# I. Anderson - Utah State University

## Contact Details

NameI. Anderson |
||

AffiliationUtah State University |
||

CityLogan |
||

CountryUnited States |
||

## Pubs By Year |
||

## External Links |
||

## Pub CategoriesMathematics - Differential Geometry (11) General Relativity and Quantum Cosmology (7) Mathematical Physics (6) Mathematics - Mathematical Physics (6) High Energy Physics - Theory (5) Physics - Materials Science (3) High Energy Physics - Phenomenology (2) High Energy Physics - Experiment (2) Physics - Instrumentation and Detectors (2) Physics - Strongly Correlated Electrons (1) Mathematics - Classical Analysis and ODEs (1) Computer Science - Robotics (1) Physics - Soft Condensed Matter (1) |

## Publications Authored By I. Anderson

The conformal Fefferman-Graham ambient metric construction is one of the most fundamental constructions in conformal geometry. It embeds a manifold with a conformal structure into a pseudo-Riemannian manifold whose Ricci tensor vanishes up to a certain order along the original manifold. Despite the general existence result of such ambient metrics by Fefferman and Graham, not many examples of conformal structures with Ricci-flat ambient metrics are known. Read More

We study a geometry associated with rank 3 distributions in dimension 8, whose symbol algebra is constant and has a simple Lie algebra sp(3,R) as Tanaka prolongation. We restrict our considerations to only those distributions that are defined in terms of a systems of ODEs of the form $\dot{z}_{ij}=\frac{\partial^2 f(\dot{x}_1,\dot{x}_2)}{\partial \dot{x}_i\partial \dot{x}_j}$, $i\leq j=1,2$. For them we built the full system of local differential invariants, by solving an equivalence problem a'la Cartan, in the spirit of his 1910's five variable paper. Read More

Biomimetic entirely soft robots with animal-like behavior and integrated artificial nervous systems will open up totally new perspectives and applications. However, until now all presented studies on soft robots were limited to partly soft designs, since all designs at least needed conventional, stiff, electronics, to sense, process signals and activate actuators. We present the first soft robot with integrated artificial nervous system entirely made of dielectric elastomers - and without any conventional stiff electronic parts. Read More

A dielectric elastomer generator (DEG) can be used for converting mechanical energy from natural motion sources such as walking, waves, trees etc, into electrical energy. A DEG is comprised of a soft and flexible Dielectric Elastomer capacitor (DE), a Priming Circuit (PC), which transfers high potential charge onto/off the DE electrodes, and a power extraction circuit which harvests the generated power. To generate power, the PC must charge and discharge the DE in synchronization with the DE's capacitance change. Read More

In this paper we describe a stretchable solid-state electronic switching material that operates at high voltage potentials, as well as a switch material benchmarking technique that utilizes a modular dielectric elastomer (artificial muscle) ring oscillator. The solid-state switching material was integrated into our oscillator, which self-started after 16s and performed 5 oscillations at a frequency of 1.05Hz with 3. Read More

**Authors:**W. Adam, T. Bergauer, M. Dragicevic, M. Friedl, R. Fruehwirth, M. Hoch, J. Hrubec, M. Krammer, W. Treberspurg, W. Waltenberger, S. Alderweireldt, W. Beaumont, X. Janssen, S. Luyckx, P. Van Mechelen, N. Van Remortel, A. Van Spilbeeck, P. Barria, C. Caillol, B. Clerbaux, G. De Lentdecker, D. Dobur, L. Favart, A. Grebenyuk, Th. Lenzi, A. Léonard, Th. Maerschalk, A. Mohammadi, L. Perniè, A. Randle-Conde, T. Reis, T. Seva, L. Thomas, C. Vander Velde, P. Vanlaer, J. Wang, F. Zenoni, S. Abu Zeid, F. Blekman, I. De Bruyn, J. D'Hondt, N. Daci, K. Deroover, N. Heracleous, J. Keaveney, S. Lowette, L. Moreels, A. Olbrechts, Q. Python, S. Tavernier, P. Van Mulders, G. Van Onsem, I. Van Parijs, D. A. Strom, A. Caudron, L. Ceard, B. De Callatay, C. Delaere, T. Du Pree, L. Forthomme, A. Giammanco, J. Hollar, P. Jez, D. Michotte, C. Nuttens, L. Perrini, D. Pagano, L. Quertenmont, M. Selvaggi, M. Vidal Marono, N. Beliy, T. Caebergs, E. Daubie, G. H. Hammad, J. Härkönen, T. Lampén, P. -R. Luukka, T. Mäenpää, T. Peltola, E. Tuominen, E. Tuovinen, P. Eerola, T. Tuuva, G. Beaulieu, G. Boudoul, C. Combaret, D. Contardo, G. Gallbit, N. Lumb, H. Mathez, L. Mirabito, S. Perries, D. Sabes, M. Vander Donckt, P. Verdier, S. Viret, Y. Zoccarato, J. -L. Agram, E. Conte, J. -Ch. Fontaine, J. Andrea, D. Bloch, C. Bonnin, J. -M. Brom, E. Chabert, L. Charles, Ch. Goetzmann, L. Gross, J. Hosselet, C. Mathieu, M. Richer, K. Skovpen, C. Autermann, M. Edelhoff, H. Esser, L. Feld, W. Karpinski, K. Klein, M. Lipinski, A. Ostapchuk, G. Pierschel, M. Preuten, F. Raupach, J. Sammet, S. Schael, G. Schwering, B. Wittmer, M. Wlochal, V. Zhukov, C. Pistone, G. Fluegge, A. Kuensken, M. Geisler, O. Pooth, A. Stahl, N. Bartosik, J. Behr, A. Burgmeier, L. Calligaris, G. Dolinska, G. Eckerlin, D. Eckstein, T. Eichhorn, G. Fluke, J. Garay Garcia, A. Gizhko, K. Hansen, A. Harb, J. Hauk, A. Kalogeropoulos, C. Kleinwort, I. Korol, W. Lange, W. Lohmann, R. Mankel, H. Maser, G. Mittag, C. Muhl, A. Mussgiller, A. Nayak, E. Ntomari, H. Perrey, D. Pitzl, M. Schroeder, C. Seitz, S. Spannagel, A. Zuber, H. Biskop, V. Blobel, P. Buhmann, M. Centis-Vignali, A. -R. Draeger, J. Erfle, E. Garutti, J. Haller, M. Hoffmann, A. Junkes, T. Lapsien, S. Mättig, M. Matysek, A. Perieanu, J. Poehlsen, T. Poehlsen, Ch. Scharf, P. Schleper, A. Schmidt, V. Sola, G. Steinbrück, J. Wellhausen, T. Barvich, Ch. Barth, F. Boegelspacher, W. De Boer, E. Butz, M. Casele, F. Colombo, A. Dierlamm, R. Eber, B. Freund, F. Hartmann, Th. Hauth, S. Heindl, K. -H. Hoffmann, U. Husemann, A. Kornmeyer, S. Mallows, Th. Muller, A. Nuernberg, M. Printz, H. J. Simonis, P. Steck, M. Weber, Th. Weiler, A. Bhardwaj, A. Kumar, A. Kumar, K. Ranjan, H. Bakhshiansohl, H. Behnamian, M. Khakzad, M. Naseri, P. Cariola, G. De Robertis, L. Fiore, M. Franco, F. Loddo, G. Sala, L. Silvestris, D. Creanza, M. De Palma, G. Maggi, S. My, G. Selvaggi, S. Albergo, G. Cappello, M. Chiorboli, S. Costa, F. Giordano, A. Di Mattia, R. Potenza, M. A. Saizu, A. Tricomi, C. Tuvè, G. Barbagli, M. Brianzi, R. Ciaranfi, C. Civinini, E. Gallo, M. Meschini, S. Paoletti, G. Sguazzoni, V. Ciulli, R. D'Alessandro, S. Gonzi, V. Gori, E. Focardi, P. Lenzi, E. Scarlini, A. Tropiano, L. Viliani, F. Ferro, E. Robutti, M. Lo Vetere, S. Gennai, S. Malvezzi, D. Menasce, L. Moroni, D. Pedrini, M. Dinardo, S. Fiorendi, R. A. Manzoni, P. Azzi, N. Bacchetta, D. Bisello, M. Dall'Osso, T. Dorigo, P. Giubilato, N. Pozzobon, M. Tosi, A. Zucchetta, F. De Canio, L. Gaioni, M. Manghisoni, B. Nodari, V. Re, G. Traversi, D. Comotti, L. Ratti, G. M. Bilei, L. Bissi, B. Checcucci, D. Magalotti, M. Menichelli, A. Saha, L. Servoli, L. Storchi, M. Biasini, E. Conti, D. Ciangottini, L. Fanò, P. Lariccia, G. Mantovani, D. Passeri, P. Placidi, M. Salvatore, A. Santocchia, L. A. Solestizi, A. Spiezia, K. Androsov, P. Azzurri, S. Arezzini, G. Bagliesi, A. Basti, T. Boccali, F. Bosi, R. Castaldi, A. Ciampa, M. A. Cioccid, R. Dell'Orso, G. Fedi, A. Giassi, M. T. Grippod, T. Lomtadze, G. Magazzu, E. Mazzoni, M. Minuti, A. Moggi, C. S. Moond, F. Morsani, F. Palla, F. Palmonari, F. Raffaelli, A. Savoy-Navarro, A. T. Serban, P. Spagnolo, R. Tenchini, A. Venturi, P. G. Verdini, L. Martini, A. Messineo, A. Rizzi, G. Tonelli, F. Calzolari, S. Donato, F. Fiori, F. Ligabue, C. Vernieri, N. Demaria, A. Rivetti, R. Bellan, S. Casasso, M. Costa, R. Covarelli, E. Migliore, E. Monteil, M. Musich, L. Pacher, F. Ravera, A. Romero, A. Solano, P. Trapani, R. Jaramillo Echeverria, M. Fernandez, G. Gomez, D. Moya, F. J. Gonzalez Sanchez, F. J. Munoz Sanchez, I. Vila, A. L. Virto, D. Abbaneo, I. Ahmed, E. Albert, G. Auzinger, G. Berruti, G. Bianchi, G. Blanchot, H. Breuker, D. Ceresa, J. Christiansen, K. Cichy, J. Daguin, M. D'Alfonso, A. D'Auria, S. Detraz, S. De Visscher, D. Deyrail, F. Faccio, D. Felici, N. Frank, K. Gill, D. Giordano, P. Harris, A. Honma, J. Kaplon, A. Kornmayer, L. Kottelat, M. Kovacs, M. Mannelli, A. Marchioro, S. Marconi, S. Martina, S. Mersi, S. Michelis, M. Moll, A. Onnela, T. Pakulski, S. Pavis, A. Peisert, J. -F. Pernot, P. Petagna, G. Petrucciani, H. Postema, P. Rose, M. Rzonca, M. Stoye, P. Tropea, J. Troska, A. Tsirou, F. Vasey, P. Vichoudis, B. Verlaat, L. Zwalinski, F. Bachmair, R. Becker, L. Bäni, D. di Calafiori, B. Casal, L. Djambazov, M. Donega, M. Dünser, P. Eller, C. Grab, D. Hits, U. Horisberger, J. Hoss, G. Kasieczka, W. Lustermann, B. Mangano, M. Marionneau, P. Martinez Ruiz del Arbol, M. Masciovecchio, L. Perrozzi, U. Roeser, M. Rossini, A. Starodumov, M. Takahashi, R. Wallny, C. Amsler, K. Bösiger, L. Caminada, F. Canelli, V. Chiochia, A. de Cosa, C. Galloni, T. Hreus, B. Kilminster, C. Lange, R. Maier, J. Ngadiuba, D. Pinna, P. Robmann, S. Taroni, Y. Yang, W. Bertl, K. Deiters, W. Erdmann, R. Horisberger, H. -C. Kaestli, D. Kotlinski, U. Langenegger, B. Meier, T. Rohe, S. Streuli, P. -H. Chen, C. Dietz, U. Grundler, W. -S. Hou, R. -S. Lu, M. Moya, R. Wilken, D. Cussans, H. Flacher, J. Goldstein, M. Grimes, J. Jacob, S. Seif El Nasr-Storey, J. Cole, P. Hobson, D. Leggat, I. D. Reid, L. Teodorescu, R. Bainbridge, P. Dauncey, J. Fulcher, G. Hall, A. -M. Magnan, M. Pesaresi, D. M. Raymond, K. Uchida, J. A. Coughlan, K. Harder, J. Ilic, I. R. Tomalin, A. Garabedian, U. Heintz, M. Narain, J. Nelson, S. Sagir, T. Speer, J. Swanson, D. Tersegno, J. Watson-Daniels, M. Chertok, J. Conway, R. Conway, C. Flores, R. Lander, D. Pellett, F. Ricci-Tam, M. Squires, J. Thomson, R. Yohay, K. Burt, J. Ellison, G. Hanson, M. Malberti, M. Olmedo, G. Cerati, V. Sharma, A. Vartak, A. Yagil, G. Zevi Della Porta, V. Dutta, L. Gouskos, J. Incandela, S. Kyre, N. McColl, S. Mullin, D. White, J. P. Cumalat, W. T. Ford, A. Gaz, M. Krohn, K. Stenson, S. R. Wagner, B. Baldin, G. Bolla, K. Burkett, J. Butler, H. Cheung, J. Chramowicz, D. Christian, W. E. Cooper, G. Deptuch, G. Derylo, C. Gingu, S. Gruenendahl, S. Hasegawa, J. Hoff, J. Howell, M. Hrycyk, S. Jindariani, M. Johnson, A. Jung, U. Joshi, F. Kahlid, C. M. Lei, R. Lipton, T. Liu, S. Los, M. Matulik, P. Merkel, S. Nahn, A. Prosser, R. Rivera, A. Shenai, L. Spiegel, N. Tran, L. Uplegger, E. Voirin, H. Yin, M. R. Adams, D. R. Berry, A. Evdokimov, O. Evdokimov, C. E. Gerber, D. J. Hofman, B. K. Kapustka, C. O'Brien, D. I. Sandoval Gonzalez, H. Trauger, P. Turner, N. Parashar, J. Stupak, D. Bortoletto, M. Bubna, N. Hinton, M. Jones, D. H. Miller, X. Shi, P. Tan, P. Baringer, A. Bean, G. Benelli, J. Gray, D. Majumder, D. Noonan, S. Sanders, R. Stringer, A. Ivanov, M. Makouski, N. Skhirtladze, R. Taylor, I. Anderson, D. Fehling, A. Gritsan, P. Maksimovic, C. Martin, K. Nash, M. Osherson, M. Swartz, M. Xiao, J. G. Acosta, L. M. Cremaldi, S. Oliveros, L. Perera, D. Summers, K. Bloom, S. Bose, D. R. Claes, A. Dominguez, C. Fangmeier, R. Gonzalez Suarez, F. Meier, J. Monroy, K. Hahn, S. Sevova, K. Sung, M. Trovato, E. Bartz, D. Duggan, E. Halkiadakis, A. Lath, M. Park, S. Schnetzer, R. Stone, M. Walker, S. Malik, H. Mendez, J. E. Ramirez Vargas, M. Alyari, J. Dolen, J. George, A. Godshalk, I. Iashvili, J. Kaisen, A. Kharchilava, A. Kumar, S. Rappoccio, J. Alexander, J. Chaves, J. Chu, S. Dittmer, G. Kaufman, N. Mirman, A. Ryd, E. Salvati, L. Skinnari, J. Thom, J. Thompson, J. Tucker, L. Winstrom, B. Akgün, K. M. Ecklund, T. Nussbaum, J. Zabel, B. Betchart, R. Covarelli, R. Demina, O. Hindrichs, G. Petrillo, R. Eusebi, I. Osipenkov, A. Perloff, K. A. Ulmer, A. G. Delannoy, P. D'Angelo, W. Johns

**Category:**Physics - Instrumentation and Detectors

The degradation of signal in silicon sensors is studied under conditions expected at the CERN High-Luminosity LHC. 200 $\mu$m thick n-type silicon sensors are irradiated with protons of different energies to fluences of up to $3 \cdot 10^{15}$ neq/cm$^2$. Pulsed red laser light with a wavelength of 672 nm is used to generate electron-hole pairs in the sensors. Read More

We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic rank 2 and 3 distributions in respective dimensions 5 and 6. Read More

In the article arXiv:1108.5443 we established a general group-theoretical approach to the construction of B\"acklund transformations. We then showed how this construction can be applied to construct B\"acklund transformation between equations which are Darboux integrable. Read More

In this paper we study a novel class of parabolic geometries which we call parabolic geometries of Monge type. These parabolic geometries are defined by special gradings of simple Lie algebras, namely, gradings with the property that their -1 component contains a nonzero co-dimension 1 abelian subspace whose bracket with its complement is non-degenerate. We completely classify the simple Lie algebras with such gradings in terms of elementary properties of the defining set of simple roots. Read More

**Authors:**S. Dawson, A. Gritsan, H. Logan, J. Qian, C. Tully, R. Van Kooten, A. Ajaib, A. Anastassov, I. Anderson, D. Asner, O. Bake, V. Barger, T. Barklow, B. Batell, M. Battaglia, S. Berge, A. Blondel, S. Bolognesi, J. Brau, E. Brownson, M. Cahill-Rowley, C. Calancha-Paredes, C. -Y. Chen, W. Chou, R. Clare, D. Cline, N. Craig, K. Cranmer, M. de Gruttola, A. Elagin, R. Essig, L. Everett, E. Feng, K. Fujii, J. Gainer, Y. Gao, I. Gogoladze, S. Gori, R. Goncalo, N. Graf, C. Grojean, S. Guindon, H. Haber, T. Han, G. Hanson, R. Harnik, S. Heinemeyer, U. Heintz, J. Hewett, Y. Ilchenko, A. Ishikawa, A. Ismail, V. Jain, P. Janot, S. Kanemura, S. Kawada, R. Kehoe, M. Klute, A. Kotwal, K. Krueger, G. Kukartsev, K. Kumar, J. Kunkle, M. Kurata, I. Lewis, Y. Li, L. Linssen, E. Lipeles, R. Lipton, T. Liss, J. List, T. Liu, Z. Liu, I. Low, T. Ma, P. Mackenzie, B. Mellado, K. Melnikov, A. Miyamoto, G. Moortgat-Pick, G. Mourou, M. Narain, H. Neal, J. Nielsen, N. Okada, H. Okawa, J. Olsen, H. Ono, P. Onyisi, N. Parashar, M. Peskin, F. Petriello, T. Plehn, C. Pollard, C. Potter, K. Prokofiev, M. Rauch, T. Rizzo, T. Robens, V. Rodriguez, P. Roloff, R. Ruiz, V. Sanz, J. Sayre, Q. Shafi, G. Shaughnessy, M. Sher, F. Simon, N. Solyak, J. Strube, J. Stupak, S. Su, T. Suehara, T. Tanabe, T. Tajima, V. Telnov, J. Tian, S. Thomas, M. Thomson, K. Tsumura, C. Un, M. Velasco, C. Wagner, S. Wang, S. Watanuki, G. Weiglein, A. Whitbeck, K. Yagyu, W. Yao, H. Yokoya, S. Zenz, D. Zerwas, Y. Zhang, Y. Zhou

This report summarizes the work of the Energy Frontier Higgs Boson working group of the 2013 Community Summer Study (Snowmass). We identify the key elements of a precision Higgs physics program and document the physics potential of future experimental facilities as elucidated during the Snowmass study. We study Higgs couplings to gauge boson and fermion pairs, double Higgs production for the Higgs self-coupling, its quantum numbers and $CP$-mixing in Higgs couplings, the Higgs mass and total width, and prospects for direct searches for additional Higgs bosons in extensions of the Standard Model. Read More

In this paper, we study the extent to which CP parity of a Higgs boson, and more generally its anomalous couplings to gauge bosons, can be measured at the LHC and a future electron-positron collider. We consider several processes, including Higgs boson production in gluon and weak boson fusion and production of a Higgs boson in association with an electroweak gauge boson. We consider decays of a Higgs boson including $ZZ, WW, \gamma \gamma$, and $Z \gamma$. Read More

To every Darboux integrable system there is an associated Lie group $G$ which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group $G$. If the Vessiot group $G$ is solvable then the Cauchy problem can be solved by quadratures. Read More

Let $T^{ab}=T^{ba}=0$ be a system of differential equations for the components of a metric tensor on $R^m$. Suppose that $T^{ab}$ transforms tensorially under the action of the diffeomorphism group on metrics and that the covariant divergence of $T^{ab}$ vanishes. We then prove that $T^{ab}$ is the Euler-Lagrange expression some Lagrangian density provided that $T^{ab}$ is of third order. Read More

We approach the construction of Backlund transformations for Darboux integrable hyperbolic partial differential equations in the plane through the reduction of exterior differential systems. For example it is shown that all the Backlund transformations in arXiv:0707.4408v2 can be constructed using symmetry reduction. Read More

We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund transformation can be constructed by the proposed symmetry reduction method. Read More

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations. Read More

By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka algebras leads to a new Lie-Backlund theorem. We prove that all flat Monge equations are successive integrable extensions of the Hilbert-Cartan equation. Read More

The combined local structure techniques, extended x-ray absorption fine structure (EXAFS) and neutron pair distribution function analysis, have been used for temperatures 4 <= T <= 330 K to rule out a large Jahn-Teller (JT) distortion of the Co-O bond in La1-xSrxCoO3 for a significant fraction of Co sites (x <= 0.35), indicating few, if any, JT-active, singly occupied e_g Co sites exist. Read More

Spin-cast all-inorganic nanoparticle solutions have been used to make a CdTe/CdSe solar cell with an efficiency of up to 2.8% without alumina or calcium buffer layers. The type of junction and non-selective nature of the contacts made to these devices is explored. Read More

In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Darboux integrable systems, and provides for systematic, algorithmic integration of such systems. Read More

We characterize Lie group actions for which there exists, at least locally, an evaluation map that defines a cochain map from the differential complex of invariant forms on a manifold to the De Rham complex for the quotient. Read More

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key feature in our theory is that we allow for non-transverse symmetry group actions, which are very common in applications. Read More

Monte-Carlo simulations of a focusing supermirror guide after the monochromator on the IN14 cold neutron three-axis spectrometer, I.L.L. Read More

**Affiliations:**

^{1}Utah State University,

^{2}Utah State University,

^{3}Utah State University

We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation where the reduced differential equations for the group invariant solutions involve both fewer dependent and independent variables. The theoretical basis for our method is provided by a general existence theorem for the invariant sections, both local and global, of a bundle on which a finite dimensional Lie group acts. Read More

**Affiliations:**

^{1}Utah State University,

^{2}Utah State University,

^{3}Utah State University

We extend Lie's classical method for finding group invariant solutions to the case of non-transverse group actions. For this extension of Lie's method we identify a local obstruction to the principle of symmetric criticality. Two examples of non-transverse symmetry reductions for the potential form of Maxwell's equations are then examined. Read More

**Affiliations:**

^{1}Utah State University,

^{2}Utah State University

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the ADM energy in general relativity. Read More

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. Read More

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Read More