Bernard F. Whiting

Black hole evaporation without information loss

An approach to black hole quantization is proposed wherein it is assumed that quantum coherence is preserved. After giving our motivations for such a quantization procedure we formulate the background field approximation, in which particles are divided into `hard particles and `soft particles. The background spacetime metric depends both on the in-states and on the out-states. A consequence of our approach is that four-geometries describing gravitational collapse will show the same topological structure as flat Minkowski space. We present some model calculations and extensive discussions. In particular, we show, in the context of a toy model, that the S-matrix describing soft particles in the hard particle background of a collapsing star is unitary; nevertheless, part of the spectrum of particles is shown to be approximately thermal. We also conclude that there is an interesting topological (and signature) constraint on manifolds underlying conventional functional integrals.

Near-Field Radiative Heat Transfer between Macroscopic Planar Surfaces

Near-field radiation allows heat to propagate across a small vacuum gap at rates several orders of magnitude above that of far-field, blackbody radiation. Although heat transfer via near-field effects has been discussed for many years, experimental verification of this theory has been very limited. We have measured the heat transfer between two macroscopic sapphire plates, finding an increase in agreement with expectations from theory. These experiments, conducted near 300xa0K, have measured the heat transfer as a function of separation over mm to μm and as a function of temperature differences between 2.5 and 30xa0K. The experiments demonstrate that evanescence can be put to work to transfer heat from an object without actually touching it.

Mode Stability of the Kerr Black Hole

Separate differential and integral transformations are introduced for the individual radial and angular equations governing the (infinitesimally) gauge invariant Newman–Penrose quantities which represent massless perturbations of the Kerr black hole. Using these new transformations it is shown, without need for numerical investigation or reference to the analytic behavior of the separation constant, that no unstable mode perturbations exist for any physical value of the spin of massless fields on the rotating black hole background.

Self force via a Green's function decomposition

The gravitational field of a particle of small mass mu moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(mu). One part is an inhomogeneous field which, near the particle, looks like the mu/r field distorted by the local Riemann tensor; it does not depend on the behavior of the source in either the infinite past or future. The other part is a homogeneous field and includes the ``tail term; it completely determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction. Self force effects for scalar, electromagnetic and gravitational fields are all described in this manner.

Mass and motion in general relativity

Preface by editors. 1 The Higgs mechanism and the origin of mass (A. Djouadi). 2 Testing basic laws of gravitation (C. Lammerzahl). 3 Mass metrology and the International System of units (R.S. Davis). 4 Mass and angular momentum in general relativity (J.L. Jaramillo and E. Gourgoulhon). 5 Post-Newtonian theory and the two-body problem (L. Blanchet) 6 Post-Newtonian methods (G. Schafer). 7 Effective one body description of the Tow-Body problem (T. Damour and A. Nagar). 8 Introduction to the self-force (R.M. Wald). 9 Derivation of Gravitational Self-Force (S.E. Gralla and R.M. Wald). 10 Elementary development of the gravitational self-force (S. Detweiler). 11 Constructing the self-force (E. Poisson). 12 Computational methods for the self force in black hole spacetimes (L. Barack). 13 Radiation reaction and energy-momentum conservation (D. Galtsov). 14 The state of current self-force research (L.M. Burko). 15 High-accuracy comparison between the post-Newtonian and self-force dynamics of black-hole binaries (L. Blanchet, S. Detweiler, A. Le Tiec and B.F. Whiting). 16 LISA and capture sources (O. Jennrich). 17 Motion in alternative thoeries of gravity (G. Esposito-Farese. 18 Mass, inertia and gravitation (M-T. Jaekel and S. Reynaud). 19 Motion in quantum gravity (K. Noui). 20 Free fall and the self-force: an historical perspective (A. Spallicci).We discuss some effects induced by quantum field fluctuations on mass, inertia and gravitation. Recalling the problem raised by vacuum field fluctuations with respect to inertia and gravitation, we show that vacuum energy differences, such as Casimir energy, do contribute to inertia. Mass behaves as a quantum observable and in particular possesses quantum fluctuations. We show that the compatibility of the quantum nature of mass with gravitation can be ensured by conformal symmetries, which allow one to formulate a quantum version of the equivalence principle. Finally, we consider some corrections to the coupling between metric fields and energy-momentum tensors induced by radiative corrections. Newton gravitation constant is replaced by two different running coupling constants in the sectors of traceless and traced tensors. There result metric extensions of general relativity, which can be characterized by modified Ricci curvatures or by two gravitation potentials. The corresponding phenomenological framework extends the usual Parametrized Post-Newtonian one, with the ability to remain compatible with classical tests of gravity while accounting for new features, such as Pioneer like anomalies or anomalous light deflection.

The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory

First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly circular orbit. Our calculation is valid through 3PN order and includes, in addition, the contributions of logarithmic terms at 4PN and 5PN orders. This first law of binary point-particle mechanics is then derived from first principles in general relativity, and analogies are drawn with the single and binary black hole cases. Some consequences of the first law are explored for PN spacetimes. As one such consequence, a simple relation between the PN binding energy of the binary system and Detweilers redshift observable is established. Through it, we are able to determine with high precision the numerical values of some previously unknown high order PN coefficients in the circular-orbit binding energy. Finally, we propose new gauge invariant notions for the energy and angular momentum of a particle in a binary system.

Approximate Killing Vectors on S^2

We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S{sup 2}. When solutions of Killings equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.

High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

We continue a previous work on the comparison between the post-Newtonian (PN) approximation and the gravitational self-force (SF) analysis of circular orbits in a Schwarzschild background. We show that the numerical SF data contain physical information corresponding to extremely high PN approximations. We nd that knowing analytically determined appropriate PN parameters helps tremendously in allowing the numerical data to be used to obtain higher order PN coecients. Using standard PN theory we compute analytically the leading 4PN and the next-to-leading 5PN logarithmic terms in the conservative part of the dynamics of a compact binary system. The numerical perturbative SF results support well the analytic PN calculations through rst order in the mass ratio, and are used to accurately measure the 4PN and 5PN non-logarithmic coecients in a particular gauge invariant observable. Furthermore we are able to give estimates of higher order contributions up to the 7PN level. We also conrm with high precision the value of the 3PN

Thermodynamic ensembles and gravitation

By including gravitation as described by general relativity as a part of a thermodynamic system, the authors have obtained formal path integral representations of partition functions for various ensembles including that appropriate to the microcanonical ensemble. This is possible because the boundary conditions for certain well posed Euclidean problems in general relativity exactly correspond to boundary conditions of certain well posed problems in thermodynamics. The different ensembles are obtained using the definition of variables conjugate both in the sense of the field theory of general relativity and in the sense of thermodynamics, the boundary data of which can be prescribed geometrically using gravity.

Self-force of a scalar field for circular orbits about a Schwarzschild black hole

The foundations are laid for the numerical computation of the actual worldline for a particle orbiting a black hole and emitting gravitational waves. The essential practicalities of this computation are illustrated here for a scalar particle of infinitesimal size and small but finite scalar charge. This particle deviates from a geodesic because it interacts with its own retarded field ψret. A recently introduced Green’s function GS precisely determines the singular part ψS of the retarded field. This part exerts no force on the particle. The remainder of the field ψR=ψret−ψS is a vacuum solution of the field equation and is entirely responsible for the self-force. A particular, locally inertial coordinate system is used to determine an expansion of ψS in the vicinity of the particle. For a particle in a circular orbit in the Schwarzschild geometry, the mode-sum decomposition of the difference between ψret and the dominant terms in the expansion of ψS provide a mode-sum decomposition of an approximation for ψR from which the self-force is obtained. When more terms are included in the expansion, the approximation for ψR is increasingly differentiable, and the mode sum for the self-force converges more rapidly.