Scientific Series

After prodigious work over several decades, binary black hole mergers can now be simulated in fully nonlinear numerical relativity. However, these simulations are still restricted to mass ratios q = m2/m1 > 1/10, initial spins a/M < 0.9, and initial separations r/M < 10. Fortunately, analytical techniques like black-hole perturbation theory and the post-Newtonian approximation allow us to study much of this region in parameter space that remains inaccessible to numerical relativity. I will use black-hole perturbation theory to establish a fundamental upper limit to the final spin that can be attained through binary mergers, and show how this limit can be used to improve predictions of final spins for finite mass ratios as well. I will also show that post-Newtonian inspirals between 1000 M < r < 10 M can align or anti-align black hole spins with each other, dramatically changing the distributions of final spins and recoil velocities that would be expected in astrophysical black hole mergers.

For the past century, there has been much discussion and debate about the equations of motion satisfied by a classical point charge when the effects of its own electromagnetic field are taken into account. Derivations by Abraham (1903), Lorentz (1904), Dirac (1938) and others suggest that the "self-force" (or "radiation reaction force") on a point charge is given in the non-relativistic limit by a term proportional to the time derivative of the acceleration of the charge. However, the resulting equations of motion then become third order in time, and they admit highly unphysical "runaway" solutions. During the past century, there also has been much discussion and debate about the interpretation of these equations of motion and the conditions that can/should be imposed to eliminate the runaway behavior. We argue that the above difficulties stem from that fact that the usual notion of a point charge is mathematically ill defined. However, a mathematically rigorous notion of a point charge arises in a perturbative description of a body if one considers a limit wherein not only the size of a body but its charge and mass go to zero in an asymptotically self-similar manner. We show how the Abraham-Lorentz-Dirac self-force then arises in a perturbative description of the body's motion, but does not give rise to runaway behavior. As a biproduct of this work, we also rigorously derive dipole forces and resolve some paradoxes of elementary physics, such as how a magnetic dipole placed in a non-uniform magnetic field can gain kinetic energy despite the fact that the magnetic field can "do no work" on the body.

Recently, a new class of topological states has been theoretically predicted and experimentally realized. The topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction[1] of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation[2]. The edge states of the QSH state supports fractionally charged excitations[3]. The QSH effect can be generalized to three dimensions as the topological magneto-electric effect (TME) of the topological insulators[4]. Bi2Te3, Bi2Se3 and Sb2Te3 are theoretically predicted to be topological insulators with a single Dirac cone on the surface[5]. I shall present a realistic experimental proposals to observe the magnetic monopoles on the surface of topological insulators[6]. Topological superconductors and superfluid have been theoretically proposed recently [7], in both two and three dimensions. They have a full pairing gap in the bulk, and their mean field Hamiltonian look identical to that of the topological insulators. However, the gapless surface states consists of a single Majorana cone, containing only half the degree of freedom compared to the single Dirac cone on the surface of a topological insulators. I shall discuss their physics properties and the search for these novel states in real materials. [1] A. Bernevig, T. Hughes and S. C. Zhang, Science, 314, 1757, (2006) [2] M. Koenig et al, Science 318, 766, (2007) [3] J. Maciejko, Chaoxing Liu, Yuval Oreg, Xiao-Liang Qi, Congjun Wu, and Shou-Cheng Zhang, , Phys. Rev. Lett. {\bf 102}, 256803 (2009). [4] Xiao-Liang Qi, Taylor Hughes and Shou-Cheng Zhang, Phys. Rev B. 78, 195424 (2008) [5] Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang, and Shou-Cheng Zhang, Nature Physics 5, 438 (2009). [6] Xiao-Liang Qi, Run-Dong Li, Jiadong Zang and Shou-Cheng Zhang, Science 323, 1184 (2009). [7] Xiao-Liang Qi, Taylor L. Hughes, Srinivas Raghu and Shou-Cheng Zhang, Phys. Rev. Lett. 102, 187001 (2009)

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. With very little structural effort (i.e. in very abstract terms) and in a very short time this categorical quantum mechanics research program has reproduced a surprisingly large fragment of quantum theory. Philosophically speaking, this framework shifts the conceptual focus from `material carriers' such as particles, fields, or other `material stuff', to `logical flows of information', by mainly encoding how things stand in relation to each other. These relations could, for example, be induced by operations. Composition of these relations is the carrier of all structure. Thus far the causal structure has been treated somewhat informally within this approach. In joint work with my student Raymond Lal, by restricting the capabilities to compose, we were able to formally encode causal connections. We call the resulting mathematical structure a CauCat, since it combines the symmetric monoidal stricture with Sorkin's CauSets within a single mathematical concept. The relations which now respect causal structure are referred to as processes, which make up the actual `happenings'. As a proof of concept, we show that if in a quantum teleportation protocol one omits classical communication, no information is transfered. We also characterize Galilean theories. Classicality is an attribute of certain processes, and measurements are special kinds of processes, defined in terms of their capabilities to correlate other processes to these classical attributes. So rather than quantization, what we do is classicization within our universe of processes. We show how classicality and the causal structure are tightly intertwined. All of this is still very much work in progress!

We apply newly-developed techniques for studying perturbative scattering amplitudes to gauge theories with matter. It is well known that the N=4 SYM theory has a very simple S-matrix; do other gauge theories see similar simplifications in their S-matrices? It turns out the one-loop gluon S-matrix simplifies if the matter representations satisfy some group theoretic constraints. In particular, these constraints can be expressed as linear Diophantine equations involving the higher order Indices (or higher-order Casimirs) of these representations. We solve these constraints to find examples of theories whose gluon scattering amplitudes are as simple as those of the N=4 theory. This class includes the N=2, SU(K) theory with a symmetric and anti-symmetric tensor hypermultiplet. Non-supersymmetric theories with appropriately tuned matter content can also see remarkable simplifications. We find an infinite class of non-supersymmetric amplitudes that are cut-constructible even though naive power counting would suggest the presence of rational remainders.

Gamma rays from WIMP annihilation are an important signal through which we search for non-gravitational interactions of dark matter. In particular, lines in the energy spectrum of gamma rays provide a signal which is difficult for conventional astrophysics to fake, and are thus promising despite the fact that such lines are generically expect to be suppressed, arising from one loop processes. I will discuss two theories which have an interesting family of gamma ray lines and discuss how such lines can reveal information about the WIMPs and the dark sector.

A quantum theory of gravity implies a quantum theory of geometries. To this end we will introduce different phases spaces and choices for the space of discretized geometries. These are derived through a canonical analysis of simplicity constraints - which are central for spin foam models - and gluing constraints. We will discuss implications for spin foam models and map out how to obtain a path integral quantization starting from a canonical quantization.

Gas accretion onto black holes is thought to power some of the most energetic astrophysical phenomena observed. Black hole accretion disks are efficient engines for converting binding energy into light, and for launching relativistic unbound flows (jets) such as in gamma ray bursts, microquasars and radio-loud active galactic nuclei (AGN). Some systems individually exhibit a wide variety of spectral and bolometric states while others remain remarkably predictable. As their brightest emission usually emanates near the black hole's event horizon, they serve as excellent environments for exploring different theories of gravity or for constraining the black hole's geometry. In this talk I will explain how investigators use modern general relativistic magnetohydrodynamic computer simulations to understand accretion observations and probe the strong-field regime of gravity. In particular, I will focus on three topics. First, I will describe how dynamical models of the accretion flow around Sagittarius A*, the supermassive black hole at the center of our galaxy, can help us predict what we will see when observations at the sub-horizon scale are made soon for the first time. Second, I will explain recent developments in simulating cooled thin disks and how their results may affect estimates of black hole spin from the disks' thermal spectra. Last, I will describe how temporal variability analysis of our dynamical simulations can offer insight into the common behavior seen in high-energy emission from black holes with masses of 10 solar masses to a billion solar masses.

Diffeomorphism symmetry is the underlying symmetry of general relativity and deeply intertwined with its dynamics. The notion of diffeomorphism symmetry is however obscured in discrete gravity, which underlies most of the current quantum gravity models. We will propose a notion of diffeomorphism symmetry in discrete models and find that such a symmetry is weakly broken in many models. This is connected to the problem of finding a consistent canonical dynamics for discrete gravity. Finally we will discuss methods to construct models with exact symmetries and elaborate on the connection between diffeomorphism symmetry and triangulation independence.

The hot, gaseous atmospheres of galaxies and clusters of galaxies are repositories for the energy output from accreting, supermassive black holes located in the nuclei of galaxies. X-ray observations show that star formation fueled by gas condensing out of hot atmospheres is strongly suppressed by feedback from active galactic nuclei (AGN). This mechanism may solve several outstanding problems in astrophysics, including the numbers of luminous galaxies and their colors, and the excess number of hot baryons in the Universe. The most energetic AGN outbursts may be powered by rapidly-spinning, ultra-massive black holes.

Stellar evolution from a protostar to neutron star is of one of the best studied subjects in modern astrophysics. Yet, it appears that there is still a lot to learn about the extreme conditions where the fundamental particle physics meets strong gravity regime. After all of the thermonuclear fuel is spent, and after the supernova explosion, but before the remaining mass crosses its own Schwarzschild radius, the temperature of the central core of the star might become higher than the electroweak symmetry restoration temperature. The source of energy, which can at least temporarily balance gravity, are baryon number violating instanton processes which are basically unsuppressed at temperatures above the electroweak scale. We constructed a solution to the Oppenheimer-Volkoff equation which describes such a star. The energy release rate is enormous at the core, but gravitational redshift and the enhanced neutrino interaction cross section at these densities make the energy release rate moderate at the surface of the star. The lifetime of this new quasi-equilibrium can be more than ten million years, which is long enough to represent a new stage in the evolution of a star.