O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'

We perform the toroidal compactification of the full Bergshoeff-de Roo version of the Heterotic Superstring effective action to first orderin $\alpha'$. The dimensionally-reduced action is given in a manifestly-O(n,n)-invariant form which we use to derive a manifestly-O(n,n)-invariant Wald entropy formula which we then use to compute the entropy of $\alpha'$-corrected, 4-dimensional, 4-charge, static, extremal, supersymmetric black holes.Comment: References and comments added. Version to be published in Journal of High Energy Physic

Spectra of absolute instruments from the WKB approximation

We calculate frequency spectra of absolute optical instruments using the WKB approximation. The resulting eigenfrequencies approximate the actual values very accurately, in some cases they even give the exact values. Our calculations confirm results obtained previously by a completely different method. In particular, the eigenfrequencies of absolute instruments form tight groups that are almost equidistantly spaced. We demonstrate our method and its results on several examples

The Early Rule-of-Faith Pattern as Emergent Biblical Theology

Peer reviewedPublisher PD

Inhomogeneous potentials, Hausdorff dimension and shrinking targets

Generalising a construction of Falconer, we consider classes of $G_\delta$-subsets of $\mathbb{R}^d$ with the property that sets belonging to the class have large Hausdorff dimension and the class is closed under countable intersections. We relate these classes to some inhomogeneous potentials and energies, thereby providing some useful tools to determine if a set belongs to one of the classes. As applications of this theory, we calculate, or at least estimate, the Hausdorff dimension of randomly generated limsup-sets, and sets that appear in the setting of shrinking targets in dynamical systems. For instance, we prove that for $\alpha \geq 1$, $$\mathrm{dim}_\mathrm{H}\, \{ \, y : | T_a^n (x) - y| < n^{-\alpha} \text{ infinitely often} \, \} = \frac{1}{\alpha},$$ for almost every $x \in [1-a,1]$, where $T_a$ is a quadratic map with $a$ in a set of parameters described by Benedicks and Carleson.Comment: 36 pages. Corrected and reorganised following referee's report. Accepted for publication in Annales Henri Lebesgu

Extending the isolated horizon phase space to string-inspired gravity models

An isolated horizon (IH) is a null hypersurface at which the geometry is held fixed. This generalizes the notion of an event horizon so that the black hole is an object that is in local equilibrium with its (possibly) dynamic environment. The first law of IH mechanics that arises from the framework relates quantities that are all defined at the horizon. IHs have been extensively studied in Einstein gravity with various matter couplings and rotation, and in asymptotically flat and asymptotically anti-de Sitter (ADS) spacetimes in all dimensions $D\geq3$. Motivated by the nonuniqueness of black holes in higher dimensions and by the black-hole/string correspondence principle, we devote this thesis to the extension of the framework to include IHs in string-inspired gravity models, specifically to Einstein-Maxwell-Chern-Simons (EMCS) theory and to Einstein-Gauss-Bonnet (EGB) theory in higher dimensions. The focus is on determining the generic features of black holes that are solutions to the field equations of the theories under consideration. We obtain various results for non-extremal, extremal and supersymmetric IHs in EM-CS theory, and for non-rotating IHs in EGB theory. (An extended abstract is given in the PDF file.)Comment: Ph.D dissertation; Memorial University of Newfoundland; 63 pages; 1 figure; v2: typos correcte