Results 11 to 20 of about 19,618 (150)

Chains in CR geometry as geodesics of a Kropina metric [PDF]

, 2019
With the help of a generalization of the Fermat principle in general relativity, we show that chains in CR geometry are geodesics of a certain Kropina metric constructed from the CR structure.
Cheng, Jih-Hsin, Marugame, Taiji, Matveev, Vladimir S., Montgomery, Richard   +3 more
core   +2 more sources

Relativity and Singularities - A Short Introduction for Mathematicians [PDF]

, 2005
We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems.
Natario, Jose
core   +5 more sources

Numerical calculations near spatial infinity [PDF]

, 2006
After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied.
Zenginoglu, Anil
core   +2 more sources

What's the Point? Hole-ography in Poincare AdS [PDF]

, 2018
In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS$_3$ via hole-ography, i.e., in terms of differential entropy of the dual CFT$_2$.
Espíndola, Ricardo, Guijosa, Alberto, Landetta, Alberto, Pedraza, Juan F.   +3 more
core   +3 more sources

Geodesics on a supermanifold and projective equivalence of super connections [PDF]

, 2012
We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in the classical case, they are the projections of the integral curves of a ...
Abraham, DeWitt, Fabian Radoux, Gijs M. Tuynman, Goertsches, Hebda, Kostant, Lecomte, Lecomte, Leites, Leuther, Mathonet, Monterde, Roberts, Roberts, Rogers, Thomas, Thomas, Thomas Leuther, Tuynman, Tuynman, Weyl, Whitehead   +22 more
core   +1 more source

Non-Abelian gauge field theory in scale relativity [PDF]

, 2006
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables.
Célérier M. N., Feynman R. P., Landau L., Laurent Nottale, Mandelbrot B., Marie-Noëlle Célérier, Nottale L., Nottale L., Salam A., Thierry Lehner, Weinberg S.   +10 more
core   +6 more sources

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow [PDF]

, 2012
We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians
A. A. Belavin, A. Avila, A. Avila, A. Eskin, A. Eskin, A. Eskin, A. Eskin, A. Eskin, A. Eskin, A. Eskin, A. Kokotov, A. Kokotov, A. Kokotov, A. Kokotov, A. Kokotov, A. McIntyre, A. Polyakov, A. Polyakov, A. Wright, A. Wright, A. Zorich, Alex Eskin, Anton Zorich, B. Maskit, B. Osgood, C. Matheus Santos, C. Matheus Santos, C. McMullen, C. Peters, D. Chen, D. Chen, D. Korotkin, D. Quillen, D. Ray, E. Gutkin, E. Lanneau, E. Lanneau, G. Forni, G. Forni, G. Forni, G. Forni, G. Forni, H. Masur, H. Masur, H. Masur, H. Masur, I. Bouw, J. Fay, J. Jorgenson, J.-M. Bismut, J.-M. Bismut, J.-M. Bismut, J.-M. Bismut, K. Calta, K. Rafi, K. Rafi, L. A. Takhtadzhyan, L. Bers, M. Bainbridge, M. Bainbridge, M. Kontsevich, M. Kontsevich, M. Möller, Maxim Kontsevich, P. Hubert, R. Lundelius, R. Treviño, S. Grushevsky, S. Lelièvre, S. Wolpert, S. Wolpert, S. Wolpert, W. A. Veech, W. Veech, W. Veech, Y. Minsky, Ya. Vorobets   +76 more
core   +6 more sources

On Lorentzian causality with continuous metrics [PDF]

, 2012
We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when metrics which
Chruściel, Piotr T., Grant, James D. E.
core   +2 more sources

Geodesic completeness of generalized space-times

, 2015
We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions.
Steinbauer, Roland, Sämann, Clemens
core   +1 more source

Photon‐Sphere Modes in Curved Optical Microcavities: A Black‐Hole Analogue Laser

Advanced Science, EarlyView.
An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Chenni Xu, Aswathy Sundaresan, Nazire‐Begüm Kazkal, Clement Lafargue, Lior Zarfaty, Li‐Gang Wang, Ofek Birnholtz, Dominique Decanini, Melanie Lebental, Patrick Sebbah   +9 more
wiley   +1 more source