The Physics of Negative Energy Densities

I review some recent results showing that the physics of negative energy densities, as predicted by relativistic quantum field theories, is more complicated than has generally been appreciated. On the one hand, in external potentials where there is a time--dependence, however slight, the Hamiltonians are unbounded below. On the other, there are limitations of quantum measurement in detecting or utilizing these negative energies.Comment: 10 pages, latex, uses sprocl, talk given at the Quantum Fields in External Potentials Workshop, Leipzig, 199

Energy-momentum and asymptotic geometry

I show that radiative space-times are not asymptotically flat; rather, the radiation field gives rise to holonomy at null infinity. (This was noted earlier, by Bramson.) This means that, when gravitational radiation is present, asymptotically covariantly constant vector fields do not exist. On the other hand, according to the Bondi-Sachs construction, a weaker class of asymptotically constant vectors does exist. Reconciling these concepts leads to a measure of the scattering of matter by gravitational waves, that is, bulk exchanges of energy-momentum between the waves and matter. Because these bulk effects are potentially larger than the tidal ones which have usually been studied, they may affect the waves' propagation more significantly, and the question of matter's transparency to gravitational radiation should be revisited. While in many cases there is reason to think the waves will be only slightly affected, some situations are identified in which the energy-momentum exchanges can be substantial enough that a closer investigation should be made. In particular, the work here suggests that gravitational waves produced when relativistic jets are formed might be substantially affected by passing through an inhomogeneous medium.Comment: 22 pages, to appear in Phys. Rev.

Black holes reconsidered

I review elements of the foundations of black-hole theory with attention to problematic issues, and describe some techniques which either seem to help with the difficulties or at least investigate their scope. The definition of black holes via event horizons has been problematic because it depends on knowing the global structure of space-time; often attempts to avoid this (e.g. apparent horizons) require knowledge of the interior geometry. I suggest studying instead the holonomy relating the exterior neighborhood of the incipient horizon to the regime of distant observers; at least in the spherically symmetric case, this holonomy will develop certain universal features, in principle observable from signals emitted from infalling objects. I discuss the theory of quantum fields in curved space-time, and the difficulties with Hawking's prediction of black-hole radiation. I then show that the usual, very natural, theory of quantum fields in curved space-time runs into difficulties when applied to measurement problems, interactions, zero-point effects and stress-energies. I suggest that we take seriously the possibility that this theory, for all its naturalness, may not be quite right.Comment: Write-up of talks given at BSCG XIV; 50 pages, 6 figure

Trans-Planckian Modes, Back-Reaction, and the Hawking Process

Hawking's prediction of black-hole evaporation depends on the application of known physics to fantastically high energies -- well beyond the Planck scale. Here, I show that before these extreme regimes are reached, another physical effect will intervene: the quantum backreaction on the collapsing matter and its effect on the geometry through which the quantum fields propagate. These effects are estimated by a simple thought experiment. When this is done, it appears that there are no matrix elements allowing the emission of Hawking quanta: black holes do not radiate.Comment: 7 pages, plain Tex, IOP macros, 1 eps figur

Quantum character of black holes

Black holes are extreme manifestations of general relativity, so one might hope that exotic quantum effects would be amplified in their vicinities, perhaps providing clues to quantum gravity. The commonly accepted treatment of quantum corrections to the physics around the holes, however, has provided only limited encouragement of this hope. The predicted corrections have been minor (for macroscopic holes): weak fluxes of low-energy thermal radiation which hardly disturb the classical structures of the holes. Here, I argue that this accepted treatment must be substantially revised. I show that when interactions among fields are taken into account (they were largely neglected in the earlier work) the picture that is drawn is very different. Not only low-energy radiation but also ultra-energetic quanta are produced in the gravitationally collapsing region. The energies of these quanta grow exponentially quickly, so that by the time the hole can be said to have formed, they have passed the Planck scale, at which quantum gravity must become dominant. The vicinities of black holes are windows on quantum gravity.Comment: 17 pages, 5 figures. Expanded treatment of the material in the 2004 Gravity Research Foundation essa

Comment on "Insensitivity of Hawking Radiation to an invariant Planck-scale cutoff"

I point out that the cutoff introduced by Agullo et al. [Phys.Rev.D80:047503,2009 arXiv:0906.5315] has little impact on the trans-Planckian problem as it is usually understood; it excludes only a small fraction of the problematic modes.Comment: 4 pages, to appear in Phys. Rev. D., see also the reply by Agullo et al

The Hamiltonians of Linear Quantum Fields: I. Existence Theory

For linear scalar field theories, I characterize those classical Hamiltonian vector fields which have self-adjoint operators as their quantum counterparts. As an application, it is shown that for a scalar field in curved space-time (in a Hadamard representation), a self-adjoint Hamiltonian for evolution along the unit timelike normal to a Cauchy surface exists only if the second fundamental form of the surface vanishes identically.Comment: 30 pages, Latex2e with AMS package

Spinor Lie derivatives and Fermion stress-energies

Stress-energies for Fermi fields are derived from the principle of general covariance. This is done by developing a notion of Lie derivatives of spinors along arbitrary vector fields. A substantial theory of such derivatives was first introduced by Kosmann; here I show how an apparent conflict in the literature on this is due to a difference in the definitions of spinors, and that tracking the Lie derivative of the Infeld-van der Waerden symbol, as well as the spinor fields under consideration, gives a fuller picture of the geometry and leads to the Fermion stress-energy. The differences in the definitions of spinors do not affect the results here, but could matter in certain quantum-gravity programs and for spinor transformations under discrete symmetries.Comment: 25 pages, to appear in Proc. R. Soc.

The Stress-Energy Operator

We compute the stress--energy operator for a scalar linear quantum field in curved space-time, modulo c-numbers. For the associated Hamiltonian operators, even those generating evolution along timelike vector fields, we find that in general on locally Fock-like (`Hadamard') representations: (a) The Hamiltonians cannot be self-adjoint operators; (b) The automorphisms of the field algebra generated by the evolution cannot be unitarily implemented; (c) The expectation values of the Hamiltonians are well-defined on a dense family of states; but (d) These expectation values are unbounded below, even for evolution along future-directed timelike vector fields and even on Hadamard states. These are all local, ultraviolet, effects.Comment: Exposition improved. To appear in Letters to Classical and Quantum Gravity. Eight pp., plain Tex, IOP macro

Fermions and gravitational gyrotropy

In conventional general relativity without torsion, high-frequency gravitational waves couple to the chiral number density of spin one-half quanta: the polarization of the waves is rotated by $2\pi N_5 {\ell_{\rm Pl}^2}$, where $N_5$ is the chiral column density and $\ell_{\rm Pl}$ is the Planck length. This means that if a primordial distribution of gravitational waves with E-E or B-B correlations passed through a chiral density of fermions in the very early Universe, an E-B correlation will be generated. This in turn will give rise to E-B and T-B correlations in the cosmic microwave background (CMB). Less obviously but more primitively, the condition Albrecht called "cosmic coherence" would be violated, changing the restrictions on the class of admissible cosmological gravitational waves. This altered class of waves would, generally speaking, probe earlier physics than do the conventional waves; their effects on the CMB would be most pronounced for low ($\lesssim 100$) multipoles. Rough estimates indicate that if the tensor-to-scalar ratio is less than about $10^{-2}$, it will be hard to constrain a spatially homogeneous primordial $N_5$ by present data.Comment: To appear in PRD. Considerably expanded from the earlier version; numerical results for effects on the CMB are given. The only substantive correction to the earlier version is to the overall sign of the effect. 21 pages, 4 figure