85 research outputs found

### 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

### 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 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

### 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

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