We calculate the self-force experienced by a point scalar charge q, a point electric charge e, and a point mass m moving in a weakly curved spacetime characterized by a time-independent Newtonian potential ⌽. We assume that the matter distribution responsible for this potential is bounded, so that ⌽ϳϪM /r at large distances r from the matter, whose total mass is M; otherwise, the Newtonian potential is left unspecified. ͑We use units in which Gϭcϭ1.͒ The self-forces are calculated by first computing the retarded Green's functions for scalar, electromagnetic, and ͑linearized͒ gravitational fields in the weakly curved spacetime, and then evaluating an integral over the particle's past world line. The self-force typically contains both a conservative and a nonconservative ͑radiation-reaction͒ part. For the scalar charge, the conservative part of the self-force is equal to 2q 2 M r/r 3 , where is a dimensionless constant measuring the coupling of the scalar field to the spacetime curvature, and r is a unit vector pointing in the radial direction. For the electric charge, the conservative part of the self-force is e 2 M r/r 3 . For the massive particle, the conservative force vanishes. For the scalar charge, the radiation-reaction force is 1 3 q 2 dg/dt, where gϭϪ"⌽ is the Newtonian gravitational field. For the electric charge, the radiation-reaction force is 2 3 e 2 dg/dt. For the massive particle, the radiation-reaction force is Ϫ 11 3 m 2 dg/dt. Our result for the gravitational self-force is disturbing: a radiation-reaction force should not appear in the equations of motion at this level of approximation, and it should certainly not give rise to radiation antidamping. In the last section of the paper we prove that while a massive particle in a vacuum spacetime is subjected only to its self-force, it is also subjected to a matter-mediated force when it moves in a spacetime that contains matter; this force originates from the changes in the matter distribution that are induced by the presence of the particle. We show that the matter-mediated force contains a radiation-damping term that precisely cancels out the antidamping contribution from the gravitational self-force. When both forces are combined, the equations of motion are conservative, and they agree with the appropriate limit of the standard post-Newtonian equations of motion.

We will apply the quantum inequality type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered "flat". These are inequalities that restrict the magnitude and extent of the negative energy which is needed to form the warp drive metric. From this we are able to place limits on the parameters of the "Warp Bubble". It will be shown that the bubble wall thickness is on the order of only a few hundred Planck lengths. Then we will show that the total integrated energy density needed to maintain the warp metric with such thin walls is physically unattainable.

Quantum weak energy inequalities (QWEI) provide state-independent lower bounds on averages of the renormalized energy density of a quantum field. We derive QWEIs for the electromagnetic and massive spin-one fields in globally hyperbolic space–times whose Cauchy surfaces are compact and have trivial first homology group. These inequalities provide lower bounds on weighted averages of the renormalized energy density as “measured” along an arbitrary timelike trajectory, and are valid for arbitrary Hadamard states of the spin-one fields. The QWEI bound takes a particularly simple form for averaging along static trajectories in ultrastatic space–times; as specific examples we consider Minkowski space (in which case the topological restrictions may be dispensed with) and the static Einstein universe. A significant part of the paper is devoted to the definition and properties of Hadamard states of spin-one fields in curved space–times, particularly with regard to their microlocal behavior.

We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum inequality for a static observer in terms of a Euclidean two-point function. In a short sampling time limit, the quantum inequality can be written as the flat space form plus subdominant correction terms dependent upon the geometric properties of the spacetime. This supports the use of flat space quantum inequalities to constrain negative energy effects in curved spacetime. Using the exact Euclidean two-point function method, we develop the quantum inequalities for perfectly reflecting planar mirrors in flat spacetime. We then look at the quantum inequalities in static de Sitter spacetime, Rindler spacetime and two-and four-dimensional black holes. In the case of a four-dimensional Schwarzschild black hole, explicit forms of the inequality are found for static observers near the horizon and at large distances. It is show that there is a quantum averaged weak energy condition (QAWEC), which states that the energy density averaged over the entire worldline of a static observer is bounded below by the vacuum energy of the spacetime. In particular, for an observer at a fixed radial distance away from a black hole, the QAWEC says that the averaged energy density can never be less than the Boulware vacuum energy density. 04.62.+v, 03.70.+k, 11.10.-z, 04.60.-m Typeset using REVT E X *

We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covariance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions. Local covariance permits us to place constraints on the renormalised stress-energy tensor in one spacetime using QEIs derived in another, in subregions where the two spacetimes are isometric. This is of particular utility where one of the two spacetimes exhibits a high degree of symmetry and the QEIs are available in simple closed form. Various general applications are presented, including a priori constraints (depending only on geometric quantities) on the ground-state energy density in a static spacetime containing locally Minkowskian regions. In addition, we present a number of concrete calculations in both two and four dimensions which demonstrate the consistency of our bounds with various known ground-and thermal state energy densities. Examples considered include the Rindler and Misner spacetimes, and spacetimes with toroidal spatial sections. In this paper we confine the discussion to globally hyperbolic spacetimes; subsequent papers will also discuss spacetimes with boundary and other related issues.