GRAVITY THEORY SEMINARS 2010
"General Relativity on trial: Gravitational waves and the parameterized post-Einstienian framework"
"Post-Newtonian corrections from effective field theory approach"
The effective field theory approach to the post-Newtonian formalism of general relativity will be introduced. I will review the main ideas of effective field theory, and demonstrate how the effective action is constructed for each scale in the problem of a binary system. I will then consider basic examples for the use of the EFT approach. Recent applications will be reviewed, from such that do not involve the PN approximation, to self-gravitating spinning objects in compact binaries - the focus of my recent works.
"The probability distribution for quantum stress tensor fluctuations"
In this talk, I will first review some propertites of the renormalized expectation values of the quantum stress tensor. These expectation values can violate classical energy conditions and exhibit negative energy density. The magnitude and duration of the negative energy density is constrained by quantum inequalities. I will next review selected aspects of quantum stress tensor fluctuations and their potential physical effects. Finally, I will report some recent work on the probability distribution for stress tensor fluctuations. It can be shown that the vacuum probability distribution for the energy density averaged with a sampling function in time is necessarily a skewed distribution with a finite lower cutoff and an infinite positive tail. Furthermore, this cutoff is at the quantum inequality bound on expectation values. An explicit result for the case of a massive scalar field in two dimensional flat spacetime will be discussed. In this case, most energy density fluctuations are negative but are counterbalanced by rarer but larger positive fluctuations. Some ongoing work in four dimensions and its possible applications will be discussed.
"Why LIGO results are already interesting"
LIGO (the Laser Interferometer Gravitational-wave Observatory) has finished its long run at initial design sensitivity, and we are analyzing the data for the next few years while the instruments are upgraded. Just before that run, I pointed out that rotating neutron stars might be strong enough sources of periodic gravitational waves to be detected now rather than after years of upgrades. A detection could provide unique information on the properties of nuclear matter. Even without a detection, LIGO now can place direct upper limits on gravitational waves from several types of neutron stars which beat the indirect upper limits derived from photon astronomy and particle theory. Since most LIGO searches for signals from neutron stars are computationally limited, photon astronomy can provide information on where to look which directly increases LIGO's science reach. I survey the issues associated with LIGO searches for periodic signals and point to the astrophysical payoffs and astronomical interactions.
"TeV physics and conformality"
I will review the possible role of conformal symmetry in developing viable theories of new physics at the TeV scale and beyond. Since strongly coupled gauge theories may describe this new physics, it is natural to employ lattice-based numerical simulations as in QCD. I will describe recent work along these lines and discuss prospects for future progress.
"Radiative effects from effective field theory"
The effective field theory description yields a systematic treatment of gravitational bound states such as binary systems. My talk will review the effective field theory setup and describe recent progress in the radiation sector of the theory. More specifically, I will discuss how the power emitted in gravitational waves is calculated and describe the matching procedure to obtain the multipole moments. When non-linearities are considered in the radiation effective theory, interesting effects such as tail effects enter and give rise to divergences, logarithms, etc. Both infrared and ultraviolet divergences arise and we show how to disentangle and treat these. We use the renormalization group equations to resum the ultraviolet logarithms.
"The stability of the Euler-Einstein system with a positive cosmological constant"
The Euler-Einstein system models the evolution of a
dynamic spacetime containing a perfect fluid. In this talk, I will discuss the
nonlinear stability of the Friedmann-Lemaitre-Robertson-Walker family of
background cosmological solutions to the Euler-Einstein system in 1+3
dimensions with a positive cosmological constant \Lambda. The background
solutions describe an initially uniform quiet fluid of positive energy density
evolving in a spacetime undergoing accelerated expansion. The main result is a
proof that under the equation of state p = c_s^2 \rho, 0 < c_s^2 < 1/3,
the background solutions are globally future-stable under small perturbations.
In particular, the perturbed spacetimes, which have the topological structure
[0,\infty) \times T^3, are future causally
geodesically complete. The results I will present are extensions of previous
joint work with Igor Rodnianski, which covered the case of an irrotational
fluid, and of work by Ringstrom on the Einstein-non-linear-scalar-field system.
Mathematically, the main result is a proof of small-data global existence for a
modified version of the Euler-Einstein equations that are equivalent to the
un-modified equations. The proof is based on the vector field method of
Christodoulou and Klainerman.
It is of special interest to note that the behavior of the fluid in an exponentially expanding spacetime differs drastically from the case of flat spacetime. More specifically, Christodoulou has recently shown that on the Minkowski space background, data arbitrarily close to that of an initially quiet uniform fluid state can lead to solutions that form shocks. In view of this fact, we remark that the proof of our result can be used to show the following: exponentially expanding spacetime backgrounds can prevent the formation of shocks.
"Cosmic rays and the quest for new physics"
Recent cosmic ray data, notably from the Pamela and Fermi satellites, indicate that previously unaccounted-for powerful sources in the Galaxy inject high-energy electrons and positrons. Interestingly, this new source class might be related to new fundamental particle physics, and specifically to pair-annihilation or decay of galactic dark matter. I will discuss how this exciting scenario is constrained by Fermi gamma-ray observations, and which astrophysical source counterparts could also be responsible for the high-energy electron-positron excess. In particular, I will review the case for nearby mature pulsars, and the impact of newly discovered radio-quiet pulsars that pulsate in gamma rays. While high-energy electron-positron measurements sample local (closer than 1 kpc) cosmic rays, diffuse radio and gamma-ray emission informs us about the global galactic cosmic ray population. I will thus offer a few thoughts on recent claims involving the detection of diffuse radio ("WMAP haze") and gamma-ray ("Fermi haze") emissions and on implications for the quest for New Physics.
"Modeling the inspiral and merger of binary neutron stars"
Investigating the final evolution of neutron star binaries promises to be particularly rewarding. These systems are in fact excellent sources of gravitational waves, they are thought to be behind the powerful engines powering short gamma-ray bursts, and they can unveil the behaviour of matter at extreme densities and temperatures. I will review the present understanding in the modeling of the inspiral and merger of binary neutron stars in full general relativity, underlining the considerable recent progress both in hydrodynamics and in MHD. Finally, I will discuss the steps that still need to be taken to use this progress to model the central engine of short gamma-ray bursts.
"An introduction to the reduced basis method"
Parameterized partial differential equations (PDEs) arise
in many fields of engineering and computational science. Solving the PDEs for a
fixed parameter value is well studied and analyzed in most cases. The
computational complexity is unnecessarily high while solving for a large number
of parameter values in a many-query context for optimization problems, model
calibration, inverse problems, etc. This mini-course gives an introduction to
the Reduced Basis Method (RBM), which is designed to solve such problems
efficiently for a large number of parameter values.
Organizers: Ricardo Nochetto (MATH and IPST) and Manuel Tiglio (PHYS and CSCAMM)
"High-order accurate modeling of extreme mass ratio binaries"
In the first half of the talk I will present a discontinuous Galerkin (dG) method for modeling an EMRB system in the context of black hole perturbation theory. dG methods provide excellent phase resolution and a natural setting for the distributional solutions common in EMRB modeling. The construction of radiation boundary conditions will be covered and I will highlight a few results from our code. In the second half of the talk I will discuss the development of static junk solutions which arise from the specification of trivial initial data. An analytic form of these junk solutions are found in terms of hypergeometric functions. I will conclude the talk by considering their impact on computed metric perturbations and waveforms, and how to remove them by a simple modification of the source terms.
"'No success like failure...': Einstein's quest for general relativity"
In 1907, Einstein set out to fully relativize all motion,
uniform or accelerated. During the decade that followed, he tried four
different strategies to eradicate absolute motion from physics, all of which
failed. His frustrations during this quest for general relativity were many. He
had to readjust his approach and his objectives at almost every step along the
way. He got himself seriously confused at times, especially over the status of
general covariance. He fooled himself with fallacious arguments and sloppy
calculations. And he later allegedly called the introduction of the
cosmological constant, part and parcel of his fourth and final attempt, the
biggest blunder of his career. There is an uplifting moral to this somber tale.
Although he never reached his orginal destination, the bounty of Einstein's
thirteen-year odyssey was rich by any measure. Most importantly, it led him to
a new theory of gravity that is still with us today. In this talk, I will
examine the different ways in which Einstein tried to relativize arbitrary motion
and I explain how and why these attempts failed. I will then address the
question of how to make sense of the success of Einstein's theory of gravity
given that some of the main considerations that led him to it turned out to be
Based on my contribution to the Cambridge Companion to Einstein (in preparation): http://www.tc.umn.edu/~janss011/pdf%20files/QuestforGR.pdf
"Jordan and the wave-particle duality of light"
In 1909, Einstein derived a formula for the mean-square
energy fluctuation in black-body radiation. This
formula is the sum of a wave term and a particle term. In a famous joint paper
with Born and Heisenberg submitted in late 1925, Pascual Jordan used the new
matrix mechanics to show that one recovers both these terms in a simple model
of quantized waves. This result not only solved Einstein's puzzle about the
wave-particle duality of light, it also provided striking evidence for matrix
mechanics and a strong argument for field quantization. After reviewing
Einstein's early work on fluctuations in black-body
radiation, I present Jordan's result and the curious story of its reception.
Rather than being hailed as a major contribution to quantum theory, Jordan's
result met mostly with skepticism, even from his co-authors. I will argue that
the skeptics were wrong.
Based on: A. Duncan and M. Janssen, "Pascual Jordan's resolution of the conundrum of the wave-particle duality of light." Studies in History and Philosophy of Modern Physics 39 (2008): 634-666. http://www.tc.umn.edu/~janss011/pdf%20files/fluctuations.pdf
"Quantum nature of the Big Bang in simple models"
According to General Relativity, space-time ends at singularities and classical physics just stops. In particular, the Big Bang is regarded as The Begining. However, General Relativity is incomplete because it ignores quantum effects. Through simple models, I will illustrate how the quantum nature of space-time geometry resolves the Big Bang singularity. Quantum physics does not stop there. Indeed, quantum space-times can be vastly larger than what General Relativity had us believe. I will discuss illustrative consequences of this new Planck scale physics.
"Bouncing alternatives to inflation"
Although inflation is, by far, the best known mechanism to explain the observed properties of our Universe, there is still some room for alternative models, most of which imply a contracting phase preceeding the current expanding one. Both phases are connected by a bounce at which the expansion rate must vanish. General relativity can only produce such a phase provided the spatial curvature is positive, in contradiction with the current observations. I will discuss the lines along which one can modify either the matter or the gravity sector (or both) in order to implement a bounce, and show the generic observable cosmological consequences it can induce, in particular in the microwave background.
In this talk I first argue that compactified string theories with broken supersymmetry and with stabilized moduli generically have one or more moduli with masses of order the gravitino mass or less. Then cosmological constraints imply the gravitino and moduli masses are of order 30 TeV or heavier, which implies the universe has a non-thermal cosmological history. This in turn suggests that the LSP is wino-like, predicting in particular a signal for galactic positrons and antiprotons consistent with that seen by the PAMELA satellite, and interesting LHC signals.
Wednesday, Sep 15, 3:00 pm, Room 4102
Aron Wall University of Maryland
Normally the entropy of an open system can decrease if entropy flows out of it. The region outside of a black hole seems to be an exception—its entropy never decreases, so long as one assigns to the horizon an area proportional to its event horizon. For a long time, this astonishing result has only been shown for quantum fields that are in an approximately steady state. I will describe a new proof of the generalized second law for semiclassical, rapidly-changing horizons. The reason it works is that the horizon is invariant under a larger symmetry group than the rest of the spacetime.
Sep 4, 3:15 pm, Room 4102
Shimon Rubin, Ben-Gurion University, Israel
Constant shift in the Einstein-Hilbert Lagrangian is a symmetry of the Normalized General Relativity action. The theory offers a simple resolution to the first cosmological constant puzzle. Unfortunately, standard Friedmann-Robertson-Walker cosmology cannot be directly addressed within the framework of such a theory because a perfect fluid energy-momentum tensor is not derivable from a matter Lagrangian. However, this technical difficulty can be effectively bypassed at the minisuperspace level, where we prove that (i) If matter is attractive then the Universe cannot be closed, and reassure that (ii) The accompanying cosmological constant generically vanishes. Interestingly, the theory also allows for non-generic solutions with non vanishing cosmological constant, which are associated with Einstein static closed and Eddington-Lemaitre universes.
Last updated: January 24, 2009
Send your comments to: Chad Galley