Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable and quantizable matter

Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry, namely to be hyperbolic, time-orientable and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics---for the general tensorial spacetime geometries satisfying the above minimum requirements---is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus the search for modified gravitational dynamics is reduced to a clear mathematical task.Comment: 47 pages, no figures, minor update

Shortcuts to Spherically Symmetric Solutions: A Cautionary Note

Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function ansatz invalidates it, as illustrated by the incorrect solutions of [1].Comment: 2 pages. Amplified derivation, accepted for publication in Class Quant Gra

The `s-rule' exclusion principle and vacuum interpolation in worldvolume dynamics

We show how the worldvolume realization of the Hanany-Witten effect for a supersymmetric D5-brane in a D3 background also provides a classical realization of the `s-rule' exclusion principle. Despite the supersymmetry, the force on the D5-brane vanishes only in the D5 `ground state', which is shown to interpolate between 6-dimensional Minkowski space and an $OSp(4^*|4)$-invariant $adS_2\times S^4$ geometry. The M-theory analogue of these results is briefly discussed.Comment: 25 pages, 9 figures, LaTeX JHEP styl

Canonical differential geometry of string backgrounds

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes.Comment: 20 pages, no figures, improved journal versio

On Dual Formulation of Gravity

In this paper we consider a possibility to construct dual formulation of gravity where the main dynamical field is the Lorentz connection \omega_\mu^{ab} and not that of tetrad e_\mu^a or metric g_\mu\nu. Our approach is based on the usual dualization procedure which uses first order parent Lagrangians but in (Anti) de Sitter space and not in the flat Minkowski one. It turns out that in d=3 dimensions such dual formulation is related with the so called exotic parity-violating interactions for massless spin-2 particles.Comment: 7 pages, plain LaTe

Thermal Casimir Force between Magnetic Materials

We investigate the Casimir pressure between two parallel plates made of magnetic materials at nonzero temperature. It is shown that for real magnetodielectric materials only the magnetic properties of ferromagnets can influence the Casimir pressure. This influence is accomplished through the contribution of the zero-frequency term of the Lifshitz formula. The possibility of the Casimir repulsion through the vacuum gap is analyzed depending on the model used for the description of the dielectric properties of the metal plates.Comment: 9 pages, 3 figures. Contribution to the Proceedings of QFEXT09, Norman, OK, September 21-25, 200

Gravity a la Born-Infeld

A simple technique for the construction of gravity theories in Born-Infeld style is presented, and the properties of some of these novel theories are investigated. They regularize the positive energy Schwarzschild singularity, and a large class of models allows for the cancellation of ghosts. The possible correspondence to low energy string theory is discussed. By including curvature corrections to all orders in alpha', the new theories nicely illustrate a mechanism that string theory might use to regularize gravitational singularities.Comment: 21 pages, 2 figures, new appendix B with corrigendum: Class. Quantum Grav. 21 (2004) 529

Spontaneous decompactification

Positive vacuum energy together with extra dimensions of space imply that our four-dimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past a barrier into the decompactifying regime. We give an overview of this process, and examine the subsequent expansion into the higher- dimensional geometry. This is governed by certain fixed-point solutions of the evolution equations, which are studied for both positive and negative spatial curvature. In the case where there is a higher-dimensional cosmological constant, we also outline a possible mechanism for compactification to a four-dimensional de Sitter cosmology.Comment: 27 pages, 5 figures, harvmac. v2: refs added, minor notation change

The alpha-prime stretched horizon in the Heterotic string

The linear alpha-prime corrections and the field redefinition ambiguities are studied for half-BPS singular backgrounds representing a wrapped fundamental string. It is showed that there exist schemes in which the inclusion of all the linear alpha-prime corrections converts these singular solutions to black holes with a regular horizon for which the modified Hawking-Bekenstein entropy is in agreement with the statistical entropy.Comment: 22 pages JHEP; new discussions and more details added to section