A Survey on Spacetime Geometries and Relativistic Models

Our analysis starts with the flat geometry, so-called Minkowski spacetime, and follows by further generalizations on specific spherically symmetric geometries whose metric elements describe solutions to the Einstein’s field equation. Next the relativistic models originated from the conservation form of the energy momentum tensor relation on these particular examples of spacetime geometries are presented. Finally we introduce certain properties of these models of interests and hence provide a conclusion including a comparison (both theoretically and numerically) of the models of related geometries.


A physical model for dimensional reduction and its effects on the observable parameters of the universe
Karaca, Koray; Bayın, Selçuk; Department of Physics (2005)
In this thesis, assuming that higher spatial dimensions existed only during the inflationary prematter phases of the universe, we construct a (1+D)-dimensional (D>3), nonsingular, homogeneous and isotropic Friedmann model for dimensional reduction. In this model, dimensional reduction occurs in the form of a phase transition that follows from a purely thermodynamical consideration that the universe heats up during the inflationary prematter phases. When the temperature reaches its Planck value Tpl,D, which ...
A density functional theory study on the structural and electronic properties of PbxSbySez (x plus y plus z=2, 3) clusters
Pekoz, Rengin; Erkoç, Şakir (2018-01-30)
The structural and electronic properties of neutral ternary PbxSbySez clusters (x y + z = 2, 3) in their ground states have been explored by means of density functional theory calculations. The geometric structures and binding energies are systematically explored and for the most stable configurations of each cluster type vibrational frequencies, charges on atoms, energy difference between highest occupied and lowest unoccupied molecular orbitals, and the possible dissociations channels have been analyzed. ...
From smooth curves to universal metrics
GÜRSES, METİN; Sisman, Tahsin Cagri; Tekin, Bayram (2016-08-22)
A special class of metrics, called universal metrics, solves all gravity theories defined by covariant field equations purely based on the metric tensor. Since we currently lack the knowledge of what the full quantum-corrected field equations of gravity are at a given microscopic length scale, these metrics are particularly important in understanding quantum fields in curved backgrounds in a consistent way. However, finding explicit universal metrics has been a difficult problem as there does not seem to be...
A general representation for classical detection theory with Euclidean geometry Klasik tespit kurami için Öklid geometrisi ile genel bir gösterim
Bayramog̃lu, Muhammet Fatih; Yılmaz, Ali Özgür (2010-12-01)
A general geometric representation for the classical detection theory which is compatible with Euclidean geometry is proposed. The proposed representation is so generic that can be employed to almost all communication problems. The a posteriori probability of a symbol given an observation occurred decreases exponentially with the square of the Eclidean distance between vectors in R N that the symbol and the observation are mapped onto.
A model for the computation of quantum billiards with arbitrary shapes
Erhan, Inci M.; Taşeli, Hasan (Elsevier BV, 2006-10-01)
An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter.
Citation Formats
B. Okutmuştur, “A Survey on Spacetime Geometries and Relativistic Models,” Diyarbakır, Türkiye, 2019, p. 41, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/81209.