Search results for " relativity"
showing 10 items of 1158 documents
Robust fault detection design for unknown inputs Takagi-Sugeno models with parametric uncertainties and time-varying delays
2014
This paper deals with the design of robust fault detection system for Takagi-Sugeno (T-S) modes with parametric uncertainties and time-varying delay. An Unknown Input Observer (UIO) is designed such that the unknown inputs are thoroughly decoupled from residual signals while they show the maximum possible sensitivity to the faults and the minimum possible sensitivity to the external disturbances. Since the system under consideration is subjected to parametric uncertainties, the H ∞ model matching approach is used to design an optimal observer. Design procedure is given in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is presented to show the effectiveness of the p…
Spacelike energy of timelike unit vector fields on a Lorentzian manifold
2004
On a Lorentzian manifold, we define a new functional on the space of unit timelike vector fields given by the L2 norm of the restriction of the covariant derivative of the vector field to its orthogonal complement. This spacelike energy is related with the energy of the vector field as a map on the tangent bundle endowed with the Kaluza–Klein metric, but it is more adapted to the situation. We compute the first and second variation of the functional and we exhibit several examples of critical points on cosmological models as generalized Robertson–Walker spaces and Godel universe, on Einstein and contact manifolds and on Lorentzian Berger’s spheres. For these critical points we have also stu…
Open data from the first and second observing runs of advanced LIGO and advanced Virgo
2021
Abbot, Rich, et al. (Virgo and MAGIC Collaboration)
Generalized Virasoro anomaly and stress tensor for dilaton coupled theories
2003
We derive the anomalous transformation law of the quantum stress tensor for a 2D massless scalar field coupled to an external dilaton. This provides a generalization of the Virasoro anomaly which turns out to be consistent with the trace anomaly. We apply it together with the equivalence principle to compute the expectation values of the covariant quantum stress tensor on a curved background. Finally we briefly illustrate how to evaluate vacuum polarization and Hawking radiation effects from these results.
Intrinsic characterization of space‐time symmetric tensors
1992
This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.
Electronic properties of graphene: A learning path for undergraduate students
2016
The purpose of this work is to present a learning path aimed at deepening student understanding of the fundamental concepts underlying the electronic properties of new materials, graphene in particular. To achieve this task, we propose a five-week long workshop where students may be introduced to fundamental concepts of advanced physics, rarely used in learning paths, such as the symmetry properties of the crystal lattice, the group theory , the features of the free electron wave functions and energy levels, the relativistic Dirac equation. Particular emphasis is given to the manner of introducing these concepts, since an essential knowledge of solid state physics, quantum physics and relat…
The Mathematicians’ Happy Hunting Ground: Einstein’s General Theory of Relativity
2004
There is hardly any doubt that for physics special relativity theory is of much greater consequence than the general theory. The reverse situation prevails with respect to mathematics: there special relativity theory had comparatively little, general relativity theory very considerable, influence, above all upon the development of a general scheme for differential geometry. —Hermann Weyl, “Relativity as a Stimulus to Mathematical Research,” pp. 536–537.
Seeing reality through Einstein's eyes: a teaching proposal for special relativity
2021
The teaching of Special Relativity is still a critical issue not only for students but also for teachers. In this paper, we describe the trial of a learning unit on the Special Relativity topic based on Minkowski's approach through spacetime diagrams, following the results in pedagogical researches in this field. The main innovation of our project consists of a mechanical instrument: it allows to physically and mechanically represent Lorentz’s transformations by hands, exploring the effects of a change of the reference frame. Teachers and students can deal “by eye” with unusual phenomena as the loss of simultaneity, time dilation, length contraction, relativistic addition of velocities and …
A quantum model of Schwarzschild black hole evaporation
1996
We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show tha…
Symmetries and solvable models for evaporating 2D black holes
1997
We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is suddenly switched off. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model. © Elsevier Science B.V