Doug Eardley's Research

Current interests

Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

Eric W. Hirschmann and Douglas M. Eardley
gr-qc/9511052// NSF-ITP-95-154
[Abstract] [Paper] [Figure]

This is an extension of our work (gr-qc/9412066, 9505041, 9506078) on Choptuik scaling for gravitational collapse of scalar fields. The matter model is now two real scalar fields, coupled as a non-linear sigma model. The target space is a 2-space of arbitrary constant curvature -2\kappa. This subsumes our previous work on free complex scalar field (9412066 -- flat target space) and on the axion/dilaton fields of low energy string theory (9505041 with Jim Horne -- target space of unit negative curvature), and is also in part equivalent to work by Steve Liebling at Texas, and work by Choptuik and Liebling, who study a free real scalar field coupled to Brans-Dicke gravity. Closely related work is the recent paper by Hamade, Horne, & Stewart on axiodil collapse, Continuous Self-Similarity and S-Duality (gr-qc/9511024). We investigate existence and stability of continuously self-similar critical solutions as a function of the target space curvature \kappa. The critical exponent \gamma is found to be a strong function of \kappa, further evidence against universality (should any more evidence be needed on this by-now-settled issue). We find a change of stability at kappa=0.075, confirming results of Choptuik and Liebling. The change is found to take the form of a Hopf bifurcation. Above the bifurcation the attractor is the continuously self-similar solution, while below the attractor is the echoing solution (the original choptuon). Further modes go unstable starting around \kappa=-0.1, strongly suggesting that the echoing solution itself may go unstable and bifurcate further. The sequence of continuously self-similar critical solutions appears to terminate at \kappa=-0.6, at least in our method of calculation. It would be very interesting to study the negative \kappa models by numerical relativity, as they may show strongly nonlinear behavior such as further bifurcations of the echoing solution.

Turbulence in accretion disks, with Kevin Miller (UCSB).

We are modelling turbulent dissipation in accretion disks, borrowing some so-called Reynolds-stress models of turbulent viscosity from the fluid dynamics and engineering literature --- the simplest of these is known as the K-\epsilon model. Generalizations to compressible, strongly sheared, rotating, and magnetized flows are necessary in astrophysical applications to cataclysmic variables, x-ray binaries, and active galactic nuclei.

Quantum tunneling of domain walls in the early universe, with Shawn Kolitch (UCSB).

We are reconsidering the origin and evolution of closed, topologically spherical domain walls in the early universe, arising from a broken discrete symmetry. As is well known, a collapsing closed domain wall may thermalize completely, leaving no remnant, or it may produce a black hole by gravitational collapse. However, in the latter case it is not widely appreciated that the closed domain wall need not fall into the spacetime singularity within the black hole. If the wall radius is somewhat larger than the Hubble radius at formation, the domain wall may avoid the spacetime singularity inside the black hole, and then expand indefinitely to create a new, inflating universe within the black hole, in a ``budding-off" process. We argue that this is generic, and gives rise to a new universe dominated by a single closed domain wall. There are several processes by which the closed domain will can ultimately decay and thermalize. In particular we discuss a novel process of quantum tunneling, by which the entire universe eventually undergoes a quantum fluctuation which destroys the wall.

Secular evolution of binary orbits under ablation, with Kaiyou Chen (LANL)

If accretion induced collapse provides a channel for formation of millisecond pulsars, some of spin down power could be used to drive a strong evaporating wind from the surface of the low mass companion. We study evolution of the binary period and the orbital eccentricity of a low mass companion under such ablation. We find conditions under which the companion can escape to infinity after a finite number of orbits, due to runaway growth of orbital eccentricity. The results are applied to three neutron star systems: Radio pulsars PSR 1820-10 and PSR 1257+12, and X-ray pulsar 1E2259+59.

Unitary mixed-state formulation of quantum field theory in the presence of closed timelike curves, with Orlando Warren (UCSB).

A number of people have shown that unitarity suffers a breakdown in quantum field theory, when one tries to turn on interactions in a causality-violating background (in a ``time machine"). We approach this problem by constructing a different free quantum field theory on a causality-violating background, by giving up the assumption that pure states persist. On the contrary, we allow for a model ``time machine" to evolve pure states into mixed states in a unique and well defined manner. Our formulation of field quantum field theory still has a good classical limit when one restricts to coherent states, which do remain pure and coherent, and do not evolve into mixed states. We are able to give a formal, general proof of conservation of probability of interacting quantum field theory in our formulation, and we show that this proof can be implemented through first order in perturbation theory for scalar \lambda\phi^4 theory in our model time machine. Our approach has some aspects in common with previous work of Deutsch, and independent work of Politzer.

Recent papers

Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field

Eric W. Hirschmann & Douglas M. Eardley
gr-qc/9506078 // NSF-ITP-95-58, Physical Review D52, 5850-5856 (1995)
[Abstract] [Paper] [Figure]

Breaking Cosmic Strings without Monopoles

Douglas M. Eardley, Gary T. Horowitz, David A. Kastor & Jennie Traschen
gr-qc/9506041 // NSF-ITP-95-48 // UCSBTH-95-13 // UMHEP-420, Physical Review Letters 75, 3390-3393 (1995)
[Abstract] [Paper]

S-Duality at the Black Hole Threshold in Gravitational Collapse

Douglas M. Eardley, Eric W. Hirschmann & James H. Horne
gr-qc/9505041 // NSF-ITP-95-15 // DAMTP-R95/27, Physical Review D52, R5793-R5797 (1995)
[Abstract] [Paper] [Figure]

Nonlinear Wave Equations for Relativity

Maurice H.P.M. van Putten & Douglas M. Eardley
gr-qc/9505023 // CRSR 1095 // NSF-ITP-95-36, Physical Review D53, 3056-3063 (1996)
[Abstract] [Paper]

Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field

Eric W. Hirschmann & Douglas M. Eardley
gr-qc/9412066 // NSF-ITP-94-119, Physical Review D51, 4198 (1995)
[Abstract] [Paper] [Figures (warning: 212KB .ps file)]

Gravitational Collapse of Vacuum Gravitational Field Configurations

Douglas M. Eardley
gr-qc/9411024 // NSF-ITP-94-47, J. Math. Physics, 36, 3004 (1995).

For an important strengthing of this result see the recent paper by Greg Burnett, Collapsing regions and black hole formation (gr-qc/9508008).
[Abstract] [Paper]

Behavior of Friedmann-Robertson-Walker Cosmological Models in Scalar-Tensor Gravity,

Shawn J. Kolitch & Douglas M. Eardley
gr-qc/9405016 // NSF-ITP-94-45, Annals of Physics 241, 128-151 (1995).
[Abstract] [Paper] [Figures (warning: 1.2Mb .ps file)]

Cosmic Censorship

Douglas M. Eardley
Ann. N.Y. Acad. Sci., 688, 408 (1993).
[Abstract] [Paper] [Postscript]