Research Interests for Carla Cederbaum
Research Interests: Mathematical Relativity; Differential Geometry; Geometric Analysis; Calculus of Variations
Mathematical Relativity, (Differential) Geometry, Geometric Analysis, and Calculus of Variations are my main mathematical interests. I particularly enjoy working on problems that are related to physics.
In my thesis, I began working on static metrics in General Relativity. My aim was and still is to obtain a deeper understanding of their geometry and to gain more insight into their physical interpretation (mass, center of mass, behaviour of test bodies etc.). I have coined the name "geometrostatics" for this endeavor. Static metrics appear in many physical and geometric settings; they are relevant for the static n-body problem as well as for Bartnik's concept of mass and his related conjecture about static metric extensions.
Moreover, together with Jörg Hennig and Marcus Ansorg, I have studied a geometric inequality between horizon area and anguar momentum for stationary and axisymmetric black holes. Our work has interesting applications in proving non-existence of multiple black hole horizons (Hennig, Neugebauer). It has been extended to general axisymmetric spacetimes containing (marginally) stable marginally outer trapped surfaces (Gabach-Clément, Jaramillo). Geometric inequalities of this type are attracting more and more attention and many different techniques have been introduced to the field (e.g. by Dain). I work on understanding how the different approaches are related and am curious about what their interrelations might reveal.
Finally, I am studying the Newtonian limit of General Relativity using Jürgen Ehlers' frame theory. I am particularly interested in proving consistence results showing that certain physical properties like relativistic mass converge to their Newtonian counterparts. In my thesis, I proved such consistence results for mass and center of mass in the geometrostatic setting. I am planning to extend my techniques and results to more general metrics in the future.
- Representative Publications
- Carla Cederbaum, The Newtonian Limit of Geometrostatics
(July, 2011) (PhD thesis.) [FUDISS_thesis_000000023871]
- Marcus Ansorg, Jörg Hennig, Carla Cederbaum, Universal properties of distorted Kerr-Newman black holes,
Gen. Relativ. Gravit., vol. 43
pp. 1205 [arXiv:1005.3128]
- Jörg Hennig, Carla Cederbaum, Marcus Ansorg, A universal inequality for axisymmetric and stationary black holes with surrounding matter in the Einstein-Maxwell theory,
Comm. Math. Phys., vol. 293 no. 2
pp. 449–467 [arXiv:0812.2811]
- Jörg Hennig, Marcus Ansorg, Carla Cederbaum, A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter,
Classical Quantum Gravity, vol. 25 no. 16
pp. 162002 [arXiv:0805.4320]