Céline Cattoën

Ph.D student

School of Mathematics, Statistics and Operations Research

Victoria University

PO Box 600 | Wellington | New Zealand

E-mail: Celine.Cattoen at msor.vuw.ac.nz

Office: Cotton 356

Phone number: +64 4 463 5233 extension 8314

Department: +64 4 463 5341

Fax: +64 4 463 5045

Celine's CV

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Research

The main field of my research is classical general relativity. Specifically, a lot of my work is focused on Cosmology, that is:

• Cosmography: A good part of cosmology is purely kinematic in character, and independent of the Einstein equations. These segments of cosmology can be treated in a purely descriptive manner, and you do not need a dynamical analysis until you try to explain the observations. For instance, many cosmologists have forgotten that the Hubble law is purely kinematic, and that it can be derived based on symmetry principles without using the Einstein equations.
• Cosmodynamics: This part of cosmology is treated in a dynamical manner once the Friedmann equations are assumed (Einstein equations). However, no specific equation of state needs to be assumed at this stage which gives more general results that are model independent and specifically independent of the matter content of the universe.
• Singularities in Cosmology: they usually refer to the Big Bang (Big Crunch reverse phenomenon), the Big Rip, Sudden Singularities.
• Energy conditions in Cosmology: The energy conditions of general relativity permit one to deduce very powerful and general theorems about the behaviour of cosmological geometries. They also give a good qualitative indication of how "strange physics" get.
• Hubble laws and the Supernova data: One can Taylor expand various Hubble relations between cosmological distances and cosmological redshift. Furthermore, the supernova data offer a great deal of information that can be fitted to various distance scales versus redshift in order to study the behaviour of the universe.

I am also working on another project in Numerical Relativity that consists of applying a very recent numerical method to solve Einstein equations for black hole simulations.

In my master thesis, I have done some work on Gravastars which are serious alternatives to the usual concept of an astrophysical black hole. The gravastar model was originally developed by Mazur and Mottola.

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Céline's Master thesis

In this thesis, two different problems relevant to general relativity are considered.

• Over the last few years, opinions on physically relevant singularities occurring in FRW cosmologies have considerably changed. An extensive catalogue of such cosmological milestones using generalized power series both at the kinematical and dynamical level are presented. The notion of "scale factor singularity" is defined and its relation to polynomial and differential curvature singularities is explored. Some dynamical information can be extracted using the Friedmann equations and necessary and sufficient conditions for the existence of cosmological milestones such as big bangs, big crunches, big rips, sudden singularities and extremality events can be derived. Specifically, this thesis contains a complete characterization of cosmological milestones for which the dominant energy condition is satisfied.
• The second problem looks at one of the very small number of serious alternatives to the usual concept of an astrophysical black hole, that is, the gravastar model developed by Mazur and Mottola. By considering a generalized class of similar models with continuous pressure (no infinitesimally thin shells) and negative central pressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropic pressures are unavoidable. We provide bounds on the necessary anisotropic pressure and show that these transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl-Bondi bound for perfect fluid stars. This thesis also comments on the qualitative features of the equation of state that such gravastar-like objects without any horizon must have.

Céline's Master thesis can be found here.

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Previous projects in applied mathematics

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Publications

Here are several links to Céline Cattoën's publications:

• Céline Cattoën's papers on the arxiv,
• Céline Cattoën's papers on spires,
• Céline Cattoën's papers on citebase.

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Publications in Journals

THE HUBBLE SERIES: CONVERGENCE PROPERTIES AND REDSHIFT VARIABLE By Céline Cattoën and Matt Visser. Nov 2007. 15pp. gr-qc/0710.1887 Class. Quantum Grav. 24 (2007) 5985-5997

NECESSARY AND SUFFICIENT CONDITIONS FOR BIG BANGS, BOUNCES, CRUNCHES, RIPS, SUDDEN SINGULARITIES, EXTREMALITY EVENTS, AND MORE... By Céline Cattoën and Matt Visser. Aug 2005. 19pp. gr-qc/0508045 Class. Quantum Grav. 22 (2005)

GRAVASTARS MUST HAVE ANISOTROPIC PRESSURES By Céline Cattoën, Tristan Faber and Matt Visser. May 2005. 15pp. gr-qc/0505137 Class. Quantum Grav. 22 (2005) 4189-4202

EFFECTIVE REFRACTIVE INDEX TENSOR FOR WEAK FIELD GRAVITY By Petarpa Boonserm, Céline Cattoën, Tristan Faber, Matt Visser and Silke Weinfurtner. Mon, 8 Nov 2004. 8pp. gr-qc/0411034 Class. Quantum Grav.22 (2005) 1905-1916

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Publications in Conference proceedings

GENERALIZED PUISIEUX SERIES EXOANSION FOR COSMOLOGICAL MILESTONES By Céline Cattoën, Matt Visser Sep 2006. 3pp. To appear in the proceedings of 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, Berlin, Germany, 23-29 Jul 2006. gr-qc/0609073

COSMOLOGICAL MILESTONES AND ENERGY CONDITIONS By Céline Cattoën, Matt Visser Sep 2006. 8pp. gr-qc/0609064 Published in J.Phys.Conf.Ser.68:012011,2007

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