Math @ Duke

Carla Cederbaum, Named Assistant Research Professor
Please note: Carla has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
Office Location:  218 Physics Building  Email Address:    Office Hours:
 By appointment only, please email me.
 Education:
PhD  Freie Universität Berlin  2011 
Dipl  Universität Freiburg  2007 
MASt  University of Cambridge  2003 
 Specialties:

Geometry
Analysis Mathematical Physics
 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 nbody 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 nonexistence of multiple black hole horizons (Hennig, Neugebauer). It has been extended to general axisymmetric spacetimes containing (marginally) stable marginally outer trapped surfaces (GabachClément, 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
(More Publications)
 Carla Cederbaum, Geometrostatics: the geometry of static spacetimes,
Conference Proceedings "Relativity and Gravitation  100 years after Einstein in Prague"
(Accepted, 0) [arXiv:1210.4436] [abs]
 Carla Cederbaum, The Newtonian Limit of Geometrostatics
(July, 2011) (PhD thesis.) [FUDISS_thesis_000000023871]
 Marcus Ansorg, Jörg Hennig, Carla Cederbaum, Universal properties of distorted KerrNewman black holes,
Gen. Relativ. Gravit., vol. 43
(2011),
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 EinsteinMaxwell theory,
Comm. Math. Phys., vol. 293 no. 2
(2010),
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
(2008),
pp. 162002 [arXiv:0805.4320]
 Selected Invited Lectures
 From Newton to Einstein: A guided tour through space and time, November 06, 2012, CUNYCSI [Poster] [Slides]
 From Newton to Einstein: a guided tour through space and time, April 27, 2012, Duke Physics Building 128 [video.html] [Poster]
 Conferences Organized
 Annual East Coast Geometry Festival, April, 2012


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

