This article presents the derivation of the stress-energy tensor of a free scalar field with a general non-linear dispersion relation in curved spacetime. This dispersion relation is used as a phenomelogical description of the short distance structure of spacetime following the conventional approach of trans-Planckian modes in black hole physics and in cosmology. This stress-energy tensor is then used to discuss both the equation of state of trans-Planckian modes in cosmology and the magnitude of their backreaction during inflation. It is shown that gravitational waves of trans-Planckian momenta but subhorizon frequencies cannot account for the form of cosmic vacuum energy density observed at present, contrary to a recent claim. The backreaction effects during inflation are confirmed to be important and generic for those dispersion relations that are liable to induce changes in the power spectrum of metric fluctuations. Finally, it is shown that in pure de Sitter inflation there is no modification of the power spectrum except for a possible magnification of its overall amplitude independently of the dispersion relation.

We consider the classical equations of the gravitating Abelian-Higgs model in an axially symmetric ansatz. Several properties of the solutions ͑the Melvin branch and the string branch͒ of these equations are presented. These solutions are also constructed for winding numbers nϭ2. It is shown that these gravitating vortices exist in attractive and repulsive phases, separated by the value of the Higgs coupling constant parameter leading to self-dual equations.

The minimal length uncertainty principle of Kemf, Mangano and Mann ͑KMM͒, as derived from a mutilated quantum commutator between coordinate and momentum, is applied to describe the modes and wave packets of Hawking particles evaporated from a black hole. The trans-Planckian problem is successfully confronted in that the Hawking particle no longer hugs the horizon at arbitrarily close distances. Rather the mode of Schwarzschild frequency deviates from the conventional trajectory when the coordinate r is given by ͉rϪ2M ͉Ӎ␤ H /2 in units of the nonlocal distance legislated into the uncertainty relation. Wave packets straddle the horizon and spread out to fill the whole nonlocal region. The charge carried by the packet ͑in the sense of the amount of ''stuff'' carried by the Klein-Gordon field͒ is not conserved in the non-local region and rapidly decreases to zero as time decreases. Read in the forward temporal direction, the non-local region thus is the seat of production of the Hawking particle and its partner. The KMM model was inspired by string theory for which the mutilated commutator has been proposed to describe an effective theory of high momentum scattering of zero mass modes. It is here interpreted in terms of dissipation which gives rise to the Hawking particle into a reservoir of other modes ͑of as yet unknown origin͒. On this basis it is conjectured that the Bekenstein-Hawking entropy finds its origin in the fluctuations of fields extending over the nonlocal region.

The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics -dubbed as trans-Planckian inflation -has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyzes, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner -without calculating the stress-tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gaugeinvariant cosmological perturbations for the single-scalar field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit time-like vector field which defines a preferred rest frame. We show that: (i) The non-linear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different than those presumed in the earlier analyzes. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power-spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.

We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions between the interior and exterior geometries imply restrictions on the physical parameters of the solutions. In particular, imposing finite sources and absence of closed timelike curves privileges negative values of the cosmological constant, yielding exterior vacuum geometries of rotating black hole type. In the special case of static sources, we prove the complete integrability of the field equations and show that the sources' masses are bounded from above and, for vanishing cosmological constant, generally equal to one. We also discuss and illustrate the stationary configurations by explicitly solving the field equations for constant mass-energy densities. If the pressure vanishes, we recover as interior geometries Gödel like metrics defined on causally well behaved domains, but with unphysical values of the mass to angular momentum ratio. The introduction of pressure in the sources cures the latter problem and leads to physically more relevant models.