Gravitációs hullámkeltési folyamatok vizsgálata az általános relativitáselméletben = Study of gravitational wave production in general relativity

A kutatasi terveinknek megfelelően az alabbi nyolc teruleten ertunk el eredmenyeket: I. A nemlinearis gombszimmetrikus dinamikai rendszerek időfejlődeset hűen leiro numerikus eljarasunkat tovabbfejlesztettuk ugy, hogy mind az szimmetriafeltetelektől mentes rendszerek leirasara, mind pedig az „adaptiv racsfinomitasos” technikai elemek alkalmazasara kepes legyen. A fejlesztesekkel parhuzamosan kulonfele altalanos relativisztikus dinamikai rendszer időfejlődeset hataroztuk meg. II. Feltartuk a gravitacios osszeomlasi folyamatok soran kialakulo dinamikai feketelyuk-teridők topologiai tulajdonsagait. III. A gravitacio geometrizalt elmeleteiben megadtuk a szingularis teridők globalis kiterjeszthetősegenek szukseges felteteleit. IV. Fizikailag realis allapotegyenletű forgo neutroncsillag-modellek megkonstrualasa. V. Gombszimmetrikus csillagmodellek vizsgalata a nem zerus kozmologiai allandoval jellemzett univerzummodellek eseten. VI. Neutroncsillag-modellek stabilitasvizsgalata, valamint a gombhejakba tomorulő anyageloszlasok altalanos dinamikajanak leirasa. VII. A deformalt stacionarius feketelyuk-teridők altalanos leirasa. VIII. Reszvetel a Virgo tudomanyos egyuttműkodes munkajaban es a CBwaves nevű programcsomag kidolgozasa es a LIGO-Virgo egyuttműkodes altal alkalmazott keresőalgoritmusokba tortenő integralasa. A palyazatban megjelolt feladatokhoz kapcsolodoan 14 elmeleti temaju, es 23 kollaboracios, magas impaktfaktoru folyoiratcikkunk jelent meg. | In accordance with our research proposal the new results belong to either of the following eight categories: I. Our numerical method capable to follow the time evolution of generic spherically symmetric dynamical systems was further developed such that both the symmetry assumptions were relaxed and the techniques of adaptive mesh refinements had been implemented. In parallel the developed code had been applied to study the evolution of various general relativistic dynamical systems. II. The topological properties of generic co-dimension two surfaces in black hole spacetime was determined. III. In metric theories of gravity the necessary conditions guaranteeing the global extendibility of singular spacetimes were given. IV. Neutron star models with physically reasonable equation of state were constructed. V. Spherically symmetric stars in models of the universe with non-zero cosmological constant were investigated. VI.The radial stability of neutron star models and the dynamics of matter distribution concentrated on spherical shells were determined. VII. A generic framework of deformed stationary black hole spacetimes was established. VIII. We joined to the Virgo scientific collaboration.The CBwaves software was developed and it was integrated it into various data analyzing algorithms of the LIGO-Virgo collaboration. In relation with the listed achievements 14 theoretical, and 23 experimental papers have been published in high impact scientific journals.