Volker Perlick
Email:
vper0433@itp.physik.tuberlin.de
Curriculum Vitae
Research Interests
Publications
Curriculum Vitae

Born 28 March 1956 in Berlin

Diploma in Physics 1984, TU Berlin

Dissertation 1989, TU Berlin, with Prof. K.E. Hellwig;
PhD Thesis: Zur Kinematik Weylscher RaumZeitModelle

Habilitation 1999, TU Berlin
Habilitation Thesis: Ray optics, Fermat's principle, and applications to
general relativity
published as Springer Lecture Notes in Physics m61, Springer, Heidelberg (2000),
more information

Positions:

Scientific Coworker (Wissenschaftlicher Mitarbeiter)
at TU Berlin (19851989)

Locum Tenens Contract (Vertretung von apl. Prof. H.J. Schmidt)
at Universität Osnabrück (19921993)

Scientific Coworker (Wissenschaftlicher Mitarbeiter)
at AlbertEinsteinInstitut Golm (19992002)

Locum Tenens Contract (Vertretung C3 Nachfolge Prof. F. W. Hehl)
at Universität zu Köln
(20022003)

Scholarships:

Wigner Stipend 198990

Habilitation Stipend from Deutsche Forschungsgemeinschaft 19921995

DAAD/FAPESP Stipends 1997 and 1999

Research Stays (not including shortterm visits):

University of Texas at Dallas (with Wolfgang Rindler) (19891990)

University of Missouri at Columbia (with John Beem) (1990)
 Universität Jena (with Gernot Neugebauer) (19931994)

Universidade de São Paulo (with Paolo Piccione)
(1997 and 1999)

Courses:

Allgemeine Relativitätstheorie,
Summer Term 1986, TU Berlin

Oberstufenmathematik für Physiker,
Compact Course, Winter Term 1992/93, Universität Osnabrück

Mathematische Methoden der Physik I,
Winter Term 1992/93, Universität Osnabrück

Mathematische Methoden der Physik II,
Summer Term 93, Universität Osnabrück

Mathematische Kosmologie,
Summer Term 93, Universität Osnabrück

Singularity theorems in general relativity,
Sep.Nov. 1997, Universidade de São Paulo

Singularity theorems in general relativity,
Compact Course, Nov. 1999, Università di Camerino

Gravitationslinsen,
Winter Term 2002/03, Universität zu Köln

Theoretische Optik I,
Summer Term 2003, Universität zu Köln

Theoretische Optik II,
Winter Term 2003/04, Universität zu Köln

Gravitational Lensing,
Compact Course, Summer Term 2004, Universität Hannover

Member of Beirat of Fachverband Gravitation und Relativätstheorie in
Deutsche Physikalische Gesellschaft, since 1994,
homepage of Fachverband

Book Review Editor of the journal General Relativity and Gravitation
since 1999,
journal homepage

Coorganizer of conferences:

Kolloquium zum 60. Geburtstag von K.E. Hellwig
Org: M. Keyl, V. Perlick, W. Stulpe, M. Trucks
Berlin, 25.  26. April 1996, program

Aktuelle Entwicklungen in der Gravitationstheorie
Org.: C. Kiefer, V. Perlick, G. Schäfer
Physikzentrum Bad Honnef, 6.  8. September 1999,
program

Mathematical Relativity. New ideas and developments
Org: J. Frauendiener, D. Giulini, V. Perlick
319. Heraeus Seminar, Physikzentrum Bad Honnef, 1.  5. March 2004
conference homepage,
conference photo
Research Interests
My research interests are concentrated on certain aspects of the theory of gravitational
lensing. In its most general sense, the name "gravitational lensing" comprises all
influences of gravitational fields (coded in the spacetime geometry) on light rays.
More specifically, I am interested in those mathematical methods where the formalism of
general relativity is not mutilated by quasiNewtonian approximations. This kind
of research goes under the heading "gravitational lensing from a
spacetime perspective" or "nonperturbative gravitational lensing".
It includes interesting applications of differential geometry, differential
topology, and global analysis. Here are some of the subjects covered.

Image distortion: Distant light sources (galaxies) appear distorted
on the observer's celestial sphere, because of the influence of the
spacetime geometry on the light rays. For highly idealized spacetime
models the distortion effect can be precisely calculated, without
quasiNewtonian approximations. Among the examples to be treated are
spherically symmetric spacetimes and spatially homogeneous spacetimes.

Geometry of caustics: The past lightcone of an observation event
in a generalrelativistic spacetime usually shows caustics (selfintersections).
The appearance of caustics is crucial for many gravitational lensing phenomena.
An important goal is the local (and, as far as possible, global) classification
of stable caustics with the help of the socalled catastrophe theory.
For the caustics of lightcones in general relativity, is was possible to
achieve important partial results in this direction (in particular owing to
the work of Robert Low), but there are still several open questions.

Applications of Morse theory:
Morse theory relates the number of solutions to a variational problem to the
topology of the space of trial paths. As light rays in general relativity can
be characterized by a variational principle (Fermat's principle), Morse
theory can be used for determining the possible number of images in a gravitational
lensing situation. The relativistic Fermat principle is due to Israel Kovner, and
a Morse theory for this particular variational principle was worked out by Fabio
Giannoni, Antonio Masiello and Paolo Piccione. With the help of these results one
can investigate whether, in a certain class of spacetimes, the total number of
images is finite or infinite, even or odd. In some situations similar results
can be deduced with the help of methods from differential topology such as
the mapping degree (also known as Brouwer degree or winding
number). In this way it was possible to get results on isolated objects
(asymptotically simple and empty spacetimes) and on black holes. It
is desirable to extend these results to other classes of spacetimes.
For details please see my Living Review: Gravitational lensing from a
spacetime perspective, Living Rev. Relativity 7 (2004) 9
[Online Article]
http://www.livingreviews.org/lrr20049
Publications
Books and Review Articles

V. Perlick: Ray optics, Fermat's principle, and applications to
general relativity,
Springer Lecture Notes in Physics m61, Springer, Heidelberg (2000),
more information

V. Perlick: Gravitational lensing from a geometric viewpoint,
in B. Schmidt (ed.) "Einstein's field equations and their physical
interpretations" Selected Essays in Honour of Jürgen Ehlers,
Springer, Heidelberg (2000) pp.373425
psfile

V. Perlick: Gravitational lensing from a spacetime perspective,
Living Rev. Relativity 7 (2004) 9 [Online Article]
http://www.livingreviews.org/lrr20049

J. Frauendiener, D. Giulini, V. Perlick (eds.): Mathematical relativity. New
ideas and developments, Proceedings of the 319. Heraeus Seminar, Bad Honnef,
March 1  5, 2004, to appear 2005, Springer, Heidelberg
conference homepage,
conference photo

M. Kriele, V. Perlick: Spacetime,
2nd edition, Springer, Heidelberg, to appear (some time, in the future,
I hope ... )
Research Articles

V. Perlick: Characterization of standard clocks by means of light
rays and freely falling particles, Gen. Rel. Grav. 19,
10591073 (1987)

W. Hasse, V. Perlick: Geometrical and kinematical characterization
of parallaxfree world models, J. Math. Phys. 29, 20642068
(1988)

V. Perlick: On redshift and parallaxes in generalrelativistic
kinematical world models, J. Math. Phys. 31, 19621971 (1990)

W. Rindler, V. Perlick: Rotating coordinates as tools for calculating
circular geodesics and gyroscopic precession, Gen. Rel. Grav. 22,
10671081 (1990)

V. Perlick: On Fermat's principle in general relativity. I. The
general case, Class Quant. Grav. 7, 13191331 (1990)

V. Perlick: On Fermat's principle in general relativity. II. The
conformally stationary case, Class Quant. Grav. 7, 18491867
(1990)

V. Perlick: Observer fields in Weylian spacetime models, Class.
Quant. Grav. 8, 13691385 (1991)

V. Perlick: A class of stationary charged dust solutions of Einstein's
field equations, Gen. Rel. Grav. 23, 13371348 (1991)

V. Perlick: The brachystochrone problem in stationary spacetimes,
J. Math. Phys. 32, 31483157 (1991)

V. Perlick: The Hamiltonization problem from a global viewpoint,
J. Math. Phys. 33, 599606 (1992)

V. Perlick: Bertrand spacetimes, Class. Quant. Grav. 9,
10091021 (1992)

V. Perlick, W. Hasse: Gravitational Faraday effect in conformally
stationary spacetimes, Class. Quant. Grav. 10, 147161 (1993)

V. Perlick: Characterization of standard clocks, in
U. Majer, H.J. Schmidt (eds.) "Semantical aspects of spacetime",
BI Wissenschaftsverlag, Mannheim (1994) pp. 169180

V. Perlick, Xu C.: Matching exterior to interior solutions in
Weyl gravity, Astrophys. J. 449, 4751 (1995)
pdffile

V. Perlick: Infinite dimensional Morse theory and Fermat's principle
in general relativity. I., J. Math. Phys. 36, 69156928 (1995)

V. Perlick: Criteria for multiple imaging in Lorentzian manifolds,
Class. Quant. Grav. 13, 529537 (1996)

W. Hasse, M. Kriele, V. Perlick: Caustics of wavefronts in general
relativity, Class. Quant. Grav. 13, 11611182 (1996)

V. Perlick: Fermat's principle, Morse theory and applications to
the gravitational lens effect, Nonlinear Analysis 30,
617615 (1997)

V. Perlick, P. Piccione: A generalrelativistic Fermat principle
for extended light sources and extended receivers, Gen. Rel. Grav.
30, 14611476 (1998)
psfile

V. Perlick: Applications of Morse theory to gravitational lensing,
in H.J. Schmidt (ed.) "Current topics in mathematical
topology", World Scientific, Singapore (1998) pp. 155164

W. Hasse, V. Perlick: On spacetime models with an isotropic Hubble
law, Class. Quant. Grav. 16, 25592576 (1999)
psfile

V. Perlick: Gravitational lensing in asymptotically simple and
empty spacetimes, Annalen der Physik 9, SI139SI142 (2000)
psfile

V. Perlick: A variational principle for light rays in a
generalrelativistic plasma, Nonlinear Analysis 47,
30193030 (2001)

V. Perlick: Global properties of gravitational lens maps in a
Lorentzian manifold setting, Commun. Math. Phys. 220,
403428 (2001)
grqc/0009105

T. Chrobok, V. Perlick: Classification of image distortion in
terms of Petrov types, Class. Quant. Grav. 18, 30593079
(2001)
grqc/0012088

W. Hasse, V. Perlick: Gravitational lensing in spherically
symmetric static spacetimes with centrifugal force reversal,
Gen. Rel. Grav. 34, 415433 (2002)
grqc/0108002

V. Perlick: Rotation of the polarization plane in the
gravitational field of rotating objects, in R. Ruffini and
C. Sigismondi (eds.) "Nonlinear gravitodynamics: The LenseThirring
effect" Proceedings of the ICRA Network Workshop on the
LenseThirring Effect, Rome and Pescara, 1998; World Scientific
(2003) pp.135144

T. Foertsch, W. Hasse, V. Perlick: Inertial forces and photon
surfaces in abitrary spacetimes, Class. Qant. Grav. 20,
46354651 (2003)
grqc/0306042

V. Perlick: Exact gravitational lens equation in spherically
symmetric and static spacetimes, Phys. Rev. D69, 064017
(2004)
grqc/0307072

V. Perlick: On totally umbilic submanifolds in semiRiemannian
manifolds, Nonlinear Analysis (to appear),
psfile