QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Superstring theoryをめぐって(放談室)

http://cds.cern.ch/record/994225/files/0610327.pdf

Four-dimensional string compactifications with D-branes, orientifolds and fluxes

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.

The Swampland: Introduction and Review

The recently introduced swampland criterion for de Sitter [17] can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter 𝜖V. This leads us to consider the other slow roll parameter ηV more closely, and we are lead to conjecture that the bound is not necessarily on 𝜖V, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at $$ \mathcal{O} $$
 (1) in Planck units in any UV complete theory. A corollary is that 𝜖V need not necesarily be $$ \mathcal{O} $$
 (1), if $$ {\eta}_V\lesssim -\mathcal{O}(1) $$
 holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate [17], and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in N -flation.

/pdf/bounds-on-slow-roll-and-the-de-sitter-swampland-4jo0gxmrvq.pdf

Bounds on Slow Roll and the de Sitter Swampland

We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kahler modulus, T, of a Calabi-Yau 4-cycle gets charged under the anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the question of U(1)-gauge invariance of the (T-dependent) non-perturbative superpotential arises. In this case an index theorem guarantees that strings, stretching between the two stacks, yield additional charged chiral fields which also appear in the superpotential from gaugino condensation. We check that the charges work out to make this superpotential gauge invariant, and we argue that the mechanism survives the inclusion of higher curvature corrections to the D7-brane action.

Gaugino Condensates and D-terms from D7-branes

We study cosmological properties of type IIA compactifications on orientifolds of SU(3)-structure manifolds with non-vanishing geometric flux. These compactifications give rise to effective 4D = 1 supergravity theories that do not fall under some recently-proven no-go theorems against de Sitter vacua and slow-roll inflation. Focusing on a well-understood class of models based on coset spaces, however, we can use a refined no-go theorem that rules out de Sitter vacua and slow-roll inflation in all but one case. The refined no-go theorem uses the dilaton and a specific linear combination of the Kahler moduli, which is different from the overall volume modulus. It puts a lower bound on the first slow-roll parameter: ≥ 2. The only case not ruled out is the manifold SU(2) × SU(2), for which we indeed find critical points with numerically zero. However, all the points we could find have a tachyon corresponding to an eta-parameter η −2.4.

On the cosmology of type IIA compactifications on SU(3)-structure manifolds

https://cds.cern.ch/record/410725/files/9912027.pdf

The gauging of five-dimensional, N=2 Maxwell–Einstein supergravity theories coupled to tensor multiplets☆

We investigate whether vacuum solutions in flux compactifications that are obtained with smeared sources (orientifolds or D-branes) still survive when the sources are localised. This seems to rely on whether the solutions are BPS or not. First we consider two sets of BPS solutions that both relate to the GKP solution through T-dualities: (p + 1)-dimensional solutions from spacetime-filling Op-planes with a conformally Ricci-flat internal space, and p-dimensional solutions with Op-planes that wrap a 1-cycle inside an everywhere negatively curved twisted torus. The relation between the solution with smeared orientifolds and the localised version is worked out in detail. We then demonstrate that a class of non-BPS AdS4 solutions that exist for IASD fluxes and with smeared D3branes (or analogously for ISD fluxes with anti-D3-branes) does not survive the localisation of the (anti) D3-branes. This casts doubts on the stringy consistency of non-BPS solutions that are obtained in the limit of smeared sources.

/pdf/smeared-versus-localised-sources-in-flux-compactifications-52rnmei80x.pdf

Smeared versus localised sources in flux compactifications

We consider string theory compactifications of the form AdS4 x M6 with orientifold six-planes, where M6 is a six-dimensional compact space that is either a nilmanifold or a coset. For all known solutions of this type we obtain the four-dimensional N=1 low energy effective theory by computing the superpotential, the Kaehler potential and the mass spectrum for the light moduli. For the nilmanifold examples we perform a cross-check on the result for the mass spectrum by calculating it alternatively from a direct Kaluza-Klein reduction and find perfect agreement. We show that in all but one of the coset models all moduli are stabilized at the classical level. As an application we show that all but one of the coset models can potentially be used to bypass a recent no-go theorem against inflation in type IIA theory.

Marco Zagermann

Papers

Gaugino Condensates and D-terms from D7-branes

On the cosmology of type IIA compactifications on SU(3)-structure manifolds

The gauging of five-dimensional, N=2 Maxwell–Einstein supergravity theories coupled to tensor multiplets☆

Smeared versus localised sources in flux compactifications

The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets