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Technicalities in the calculation of the 3rd post-Newtonian dynamics

Piotr Jaranowski (1997)

Banach Center Publications

Dynamics of a point-particle system interacting gravitationally according to the general theory of relativity can be analyzed within the canonical formalism of Arnowitt, Deser, and Misner. To describe the property of being a point particle one can employ Dirac delta distribution in the energy-momentum tensor of the system. We report some mathematical difficulties which arise in deriving the 3rd post-Newtonian Hamilton's function for such a system. We also offer ways to overcome partially these difficulties....

The closed Friedman world model with the initial and final singularities as a non-commutative space

Michael Heller, Wiesław Sasin (1997)

Banach Center Publications

The most elegant definition of singularities in general relativity as b-boundary points, when applied to the closed Friedman world model, leads to the disastrous situation: both the initial and final singularities form the single point of the b-boundary which is not Hausdorff separated from the rest of space-time. We apply Alain Connes' method of non-commutative geometry, defined in terms of a C*-algebra, to this case. It turns out that both the initial and final singularities can be analysed as...

The graded differential geometry of mixed symmetry tensors

Andrew James Bruce, Eduardo Ibarguengoytia (2019)

Archivum Mathematicum

We show how the theory of ℤ 2 n -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

The Group of Large Diffeomorphisms in General Relativity

Domenico Giulini (1997)

Banach Center Publications

We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.

The laser interferometer gravitational wave observatory project LIGO

James Blackburn (1997)

Banach Center Publications

The Laser Interferometer Gravitational Wave Observatory (LIGO) will search for direct evidence of gravitational waves emitted by astrophysical sources in accord with Einstein’s General Theory of Relativity. State of the art laser interferometers located in Hanford, Washington and Livingston Parish, Louisiana will unambiguously measure the infinitesimal displacements of isolated test masses which convey the signature of these gravitational waves. The initial implementation of LIGO will consist of...

The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant

Igor Rodnianski, Jared Speck (2013)

Journal of the European Mathematical Society

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1 + 3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p = c 2 ρ , 0 < c 2 < 1 / 3 , the background metric + fluid solutions...

The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

Jonathan Luk (2013)

Journal of the European Mathematical Society

We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region { r ≤ t 4 } .

The Pioneer anomaly.

Turyshev, Slava G., Toth, Viktor T. (2010)

Living Reviews in Relativity [electronic only]

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