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A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski spacetime and introduces a framework for studing in a precise manner membranes behavior near the black hole horizon and on the other hand, introduces a more general framework for examining the stability of topological defects in curved spacetimes., Comment: 8 pages. arXiv admin note: text overlap with arXiv:gr-qc/9411060 by other authors

We study the photon axion mixing in the presence of large extra dimensions. The eigenvalues and eigenstates of the mixing matrix are analyzed and we establish the resonance condition for the total conversion of a high energy photon into a Kaluza-Klein (KK) axion state. This resonant transition, a photon transformed into a KK axion travelling freely through the bulk and converting back into a photon, may provide a plausible explanation for the transparency of the universe to energetic photons. If the brane we live in is curved, then there are shortcuts through the bulk, which the axion can take. Within our model, the photons having the appropriate resonance energy are using the axionic shortcut and arrive earlier compared to the photons which follow the geodesic on the brane. We suggest that such axionic shortcuts are at the root of the dispersion of time arrival of photons observed by the MAGIC telescope. We indicate also the cosmological significance of the existence of axionic shortcuts for the photon., Comment: 7 pages

The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late nineteenth century. The Peircean logic has the mathematical structure of a category with the relation $R_{ij}$ among two individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus indicating category theory as the foundation of Quantum Mechanics. The same relational algebra generates a number of group structures, among them $W_{\infty}$. The group $W_{\infty}$ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories., Comment: To appear in International Journal of Modern Physics A

In TeV scale unification models, gravity propagates in 4+d dimensions while gauge and matter fields are confined to a four dimensional brane, with gravity becoming strong at the TeV scale. For a such scenario, we study strong gravitational interactions in a effective Schwarzschild geometry. Two regimes appear. For large impact parameters, the ratio rho=(Rs/ro)1+d, (with Rs the Schwarzschild radius and ro the closest approach to the black hole), is small and the deflection angle is proportional to rho (like Rutherford-type scattering).For small impact parameters, the deflection angle develops a logarithmic singularity and becomes infinite for rho=rho crit= 2/(3+d). This singularity is reflected into a strong enhancement of the backward scattering (like a glory-type effect). We suggest a distinctive signature of black hole formation in particle collisions at TeV energies, the observation of the backward scattering events and its associated diffractive effects., Comment: Expanded version, references added, 8 pages, no figures

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessaary for a consistent computation of the energy. We also quantize the perturbations and derive the mass-formula up to second order in perturbations for an observer using world-sheet time $\tau $. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass-spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind., Comment: New discussion about the quantum mass-spectrum in chapter 4

The phenomenon of string spreading on the black hole horizon, as originally discussed by Susskind, is considered in the {\it exact} curved Schwarzschild background. We consider an oscillating string encircling the black hole and contracting towards the horizon. We then compute the angular and radial spreading of the string, as seen by a static observer at spatial infinity using fixed finite resolution time. Within our case study we find that there is indeed a spreading of the string in the angular direction, such that the string eventually covers the whole horizon. However, regarding the radial direction, we find that Lorentz-contraction suppresses the radial string spreading., Comment: 14 pages, Latex. No figures

The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension $T_{0}$ as a small perturbation. The expansion parameter is the worldsheet speed of light c, which is proportional to $T_{0}$ . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders $ c^{2} $ and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to $ c^{2} $. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly., Comment: More references are included. Final version, to appear in Phys.Rev.D. 6 pages, LaTex, no figures

We study quantum strings in strong gravitational fields. The relevant small parameter is $g=R_c{\sqrt T_0}$, where $R_c$ is the curvature of the spacetime and $T_0$ is the string tension. Within our systematic expansion we obtain to zeroth order the null string (string with zero tension), while the first order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the world-sheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated however that the conformal anomaly will appear when the first order corrections proportional to $T_0$, are introduced., Comment: 6 pages, plain Tex, no figures