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Evolution of an extended Ricci flow system
, 2006
"... We show that Hamilton’s Ricci flow and the static Einstein vacuum equations are closely connected by the following system of geometric evolution equations: ∂tg = −2Rc(g) + 2αndu ⊗ du, ∂tu = Δgu, where g(t) is a Riemannian metric, u(t) a scalar function and αn a constant depending only on the dimens ..."
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We show that Hamilton’s Ricci flow and the static Einstein vacuum equations are closely connected by the following system of geometric evolution equations: ∂tg = −2Rc(g) + 2αndu ⊗ du, ∂tu = Δgu, where g(t) is a Riemannian metric, u(t) a scalar function and αn a constant depending only on the dimension n ≥ 3. This provides an interesting and useful link from problems in lowdimensional topology and geometry to physical questions in general relativity. 1.
Radiative gravitational fields and asymptotically static or stationary initial data
, 2008
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QUASIMAXWELL INTERPRETATION OF THE SPINCURVATURE COUPLING
, 2007
"... Abstract. We write the MathissonPapapetrou equations of motion for a spinning particle in a stationary spacetime using the quasiMaxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particle ..."
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Abstract. We write the MathissonPapapetrou equations of motion for a spinning particle in a stationary spacetime using the quasiMaxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particles in the NUT spacetime.
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, 2008
"... Initial data for stationary spacetimes near spacelike infinity ..."
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1 Matching stationary spacetimes
, 2008
"... Using the quasiMaxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2dimensional matching surface on the space manifold ..."
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Using the quasiMaxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with spherical, planar, hyperbolic and cylindrical symmetry. Finally, we find an explicit interior for the cylindrical analogue of the NUT spacetime.
Gravitating discs around black holes
, 2004
"... Fluid discs and tori around black holes are discussed within different approaches and with the emphasis on the role of disc gravity. First reviewed are the prospects of investigating the gravitational field of a black hole–disc system by analytical solutions of stationary, axially symmetric Einstein ..."
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Fluid discs and tori around black holes are discussed within different approaches and with the emphasis on the role of disc gravity. First reviewed are the prospects of investigating the gravitational field of a black hole–disc system by analytical solutions of stationary, axially symmetric Einstein’s equations. Then, more detailed considerations are focused to middle and outer parts of extended disclike configurations where relativistic effects are small and the Newtonian description is adequate. Within general relativity, only a static case has been analysed in detail. Results are often very inspiring, however, simplifying assumptions must be imposed: ad hoc profiles of the disc density are commonly assumed and the effects of framedragging and completely lacking. Astrophysical discs (e.g. accretion discs in active galactic nuclei) typically extend far beyond the relativistic domain and are fairly diluted. However, selfgravity is still essential for their structure and evolution, as well as for their radiation emission and the impact on the environment around. For example, a nuclear star cluster in a galactic centre may bear various imprints of mutual star–disc interactions, which can be recognised in observational properties, such as the relation between the central mass and stellar velocity dispersion.