463 research outputs found

### 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. LeviCivitaâ€™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 inï¬‚uenced 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

### 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.

### Cosmological constant from quantum spacetime

http://dx.doi.org/10.1103/PhysRevD.91.124028Â© 2015, Physical Review

### Heun equation, Teukolsky equation, and type-D metrics

Starting with the whole class of type-D vacuum backgrounds with cosmological
constant we show that the separated Teukolsky equation for zero rest-mass
fields with spin $s=\pm 2$ (gravitational waves), $s=\pm 1$ (electromagnetic
waves) and $s=\pm 1/2$ (neutrinos) is an Heun equation in disguise.Comment: 27 pages, corrected typo in eq. (1

### Accelerated black holes in an anti-de Sitter universe

The C-metric is one of few known exact solutions of Einstein's field
equations which describes the gravitational field of moving sources. For a
vanishing or positive cosmological constant, the C-metric represents two
accelerated black holes in asymptotically flat or de Sitter spacetime. For a
negative cosmological constant the structure of the spacetime is more
complicated. Depending on the value of the acceleration, it can represent one
black hole or a sequence of pairs of accelerated black holes in the spacetime
with an anti-de Sitter-like infinity. The global structure of this spacetime is
analyzed and compared with an empty anti-de Sitter universe. It is illustrated
by 3D conformal-like diagrams.Comment: 14 pages, 17 figures [see
http://utf.mff.cuni.cz/~krtous/physics/CADS/ for the version with the high
quality figures and for related animations and interactive 3D diagrams

### Cylindrically and toroidally symmetric solutions with a cosmological constant

Cylindrical-like coordinates for constant-curvature 3-spaces are introduced
and discussed. This helps to clarify the geometrical properties, the coordinate
ranges and the meaning of free parameters in the static vacuum solution of
Linet and Tian. In particular, when the cosmological constant is positive, the
spacetimes have toroidal symmetry. One of the two curvature singularities can
be removed by matching the Linet-Tian vacuum solution across a toroidal surface
to a corresponding region of the dust-filled Einstein static universe. Some
other properties and limiting cases of these space-times are also described,
together with their generalisation to higher dimensions.Comment: 4 pages, 2 figures. To appear in the Proceedings of The Spanish
Relativity Meeting (ERE2010), Journal of Physics: Conference Serie

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