A Rigorous Derivation of Electromagnetic Self-force

During the past century, there has been considerable discussion and analysis of the motion of a point charge, taking into account "self-force" effects due to the particle's own electromagnetic field. We analyze the issue of "particle motion" in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density $J^a(\lambda)$ and stress-energy tensor $T_{ab} (\lambda)$ scale to zero size in an asymptotically self-similar manner about a worldline $\gamma$ as $\lambda \to 0$. In this limit, the charge, $q$, and total mass, $m$, of the body go to zero, and $q/m$ goes to a well defined limit. The Maxwell field $F_{ab}(\lambda)$ is assumed to be the retarded solution associated with $J^a(\lambda)$ plus a homogeneous solution (the "external field") that varies smoothly with $\lambda$. We prove that the worldline $\gamma$ must be a solution to the Lorentz force equations of motion in the external field $F_{ab}(\lambda=0)$. We then obtain self-force, dipole forces, and spin force as first order perturbative corrections to the center of mass motion of the body. We believe that this is the first rigorous derivation of the complete first order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the "reduction of order" procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. There is no corresponding justification for the non-reduced-order equations.Comment: 52 pages, minor correction

Killing Horizons Decohere Quantum Superpositions

We recently showed that if a massive (or charged) body is put in a quantum spatial superposition, the mere presence of a black hole in its vicinity will eventually decohere the superposition. In this paper we show that, more generally, decoherence of stationary superpositions will occur in any spacetime with a Killing horizon. This occurs because, in effect, the long-range field of the body is registered on the Killing horizon which, we show, necessitates a flux of "soft horizon gravitons/photons" through the horizon. The Killing horizon thereby harvests "which path" information of quantum superpositions and will decohere any quantum superposition in a finite time. It is particularly instructive to analyze the case of a uniformly accelerating body in a quantum superposition in flat spacetime. As we show, from the Rindler perspective the superposition is decohered by "soft gravitons/photons" that propagate through the Rindler horizon with negligible (Rindler) energy. We show that this decoherence effect is distinct from--and larger than--the decoherence resulting from the presence of Unruh radiation. We further show that from the inertial perspective, the decoherence is due to the radiation of high frequency (inertial) gravitons/photons to null infinity. (The notion of gravitons/photons that propagate through the Rindler horizon is the same notion as that of gravitons/photons that propagate to null infinity.) We also analyze the decoherence of a spatial superposition due to the presence of a cosmological horizon in de Sitter spacetime. We provide estimates of the decoherence time for such quantum superpositions in both the Rindler and cosmological cases. Although we explicitly treat the case of spacetime dimension $d=4$, our analysis applies to any dimension $d \geq 4$.Comment: 16 pages, 1 figure. Accepted for publication in Phys. Rev. D. v2: Added clarifying remarks and a figure, and pointed out that the effect arises for any d>=4; corrected equation (3.18

Killing horizons decohere quantum superpositions

We recently showed that if a massive (or charged) body is put in a quantum spatial superposition, the mere presence of a black hole in its vicinity will eventually decohere the superposition. In this paper we show that, more generally, decoherence of stationary superpositions will occur in any spacetime with a Killing horizon. This occurs because, in effect, the long-range field of the body is registered on the Killing horizon which, we show, necessitates a flux of "soft horizon gravitons/photons"through the horizon. The Killing horizon thereby harvests "which path"information of quantum superpositions and will decohere any quantum superposition in a finite time. It is particularly instructive to analyze the case of a uniformly accelerating body in a quantum superposition in flat spacetime. As we show, from the Rindler perspective the superposition is decohered by "soft gravitons/photons"that propagate through the Rindler horizon with negligible (Rindler) energy. We show that this decoherence effect is distinct from - and larger than - the decoherence resulting from the presence of Unruh radiation. We further show that from the inertial perspective, the decoherence is due to the radiation of high frequency (inertial) gravitons/photons to null infinity. (The notion of gravitons/photons that propagate through the Rindler horizon is the same notion as that of gravitons/photons that propagate to null infinity.) We also analyze the decoherence of a spatial superposition due to the presence of a cosmological horizon in de Sitter spacetime. We provide estimates of the decoherence time for such quantum superpositions in both the Rindler and cosmological cases. Although we explicitly treat the case of spacetime dimension $d=4$, our analysis applies to any dimension $d≥4$

A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes

The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the Noether charge approach (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods, specifically, (i) the microcanonical ensemble approach of Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and Zanelli which ultimately expresses black hole entropy in terms of the Hilbert action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli (also used by Susskind and Uglum) which views black hole entropy as conjugate to a conical deficit angle, and (iv) the pair creation approach of Garfinkle, Giddings, and Strominger. All of these approaches have a more restrictive domain of applicability than the Noether charge approach. Specifically, approaches (i) and (ii) appear to be restricted to a class of theories satisfying certain properties listed in section 2; approach (iii) appears to require the Lagrangian density to be linear in the curvature; and approach (iv) requires the existence of suitable instanton solutions. However, we show that within their domains of applicability, all of these approaches yield results in agreement with the Noether charge approach. In the course of our analysis, we generalize the definition of Brown and York's quasilocal energy to a much more general class of diffeomorphism invariant, Lagrangian theories of gravity. In an appendix, we show that in an arbitrary diffeomorphism invariant theory of gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a time evolution vector field $t^a$ always can be expressed as the spatial integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late

Topological Censorship

All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the topology of spacetime: any topological structure collapses too quickly to allow light to traverse it. More precisely, in a globally hyperbolic, asymptotically flat spacetime satisfying the null energy condition, every causal curve from \scri^- to {\scri}^+ is homotopic to a topologically trivial curve from \scri^- to {\scri}^+. (If the Poincar\'e conjecture is false, the theorem does not prevent one from probing fake 3-spheres).Comment: 12 pages, REVTEX; 1 postscript figure in a separate uuencoded file. Our earlier version (PRL 71, 1486 (1993)) contained a secondary result, mistakenly attributed to Schoen and Yau, regarding ``passive topological censorship'' of a certain class of topologies. As Gregory Burnett has pointed out (gr-qc/9504012), this secondary result is false. The main topological censorship theorem is unaffected by the erro

Initial Conditions for Bubble Universes

The "bubble universes" of Coleman and De Luccia play a crucial role in string cosmology. Since our own Universe is supposed to be of this kind, bubble cosmology should supply definite answers to the long-standing questions regarding cosmological initial conditions. In particular, it must explain how an initial singularity is avoided, and also how the initial conditions for Inflation were established. We argue that the simplest non-anthropic approach to these problems involves a requirement that the spatial sections defined by distinguished bubble observers should not be allowed to have arbitrarily small volumes. Casimir energy is a popular candidate for a quantum effect which can ensure this, but [because it violates energy conditions] there is a danger that it could lead to non-perturbative instabilities in string theory. We make a simple proposal for the initial conditions of a bubble universe, and show that our proposal ensures that the system is non-perturbatively stable. Thus, low-entropy conditions can be established at the beginning of a bubble universe without violating the Second Law of thermodynamics and without leading to instability in string theory. These conditions are inherited from the ambient spacetime.Comment: Further clarifications; 28 pages including three eps files. This is the final [accepted for publication] versio

The fate of black branes in Einstein-Gauss-Bonnet gravity

Black branes are studied in Einstein-Gauss-Bonnet (EGB) gravity. Evaporation drives black branes towards one of two singularities depending on the sign of $\alpha$, the Gauss-Bonnet coupling. For positive $\alpha$ and sufficiently large ratio $\sqrt{\alpha}/L$, where $L/2\pi$ is the radius of compactification, black branes avoid the Gregory-Laflamme (GL) instability before reaching a critical state. No black branes with the radius of horizon smaller than the critical value can exist. Approaching the critical state branes have a nonzero Hawking temperature. For negative $\alpha$ all black branes encounter the GL instability. No black branes may exist outside of the interval of the critical values, $0\leq\beta<3$, where $\beta=1- 8\alpha/r_h^2$ and $r_h$ is the radius of horizon of the black brane. The first order phase transition line of GL transitions ends in a second order phase transition point at $\beta=0$

Generalized entropy and Noether charge

We find an expression for the generalized gravitational entropy of Hawking in terms of Noether charge. As an example, the entropy of the Taub-Bolt spacetime is calculated.Comment: 6 pages, revtex, reference correcte

Realistic Exact Solution for the Exterior Field of a Rotating Neutron Star

A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass--quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett. 11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011 (1998)) and, our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions.Comment: 13 pages, 13 figures, LaTeX documen

Quasilocal Thermodynamics of Dilaton Gravity coupled to Gauge Fields

We consider an Einstein-Hilbert-Dilaton action for gravity coupled to various types of Abelian and non-Abelian gauge fields in a spatially finite system. These include Yang-Mills fields and Abelian gauge fields with three and four-form field strengths. We obtain various quasilocal quantities associated with these fields, including their energy and angular momentum, and develop methods for calculating conserved charges when a solution possesses sufficient symmetry. For stationary black holes, we find an expression for the entropy from the micro-canonical form of the action. We also find a form of the first law of black hole thermodynamics for black holes with the gauge fields of the type considered here.Comment: 41 pages, latex, uses fonts provided by AMSTe