Search results for "General Relativity"
showing 10 items of 1057 documents
How to interpret black hole entropy?
1998
We consider a possibility that the entropy of a Schwarzschild black hole has two different interpretations: The black hole entropy can be understood either as an outcome of a huge degeneracy in the mass eigenstates of the hole, or as a consequence of the fact that the interior region of black hole spacetime is separated from the exterior region by a horizon. In the latter case, no degeneracy in the mass eigenstates needs to be assumed. Our investigation is based on calculations performed with Lorentzian partition functions obtained for a whole maximally extended Schwarzschild spacetime, and for its right-hand-side exterior region. To check the correctness of our analysis we reproduce, in th…
Relativistic Positioning Systems: Numerical Simulations
2014
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true location may be found using additional information (angles or times). The zone where the Jacobian, J, of the transformation from inertial to emission coordinates vanishes is also represented and interpreted. It is shown that the uncertainties in the satellite world lines produce positioning errors, which depend on the value of |J|. The smaller this quantity the greater the expected positioning errors. Among all the available 4-tuples of satellites, the most app…
The galaxy power spectrum take on spatial curvature and cosmic concordance
2020
The concordance of the $\Lambda$CDM cosmological model in light of current observations has been the subject of an intense debate in recent months. The 2018 Planck Cosmic Microwave Background (CMB) temperature anisotropy power spectrum measurements appear at face value to favour a spatially closed Universe with curvature parameter $\Omega_K<0$. This preference disappears if Baryon Acoustic Oscillation (BAO) measurements are combined with Planck data to break the geometrical degeneracy, although the reliability of this combination has been questioned due to the strong tension present between the two datasets when assuming a curved Universe. Here, we approach this issue from yet another point…
Correlation functions for a strongly coupled boson system and plane partitions.
2011
A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q -boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.
Singularities of lightlike hypersurfaces in Minkowski four-space
2006
We classify singularities of lightlike hypersurfaces in Minkowski 4-space via the contact invariants for the corresponding spacelike surfaces and lightcones.
Supermanifolds, Symplectic Geometry and Curvature
2016
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
Flat lightlike hypersurfaces in Lorentz–Minkowski 4-space
2009
Abstract The lightlike hypersurfaces in Lorentz–Minkowski space are of special interest in Relativity Theory. In particular, the singularities of these hypersurfaces provide good models for the study of different horizon types. We introduce the notion of flatness for these hypersurfaces and study their singularities. The classification result asserts that a generic classification of flat lightlike hypersurfaces is quite different from that of generic lightlike hypersurfaces.
Global properties of codimension two spacelike submanifolds in Minkowski space
2009
Abstract We consider codimension two spacelike submanifolds with a parallel normal field (i.e. vanishing normal curvature) in Minkowski space. We use the analysis of their contacts with hyperplanes and hyperquadrics in order to get some global information on them. As a consequence we obtain new versions of Carathéodory's and Loewner's conjectures on spacelike surfaces in 4-dimensional Minkowski space and 4-flattenings theorems for closed spacelike curves in 3-dimensional Minkowski space.
Comments on `A new efficient method for calculating perturbation energies using functions which are not quadratically integrable'
1996
The recently proposed method of calculating perturbation energies using a non-normalizable wavefunction by Skala and Cizek is analysed and rigorously proved.
New approach to describe two coupled spins in a variable magnetic field
2021
We propose a method to describe the evolution of two spins coupled by hyperfine i nteraction in an external time- dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to t reat t he n onstationary d ynamical p roblem, we modify the time-dependent Schrödinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrödinger FRVBUJPO in the form of chronologically ordered exponents with transpar…