15 research outputs found
Gravitational non-commutativity and G\"odel-like spacetimes
We derive general conditions under which geodesics of stationary spacetimes
resemble trajectories of charged particles in an electromagnetic field. For
large curvatures (analogous to strong magnetic fields), the quantum
mechanicical states of these particles are confined to gravitational analogs of
{\it lowest Landau levels}. Furthermore, there is an effective
non-commutativity between their spatial coordinates. We point out that the
Som-Raychaudhuri and G\"odel spacetime and its generalisations are precisely of
the above type and compute the effective non-commutativities that they induce.
We show that the non-commutativity for G\"odel spacetime is identical to that
on the fuzzy sphere. Finally, we show how the star product naturally emerges in
Som-Raychaudhuri spacetimes.Comment: Two sections added (Relation to the fuzzy sphere, Emergence of the
star product). 10 pages, Revtex. To appear in General Relativity and
Gravitatio
Collapsing shear-free perfect fluid spheres with heat flow
A global view is given upon the study of collapsing shear-free perfect fluid
spheres with heat flow. We apply a compact formalism, which simplifies the
isotropy condition and the condition for conformal flatness. This formalism
also presents the simplest possible version of the main junction condition,
demonstrated explicitly for conformally flat and geodesic solutions. It gives
the right functions to disentangle this condition into well known differential
equations like those of Abel, Riccati, Bernoulli and the linear one. It yields
an alternative derivation of the general solution with functionally dependent
metric components. We bring together the results for static and time- dependent
models to describe six generating functions of the general solution to the
isotropy equation. Their common features and relations between them are
elucidated. A general formula for separable solutions is given, incorporating
collapse to a black hole or to a naked singularity.Comment: 26 page