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Título
Geometry of abstract null hypersurfaces and matching of spacetimes
Autor(es)
Director(es)
Palabras clave
Tesis y disertaciones académicas
Universidad de Salamanca (España)
Tesis Doctoral
Academic dissertations
Hipersuperficies
Espacio-Tiempo
Clasificación UNESCO
22 Física
Fecha de publicación
2023
Resumen
[EN] The purpose of this thesis is two-fold. As already mentioned, we are firstly interested
in the geometry of null hypersurfaces. In this context
the formalism of hypersurface data becomes a powerful mathematical framework.
Our second aim (and actually the starting point of the thesis) is the study of the
problem of matching two completely general spacetimes across a null hypersurface,
which we address in Chapters 7, 8, 9.
Concerning the part of the thesis where we expand the formalism of hypersurface
data, the motivations described above have lead us to study how to characterize
curvature information at the abstract level. Also, they have allowed
us to understand how the data is affected by the existence of a privileged vector
field. In particular, this has permitted that we construct abstract notions
of Killing horizons of order zero and one which do not require of any ambient
space and which generalize the concepts of non-expanding, (weakly) isolated and
Killing horizons. Finally, we have been able to derive an equation, called generalized
master equation, that governs the geometry of null hypersurfaces with an extra null
tangent vector field. The analysis of this equation reveals properties
about the surface gravity of such vector and about homothetic Killing horizons
and Killing horizons of order zero and one. Moreover, it allows us to recover, as
particular cases, the well-known near horizon equation of isolated horizons as well
as the so-called master equation of multiple Killing horizons.
The problem of matching two spacetimes across a null hypersurface constitutes
the second part of the thesis. In a spacetime context and by requiring a simple
topology of the boundaries, we have been able to encode the whole matching
information in a function and a diffeomorphism between the set of null generators
of both matching hypersurfaces. We have also derived explicit expressions for the
matter-energy content of the shell. Finally, we have exploited the formalism of
hypersurface data to address the problem of matching in a completely abstract
context and without requiring topological restrictions upon the boundaries. This
approach, as we will see, has many advantages that will be discussed later.
URI
DOI
10.14201/gredos.157719
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