The same processes may be seen in a different way as a continuous symmetry breaking of the symmetry on average of the ramified hyperbolic “tiling” geometry of the VAK of the E Infinity vacuum. That means the vacuum fluctuation is the “mechanism” of the symmetry breaking of the VAK. Since symmetry breaking is always accompanied physically by the appearance of a new particle, this VAK fluctuation produces a large family of such symmetry breaking particles of which the axion of the P–Q symmetry breaking is but one of many others. In this manner, the excess production in positrons may be attributed to the disintegration of particles such as the axion which in turn are a consequence of the continuous disintegration and reformation of the symplictic E Infinity VAK via the continuous symmetry breaking vacuum fluctuation. Of course, it is a well-known fact that in the classical limit the rate of production of the aforementioned black holes equals that of ordinary quantum field theory in the sense of Schwinger. However, from a number theoretical view point, E Infinity theory is effectively an extension of quantum field theory into the irrational domain and prior to such limit there is the possibility of a considerably large black hole pair production which could be observed and may be interpreted as anomalous positron production in an experiment using a stack of nuclear emulsions exposed for instance to a beam of 12 C or 22 Ne ions as done by El-Nadi et al. at Cairo University rather than using modern electronic detectors joined to a huge heavy ion accelerator. The paper concludes with observing that the complex symplictic modular group could be used to unify quantum mechanics and general relativity.

Topology change and causal continuity

The result that, for a scalar quantum field propagating on a ``trousers'' topology in $1+1$ dimensions, the crotch singularity is a source for an infinite burst of energy has been used to argue against the occurrence of topology change in quantum gravity. We draw attention to a conjecture due to Sorkin that it may be the particular type of topology change involved in the trousers transition that is problematic and that other topology changes may not cause the same difficulties. The conjecture links the singular behavior to the existence of ``causal discontinuities'' in the spacetime and relies on a classification of topology changes using Morse theory. We investigate various topology changing transitions, including the pair production of black holes and of topological geons, in the light of these ideas.

Charged Gravitational Instantons in Five-Dimensional Einstein-Gauss-Bonnet-Maxwell Theory

We study a solution of the Einstein-Gauus-Bonnet theory in 5 dimensions coupled to a Maxwell field, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.

SPACE–TIME FOAM, CASIMIR ENERGY AND BLACK HOLE PAIR CREATION

We conjecture that the neutral black hole pair production is related to the vacuum fluctuation of pure gravity via the Casimir-like energy. Implications on the foam-like structure of space–time are discussed.

Selection Rules for Splitting Strings

It has been pointed out that Nielsen-Olesen vortices may be able to decay by pair production of black holes. We show that when the Abelian-Higgs model is embedded in a larger theory, the additional fields may lead to selection rules for this process---even in the absence of fermions---due to the failure of a charge quantization condition. We show that when there is topology change, the criterion based on the charge quantization condition supplements the usual criterion based on ${\ensuremath{\pi}}_{0}(H)$. In particular, we find that unless $2{sin}^{2}{\ensuremath{\theta}}_{W}$ is a rational number, the thermal splitting of electroweak $Z$ strings by magnetically neutral black holes is impossible, even though ${\ensuremath{\pi}}_{0}(H)$ is trivial.

In defense of the “tunneling” wave function of the universe

The tunneling approach to the wave function of the universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the `inverse' of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophy as Bousso and Hawking's argument would suggest.

Smooth metrics for snapping strings.

We construct two possible metrics for abelian Higgs vortices with ends on black holes. We show how the detail of the vortex fields smooths out the nodal singularities which exist in the idealized metrics. A corollary is that apparently topologically stable strings might be able to split by black hole pair production. We estimate the rate per unit length by reference to related Ernst and C-metric instantons, concluding that it is completely negligible for GUT-scale strings. The estimated rate for macroscopic superstrings is much higher, although still extremely small, unless there is an early phase of strong coupling.

Breaking cosmic strings without monopoles.

It is shown that topologically stable cosmic strings can, in fact, appear to end or to break, even in theories without monopoles. This can occur whenever the spatial topology of the universe is nontrivial. For the case of Abelian-Higgs strings, we describe the gauge and scalar field configurations necessary for a string to end on a black hole. We give a lower bound for the rate at which a cosmic string will break via black hole pair production, using an instanton calculation based on the Euclidean C-metric.

Toward one-loop tunneling rates of near-extremal magnetic black hole pair production.

Pair-production of magnetic Reissner-Nordstr\"{o}m black holes (of charges $\pm q$) was recently studied in the leading WKB approximation. Here, we consider generic quantum fluctuations in the corresponding instanton geometry given by the Euclidean Ernst metric, in order to simulate the behaviour of the one-loop tunneling rate. A detailed study of the Ernst metric suggests that for sufficiently weak field $B$, the problem can be reduced to that of quantum fluctuations around a single near-extremal Euclidean black hole in thermal equilibrium with a heat bath of finite size. After appropriate renormalization procedures, typical one-loop contributions to the WKB exponent are shown to be inversely proportional to $B$, as $B\rightarrow 0$, indicating that the leading Schwinger term is corrected by a small fraction $\sim \hbar /q^2$. We demonstrate that this correction to the Schwinger term is actually due to a semiclassical shift of the black hole mass-to-charge ratio that persists even in the extremal limit. Finally we discuss a few loose ends.

Pair production of black holes in a U(1)

Charged dilaton black hole solutions have recently been found for an action with two $U(1)$ gauge fields and a dilaton field. I investigate new exact solutions of this theory analogous to the C-metric and Ernst solutions of classical general relativity. The parameters in the latter solution may be restricted so that it has a smooth Euclidean section with topology $S^2 \times S^2 - \{pt\}$, which gives an instanton describing pair production of the charged dilaton black holes. These instantons generalise those found recently by Dowker {\it et al}.

Entropy in black hole pair production.

Pair production of Reissner-Nordstrom black holes in a magnetic field can be described by a euclidean instanton. It is shown that the instanton amplitude contains an explicit factor of $e^{A/4}$, where $A$ is the area of the event horizon. This is consistent with the hypothesis that $e^{A/4}$ measures the number of black hole states.