S-matrix for s-wave gravitational scattering

In the s-wave approximation the 4D Einstein gravity with scalar fields can be reduced to an effective 2D dilaton gravity coupled nonminimally to the matter fields. We study the leading order (tree level) vertices. The 4-particle matrix element is calculated explicitly. It is interpreted as scattering with formation of a virtual black hole state. As one novel feature we predict the gravitational decay of s-waves.Comment: 9 pages, 1 figure, added clarifying comments in the introduction, the conclusion, and the virtual black hole sectio

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g. dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g. spherically reduced Scalar-Tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.Comment: 23 pages, 1 tabl

Effective Action and Hawking Flux from Covariant Perturbation Theory

The computation of the radiation flux related to the Hawking temperature of a Schwarzschild Black Hole or another geometric background is still well-known to be fraught with a number of delicate problems. In spherical reduction, as shown by one of the present authors (W. K.) with D.V. Vassilevich, the correct black body radiation follows when two ``basic components'' (conformal anomaly and a ``dilaton'' anomaly) are used as input in the integrated energy-momentum conservation equation. The main new element in the present work is the use of a quite different method, the covariant perturbation theory of Barvinsky and Vilkovisky, to establish directly the full effective action which determines these basic components. In the derivation of W. K. and D.V. Vassilevich the computation of the dilaton anomaly implied one potentially doubtful intermediate step which can be avoided here. Moreover, the present approach also is sensitive to IR (renormalisation) effects. We realize that the effective action naturally leads to expectation values in the Boulware vacuum which, making use of the conservation equation, suffice for the computation of the Hawking flux in other quantum states, in particular for the relevant Unruh state. Thus, a rather comprehensive discussion of the effects of (UV and IR) renormalisation upon radiation flux and energy density is possible.Comment: 26 page

Semantic Technologies for Manuscript Descriptions — Concepts and Visions

The contribution at hand relates recent developments in the area of the World Wide Web to codicological research. In the last number of years, an informational extension of the internet has been discussed and extensively researched: the Semantic Web. It has already been applied in many areas, including digital information processing of cultural heritage data. The Semantic Web facilitates the organisation and linking of data across websites, according to a given semantic structure. Software can then process this structural and semantic information to extract further knowledge. In the area of codicological research, many institutions are making efforts to improve the online availability of handwritten codices. If these resources could also employ Semantic Web techniques, considerable research potential could be unleashed. However, data acquisition from less structured data sources will be problematic. In particular, data stemming from unstructured sources needs to be made accessible to SemanticWeb tools through information extraction techniques. In the area of museum research, the CIDOC Conceptual Reference Model (CRM) has been widely examined and is being adopted successfully. The CRM translates well to Semantic Web research, and its concentration on contextualization of objects could support approaches in codicological research. Further concepts for the creation and management of bibliographic coherences and structured vocabularies related to the CRM will be considered in this chapter. Finally, a user scenario showing all processing steps in their context will be elaborated on

Two results on the size of spectrahedral descriptions

A spectrahedron is a set defined by a linear matrix inequality. Given a spectrahedron we are interested in the question of the smallest possible size $r$ of the matrices in the description by linear matrix inequalities. We show that for the $n$-dimensional unit ball $r$ is at least $\frac{n}{2}$. If $n=2^k+1$, then we actually have $r=n$. The same holds true for any compact convex set in $\mathbb{R}^n$ defined by a quadratic polynomial. Furthermore, we show that for a convex region in $\mathbb{R}^3$ whose algebraic boundary is smooth and defined by a cubic polynomial we have that $r$ is at least five. More precisely, we show that if $A,B,C$ are real symmetric matrices such that $f(x,y,z)=\det(I+A x+B y+C z)$ is a cubic polynomial, the surface in complex projective three-space with affine equation $f(x,y,z)=0$ is singular.Comment: 10 pages, 2 figures, minor mistakes correcte