Kerr black holes and their generalizations

Cebeci, Hakan
The scalar tensor theory of gravitation is constructed in D dimensions in all possible geometries of spacetime. In Riemannian geometry, theory of gravitation involves a spacetime metric g with a torsion-free, metric compatible connection structure. If the geometry is non-Riemannian, then the gauge theory of gravitation can be constructed with a spacetime metric g and a connection structure with torsion. In non-Riemannian theory, connections may be metric compatible or non-metric compatible. It is shown that theory of gravitation which involves non-metric compatible connection and torsion, can be rewritten in terms of torsion-free theory. It is also shown that scalar tensor theory can be reformulated in Einstein frame by applying a conformal transformation. By adding an antisymmetric axion field, the axi-dilaton theory is studied in Riemannian and non-Riemannian geometries. Motion of massive test particles is examined in all these geometries. The static, spherically symmetric and stationary, Kerr-type axially symmetric solutions of the scalar tensor and axi-dilaton theories are presented. As an application, the geodesic elliptical orbits based on a torsion-free connection and the autoparallel orbits based on a connection with a torsion, are examined in Kerr Brans-Dicke geometry. Perihelion shift of the elliptical orbit is calculated in both cases and the results are compared.


BAYM, SS; OZCAN, M (1994-05-15)
We calculate the renormalized quantum vacuum energy-momentum tensor inside a spherical boundary, where the background geometry inside the boundary is represented by the closed static Friedmann metric. The remormalized energy density has two terms, one of which comes from the local curvature and the other one is due to the presence of the boundary. The renormalized energy density has a nonintegrable divergence as the boundary is approached.
Topologically massive gravity as a Pais-Uhlenbeck oscillator
Sarıoğlu, Bahtiyar Özgür; Tekin, Bayram (IOP Publishing, 2006-12-21)
We give a detailed account of the free- field spectrum and the Newtonian limit of the linearized ` massive' ( Pauli -Fierz), 'topologically massive' ( Einstein Hilbert - Chern - Simons) gravity in 2 + 1 dimensions about a Minkowski spacetime. For a certain ratio of the parameters, the linearized free theory is Jordan diagonalizable and reduces to a degenerate ` Pais - Uhlenbeck' oscillator which, despite being a higher derivative theory, is ghost free.
Spectra, vacua, and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes
Sisman, Tahsin Cagri; Gullu, Ibrahim; Tekin, Bayram (2012-08-24)
We explicitly confirm the expectation that generic Lovelock gravity in D dimensions has a unitary massless spin-2 excitation around any one of its constant curvature vacua just like the cosmological Einstein gravity. The propagator of the theory reduces to that of Einstein's gravity, but scattering amplitudes must be computed with an effective Newton's constant which we provide. Tree-level unitarity imposes a single constraint on the parameters of the theory yielding a wide range of unitary region. As an ex...
Entangled Harmonic Oscillators and Space-Time Entanglement
Başkal, Sibel; Kim, Young S.; Noz, Marilyn E. (MDPI AG, 2016-6-28)
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent p...
Equivariant Reduction of Gauge Theories over Fuzzy Extra Dimensions
Kürkcüoğlu, Seçkin (IOP Publishing, 2012-2-8)
In SU(N) Yang-Mills theories on a manifold M, which are suitably coupled to a set of scalars, fuzzy spheres may be generated as extra dimensions by spontaneous symmetry breaking. This process results in gauge theories over the product space of the manifold M and the fuzzy spheres with smaller gauge groups. Here we present the SU(2)- and SU(2) x SU(2)-equivariant parametrization of U(2) and U(4) gauge fields on S-F(2), and S-F(2), x S-F(2), respectively and outline the dimensional reduction of these theories...
Citation Formats
H. Cebeci, “Kerr black holes and their generalizations,” Ph.D. - Doctoral Program, Middle East Technical University, 2003.