Levi-Civita,Tullio

International audienceTullio Levi-Civita (29 March 1873 to 29 December 1941) has been an Italian mathematician and mathematical physicist, known above all for his work on the absolute differential calculus. Levi-Civita came from a rigorous and creative school of mathematical physicists and was a pupil of Gregorio Ricci-Curbastro. LeviCivita’s work included outstanding results in pure and applied mathematics and in celestial and analytic mechanics but also celebrated textbooks. These last, even those written in Italian, have influenced mathematical physicists all over the world.Levi-Civita has perfected some conceptual tools of great importance in modern science, particularly in general relativity, number theory, and continuum mechanics

Expanding perfect fluid generalizations of the C-metric

We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike non-shearing and non-rotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum C-metric as a limit case, can have \emph{non-zero} expansion, contrary to the conclusion in the original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type $D$ spacetimes in general, which we add in an appendix.Comment: 16 pages, extended and amended versio

Gravitational Model of the String

It is shown that an infinite gravitational flux tube solution in 5D Kaluza-Klein gravity with the cross section in the Planck region after $5D \to 4D$ reduction and isometrical embedding in a Minkowski spacetime can be considered as a moving infinite string-like object. Such object has a flux of the electric and magnetic fields. The 4D gravitational waves on the tube are considered.Comment: some changes in tex

Tunneling between single and multi-centered black hole configurations

We find a gravitational instanton that connects an initial state corresponding to a single-centered extremal Reissner-Nordstrom (ERN) black hole configuration, to a final state corresponding to a multi-centered configuration. This instanton is interpreted as describing quantum tunneling between the two different black hole solutions. We evaluate the Euclidean action for this instanton and find that the amplitude for the tunneling process is equal to half the difference in entropy between the initial and final configurations.Comment: 8 pages, 4 figures. v4: final version accepted for publication in Phys. Rev.

Strings and Branes under Microscope

It is shown that in the standard vacuum 5D Kaluza-Klein gravity there is wormhole-like solutions which look like strings attached to two D-branes. The asymptotical behaviour of the corresponding metric is investigated.Comment: comparison with known solutions is adde

Two remarks on PQϵPQ^{\epsilon}-projectivity of Riemannian metrics

We show that $PQ^{\epsilon}$-projectivity of two Riemannian metrics introduced in \cite{Top2003} implies affine equivalence of the metrics unless $\epsilon\in\{0,-1,-3,-5,-7,...\}$. Moreover, we show that for $\epsilon=0$, $PQ^{\epsilon}$-projectivity implies projective equivalence.Comment: 6 pages, 2 figure