78 research outputs found
Interacciones mediadas por la curvatura en curvas y superficies /
No full text\ua0tesis que para obtener el grado de Doctor en Ciencias (Física), presenta Pablo Agustín Vázquez Montejo ; asesor Jemal Janer Guven Seery, Marcelo Salgado, Riccardo Capovilla. 146 páginas :\ua0ilustraciones. Doctorado en Ciencias (Física)\ua0UNAM, Instituto de Ciencias Nucleares,\ua0201
Flat foliations of spherically symmetric geometries
No full textWe examine the solution of the constraints in spherically symmetric general relativity when spacetime has a flat spatial hypersurface. It is demonstrated explicitly that, given one hat slice, a foliation by flat slices can be consistently evolved. We show that when the sources are finite these slices do not admit singularities and we provide an explicit bound on the maximum value assumed by the extrinsic curvature. If the dominant energy condition is satisfied, the projection of the extrinsic curvature orthogonal to the radial direction possesses a definite sign. We provide both necessary and sufficient conditions for the formation of apparent horizons in this gauge which are qualitatively identical to those established earlier for extrinsic time foliations of spacetime, (J. Guven and N. O Murchadha, Phys. Rev. D 56 7658 (1997); 56, 7666 (1997)), which suggests that these conditions possess a gauge invariant validity, (S0556-2821(99)02420-0)
Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data
No full textWe establish necessary conditions for the appearance of both apparent horizons and singularities in the initial data of spherically symmetric general relativity when spacetime is foliated extrinsically. When the dominant energy condition is satisfied these conditions assume a particularly simple form. Let ae Max be the maximum value of the energy density and ` the radial measure of its support. If ae Max ` 2 is bounded from above by some numerical constant, the initial data cannot possess an apparent horizon. This constant does not depend sensitively on the gauge. An analogous inequality is obtained for singularities with some larger constant. The derivation exploits Poincar'e type inequalities to bound integrals over certain spatial scalars. A novel approach to the construction of analogous necessary conditions for general initial data is suggested. Typeset using REVT E X [email protected] y [email protected] I. INTRODUCTION In this paper we cast necessary conditions for the a..
Sufficient Conditions for Apparent Horizons in Spherically Symmetric Initial Data
No full textWe establish sufficient conditions for the appearance of both apparent horizons and singularities in spherically symmetric initial data when spacetime is foliated extrinsically. Let M and P be respectively the total material energy and the total material current contained in some ball of radius `. Suppose that the dominant energy condition is satisfied. We show that if M \Gamma P ` then the region must possess a future apparent horizon for some non-trivial closed subset of such gauges. The same inequality holds on a larger subset of gauges but with a larger constant of proportionality which depends weakly on the gauge. This work extends substantially both our joint work on moment of time symmetry initial data as well as the work of Bizon, Malec and ' O Murchadha on a maximal slice. Typeset using REVT E X [email protected] y [email protected] I. INTRODUCTION This paper is part of an ongoing examination of the constraints in spherically symmetric general relativity [1--3]. Here we..
Faculty of Business and Law School of Accounting, Economics and Finance ECONOMICS SERIES
No full textWhy is the world getting older? The influence of happiness on mortality Cahit Guven, Rudolph Saloumidis. The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd. Why is the world getting older? The influence of happiness on mortalit
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No full textConstraints in spherically symmetric classical general relativity. II. Identifying the configuration space: A moment of time symmetry
No full textWe continue our investigation of the configuration space of general relativity begun in the preceding paper. Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We begin with a heuristic description of the presence of apparent horizons and singularities. A peculiarity of MS configurations is that not only do they satisfy the positive quasilocal mass (QLM) theorem, they also satisfy its converse: the QLM is positive everywhere, if and only if the (nontrivial) spatial geometry is nonsingular. We derive an analytical expression for the spatial metric in the neighborhood of a generic singularity. The corresponding curvature singularity shows up in the traceless component of the Ricci tenser. As a consequence of the converse, if the energy density of matter is monotonically decreasing, the geometry cannot be singular. A. supermetric on the configuration space which distinguishes between singular geometries and nonsingular ones is constructed explicitly. Global necessary and sufficient criteria for the formation of trapped surfaces and singularities are framed in terms of inequalities which relate some appropriate measure of the material energy content on a given support to a measure of its volume. The sufficiency criteria are cast in the following form: if the material energy exceeds some universal constant times the proper radius l(0) of the distribution, the geometry will possess an apparent horizon for one constant and a singularity for some other larger constant. A more appropriate measure of the material energy for casting the necessary criteria is the maximum value of the energy density of matter rho(max): if rho(max)l(0)(2) < some constant the distribution of matter will not possess a singularity for one constant and an apparent horizon for some other smaller constant. These inequalities provide an approximate characterization of the singular (nonsingular) and trapped (nontrapped) partitions on the configuration space. Their strength is gauged by exploiting the exactly solvable piecewise constant density star as a template. Finally, we provide a more transparent derivation of the lower bound on the binding energy conjectured by Arnowitt, Deser, and Misner and proven by Bizon, Malec, and O Murchadha and speculate on possible improvements
Sufficient conditions for apparent horizons in spherically symmetric initial data
No full textWe establish sufficient conditions for the appearance of both apparent horizons and singularities in spherically symmetric initial data when spacetime is foliated extrinsically. Let M and P be, respectively, the total material energy and the total material current contained in some ball of radius l. Suppose that the dominant energy condition is satisfied. We show that if M - P greater than or equal to l then the region must possess a future apparent horizon for some nontrivial closed subset of such gauges. The same inequality holds on a larger subset of gauges but with a larger constant of proportionality which depends weakly on the gauge. This work extends substantially both our joint work on moment of time symmetry initial data as well as the work of Bizon, Malec, and O Murchadha on a maximal slice. (S0556-2821(97)00524-9)
Large deformations of relativistic membranes: A generalization of the Raychaudhuri equations
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