43 research outputs found
Myron Mathisson: What little we know of his life
Myron Mathisson (1897â1940) was a Polish Jew known for his work on
the equations of motion of bodies in general relativity and for developing
a new method to analyze the properties of fundamental solutions of linear
hyperbolic differential equations. In particular, he derived the equations for
a spinning body moving in a gravitational field and proved, in a special case,
the Hadamard conjecture on the class of equations that satisfy the Huygens
principle. His work still exerts influence on current research. Drawing on
various archival and secondary sources, in particular his correspondence
with Einstein, we outline Mathissonâs biography and scientific career
Robinson Manifolds as the Lorentzian Analogs of Hermite Manifolds
A Lorentzian manifold is defined here as a smooth pseudo-Riemannian manifold
with a metric tensor of signature ((2n +1, 1)). A Robinson manifold is a
Lorentzian manifold (M) of dimension (\geqslant 4) with a subbundle (N) of the
complexification of (TM) such that the fibers of (N\to M) are maximal totally
null (isotropic) and ([\Sec N, \Sec N]\subset \Sec N). Robinson manifolds are
close analogs of the proper Riemannian, Hermite manifolds. In dimension 4, they
correspond to space-times of general relativity, foliated by a family of null
geodesics without shear. Such space-times, introduced in the 1950s by Ivor
Robinson, played an important role in the study of solutions of Einstein's
equations: plane and sphere-fronted waves, the G\"odel universe, the Kerr
solution, and their generalizations, are among them. In this survey article,
the analogies between Hermite and Robinson manifolds are presented in
considerable detail
A criterion for compatibility of conformal and projective structures
In a space-time, a conformal structure is defined by the distribution of
light-cones. Geodesics are traced by freely falling particles, and the
collection of all unparameterized geodesics determines the projective structure
of the space-time. The article contains a formulation of the necessary and
sufficient conditions for these structures to be compatible, i.e. to come from
a metric tensor which is then unique up to a constant factor. The theorem
applies to all dimensions and signatures.Comment: 5 page