GRAVITY THEORY SEMINARS 2003
``Lambda < 0 Quantum Gravity in 2+1 Dimensions''
Negative cosmological constant gravity in 2+1 dimensions is known to have black hole solutions. In addition, it has solutions describing pointlike matter: point particles trace a line of conical singularities in spacetime. Few years ago Matschull has shown how a black hole can be created in a process of particle collision. It would be of interest to find the corresponding quantum theory. This would be a theory describing black holes, point particles and processes involving them. It would therefore provide us with a toy model of quantum gravity with all essential elements. We give a sketch of such a theory.
``Nonlinear optics of surface plasmons in nanoholes: similarities with Kaluza-Klein theories''
Surface plasmons are collective excitations of the conductive electrons and the electromagnetic field. They exist in "curved three-dimensional space-times" defined by the shape of the metal-vacuum interface. In many experimental geometries they are weakly coupled to free space photons. Thus, nonlinear optics of surface plasmons may be treated as a field theory in a curved space-time background. For example, a nanohole in a thin metal membrane may be treated as a "wormhole" connecting two "flat" surface plasmon worlds located on the opposite interfaces of the membrane. This point of view allows to justify and explore an analogy between the nonlinear optics of cylindrical surface plasmons of nanowires and nanoholes and the Kaluza-Klein theories.
``UV and IR Modifications of Gravity''
This talk will review recent proposals for consistently modifying general relativity in the infrared, and how they lead to new strong interactions in the ultraviolet. New results presented include the stability of massive gravity as an effective field theory, and a determination of the scale of strong interactions in the model of Dvali, Gabadadze, and Porrati.
``Dynamical Horizons: How Black Holes Grow''
Dynamical horizons, of the type that naturally arise in numerical simulations of black hole evolutions, are considered in full, non-linear general relativity. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local, the energy flux is positive and change in the horizon area is related to these fluxes. The flux formulas also give rise to balance laws analogous to the ones obtained by Bondi and Sachs at null infinity and provide dynamical generalizations of the first and second laws of black hole mechanics. The framework will have applications to mathematics, fundamental physics and and astrophysical numerical relativity.
``Beyond Planck scale constraints on Lorentz violation from the Crab nebula''
The structure of spacetime at the Planck scale may lead to the breakdown of Lorentz invariance, possibly manifesting as modified particle dispersion relations. Current astrophysical observations show that for dispersion modifications to the electron and photon at O(E/E_QG), E_QG must be at or above the Planck scale. In particular, synchrotron emission from the Crab nebula constrains E_QG for subluminal electron modifications to be greater than 4.5 10^27 GeV, an astounding eight orders of magnitude larger than the Planck energy.
``The theorem that violation of CPT implies violation of Lorentz covariance is valid''
First I give a brief summary of the theorem. Then I reformulate the model of the proposed counter example in a transparent way. Using elementary arguments, I show that the claims concerning Lorentz covariance and causality (in the form of locality at spacelike separation) are incorrect. Finally I point out that the specific model that is claimed to violate CPT does not violate CPT.
``Black holes in pp-waves?''
I will mostly summarize the attempts to find asymptotically pp-wave solutions with horizons. I will first show why exact pp-waves can't admit event horizons, then digress into causal structure of pp-waves, and finally discuss construction of asymptotically plane wave black holes.
simulations of binary black hole mergers with the puncture method''
The current numerical predictions for gravitational waves from black hole mergers are based on the so-called puncture method. In this approach the black hole space time is foliated by spatial hypersurfaces that are topologically R3 after treating the coordinate singularities due to compactification analytically. I will discuss the advantages and the limitations of the puncture method for black hole initial data and black hole evolutions.
``Quantum Stress Tensor Fluctuations and their Gravitational Effects''
The problem of the quantum fluctuations of the stress tensor operator will be reviewed. In general the stress tensor correlation function contains singular parts even if the stress tensor operators themselves have been renormalized. These singular parts will be discussed, and it will be argued that only spacetime averages have well-defined fluctuations. Stress tensor flucutations in turn lead to flucutations of the spacetime geometry. Some operational approaches to studying these effect will be discussed. One approach is to examine flucutations in the focusing of a bundle of geodesics using the Raychaudhuri equation. In principle, sufficiently large stress tensor flucutations would produce blurring of the images of distant objects, so observational bounds may be placed on the magnitude of their effects.
``Stochastic gravity: fundamental issues and applications''
We will describe how a stochastic description can be introduced to gain information on quantum properties of open systems. This will then be applied to the case of metric perturbations interacting with quantum matter fields, and some fundamental aspects in that case will be discussed. Finally, possible applications will be described including the formulation of a criterion for the stability of solutions of semiclassical gravity with respect to small quantum corrections, as well as the study of the area fluctuations for black hole horizons.
``Taming the constraints of numerical relativity''
Einstein's equations for general relativity divide into two classes. Evolution equations, which provide time-update information, and constraint equations, which should be satisfied on every spatial slice. My talk will focus on the role that the constraints play in the system of equations, reasons that taming (if not outright controlling) the constraints is a good idea, and methods for taming the constraints in real evolution codes.
``Stochastic gravity (II): applications''
The stochastic gravity formalism will be applied to discuss the stability of semiclassical gravity solutions with respect to small quantum corrections. A sketch on how to apply the formalism to the study of the area fluctuations for black hole horizons will be provided as well.
``Coherent dynamics in atom-field interactions''
Coherent evolution of interacting systems can be the source of unexpected behavior. The best known example is Rabi oscillations of an atom+single mode. The key in that case is entangled evolution of the interacting pair. When the single mode becomes an EMF bath, the coherence of the atom with each mode is "washed out" by the multitude of modes. Many successful theories exploit this "wash out" by partially neglecting system+bath correlations. However, a residual coherence effect can remain, due to the non-zero correlation time. To predict such coherence effects we have focused on the system of a two-level atom interacting with the EMF, in the influence functional formalism. In three applications, which we describe, we find modification from those predictions which neglect system+bath correlations, and in a least one case (correction to the Casimir-Polder retardation force) the modification is measurable.
``Our newly discovered universe''
This will be a summary of cosmological research intended for a general university audience. Observations and their theoretical interpretations, including the recent results of the first year's operation of the NASA observatory WMAP, lead to the conclusion that 99.6% (by weight) of the present Universe was unknown a couple decades ago. The newfound material pervades our own Milky Way, not just other parts of the Universe. The nature and/or mystery of the difficult-to-notice constituents (other than stars and their predecessors and remnants) will be outlined. An attempt will be made to give some senseof the kinds of observations and analyses that lead to the current picture, and of the changes in technology that now allow one to speak of precision cosmology.
``Probing semiclassical analogue gravity in Bose-Einstein condensates with widely tunable interactions''
Bose-Einstein condensates (BEC) have recently been the subject of considerable study as possible analogue models of general relativity. In particular it was shown that the propagation of phase perturbations in a BEC can, under certain conditions, closely mimic the dynamics of scalar quantum fields in curved spacetimes. A varying scattering length in the BEC corresponds to a varying speed of light in the ``effective metric''. Recent experiments have indeed achieved a controlled tuning of the scattering length in Rubidium 85. In this talk I shall discuss the prospects for the use of this particular experimental effect to test some of the predictions of semiclassical quantum gravity, for instance, particle production in an expanding universe.
``Probing extra dimensions down to a few micrometers using a superconducting accelerometer''
In string theories, extra dimensions must be compactified. The possibility that gravity can have large radii of compactification leads to a violation of the inverse square law at submillimeter distances. We are preparing a null test of Newton's law with a resolution of one part in one thousand at 100 µm, which will probe the extra dimensions down to a few micrometers. The experiment will be cooled to 4.2 K. To minimize Newtonian errors, a near null source in the form of a circular disk of large diameter-to-thickness ratio is employed. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a nominal distance of 100 µm. The signal is detected by a superconducting differential accelerometer. We are also designing a space experiment which will improve the resolution by more than two orders of magnitude over the ground experiment.
``How uncertain is the standard cosmological vacuum?''
I discuss the minimal theoretical uncertainty in inflationary curvature fluctuations due to the nonuniqueness of the vacuum, even in the absence of any trans-Planckian uncertainties or effective field theory cutoff related effects.
``Light Cone Estimates for Einstein's Equations''
During the early 1980's Douglas Eardley and I derived some light cone estimates for the Yang-Mills (-Higgs) equations in Minkowski spacetime which showed that the Yang-Mills curvature could not blow up point-wise in a finite time. From this it was easy to show that the Yang-Mills potential (together with the Higgs field), when expressed in a suitable gauge, could not blow up at all and hence that Yang-Mills-Higgs fields are globally defined on Minkowski space. Our aim had been to lay the groundwork for a similar study of the Einstein equations even though strict global existence can of course not be true in this case. Inspired by recent results of Chrusciel and Shatah on Yang-Mills fields in a curved background space-time I have been encouraged to return to this problem and analyze the extent to which point-wise spacetime curvature is controlled by the L2-norm of curvature (essentially the Bel-Robinson energy). A key step in the derivation of light cone estimates is to show that, in a suitably chosen frame, the connection and frame fields can be written explicitly in terms of curvature. An open question involves the contribution of the "tail term" in the fundamental solution to the tensor wave equation for curvature to the light cone estimates.
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