There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

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Inflationary helical magnetic fields with a sawtooth coupling

We consider a new class of 5-dimensional dilatonic actions which are invariant under T-duality transformations along three compact coordinates, provided that an appropriate potential is chosen. We show that the invariance remains when we add a boundary term corresponding to a moving 3-brane, and we study the effects of the T-duality symmetry on the brane cosmological equations. We find that T-duality transformations in the bulk induce scale factor duality on the brane, together with a change of sign of the pressure of the brane cosmological matter. However, in a remarkable analogy with the Pre-Big Bang scenario, the cosmological equations are unchanged. Finally, we propose a model where the dual phases are connected through a scattering of the brane induced by an effective potential. We show how this model can realise a smooth, non-singular transition between a pre-Big Bang superinflationary Universe and a post-Big Bang accelerating Universe.

Pre-Big Bang Scenario on Self-T-Dual Bouncing Branes

We analytically derive a class of non-singular, static and spherically symmetric topological black hole metrics inF(R)-gravity. These have not a de Sitter core at their centre, as most model in standard General Relativity. We study the geometric properties and the motion of test particles around these objects. Since they have two horizons, the inner being of Cauchy type, we focus on the problem of mass inflation and show that it occurs except when some extremal conditions are met.

Non-Singular Black Holes and mass inflation in modified gravity

We investigate bounce solutions for single scalar field theories, with and without Einstein-Hilbert gravity, considering a false vacuum living on flat Euclidean spacetime. We find that, under appropriate conditions, the behaviour of the scalar field far away from the bubble is independent on the form of the potential and it may be determined analytically. In particular, we need the scalar field to be massless, or light, and cubic self-interactions should be small. We mainly discuss Einstein-Hilbert gravity, and, in particular, the case of the Higgs decay, but generalizations to modified gravity are in principle possible. We use our findings to introduce a novel numerical procedure based on minimization, as an alternative to the shooting method.

A novel method to compute bounce solutions

Metastable states decay at zero temperature through quantum tunneling at an exponentially small rate, which depends on the Coleman-de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein-Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behavior at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action. We also comment on the numerical implications of our findings.

Massimiliano Rinaldi

Papers

Inflationary helical magnetic fields with a sawtooth coupling

Pre-Big Bang Scenario on Self-T-Dual Bouncing Branes

Non-Singular Black Holes and mass inflation in modified gravity

A novel method to compute bounce solutions

Vacuum decay in quadratic gravity