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In den vergangen Jahren wurde erkannt, dass eine Quantenfeldtheorie (QFT) namens Quantenchromodynamik (QCD) die richtige Theorie der starken Wechselwirkungen ist. QCD beschreibt erfolgreich die starken Wechselwirkungen, die Quarks zu Nukleonen und Nukleonen zu Atomkernen zusammenbinden. Jedoch ist die theoretische Beschreibung vieler Phänomene der starken Wechselwirkung aufgrund des starken Kopplungsverhaltens bei niedrigen Energien schwierig. Stoßexperimente mit Schwerionen sind ein möglicher Weg, um die charakteristischen Phänomene und Eigenschaften der QCD-Materie zu untersuchen. In Stoßexperimenten mit Schwerionen werden schwere (d.h. große) Atomkerne aufeinander geschossen, beispielsweise Gold (am RHIC) oder Blei (am CERN, LHC), mit einer ultrarelativistischen Energie √s im Schwerpunktsystem. Auf diese Art ist es möglich, eine große Menge von Materie mit hoher Energiedichte hervorzubringen. Das Ziel von Schwerionenkollisionen ist die Erzeugung und Charakterisierung einer makroskopischen Phase von freien Quarks und Gluonen im lokalen thermischen Gleichgewicht. Ein solcher Aggregatzustand kann neue Informationen über das QCD-Phasendiagramm und den QCD-Phasenübergang liefern. Man nimmt an, dass ein solcher Übergang stattfand, als sich die Materie des frühen Universums von einem Plasma aus Quarks und Gluonen (QGP) in ein Gas von Hadronen umwandelte...
In this thesis, Planck size black holes are discussed. Specifically, new families of black holes are presented. Such black holes exhibit an improved short scale behaviour and can be used to implement gravity self-complete paradigm. Such geometries are also studied within the ADD large extra dimensional scenario. This allows black hole remnant masses to reach the TeV scale. It is shown that the evaporation endpoint for this class of black holes is a cold stable remnant. One family of black holes considered in this thesis features a regular de Sitter core that counters gravitational collapse with a quantum outward pressure. The other family of black holes turns out to nicely fit into the holographic information bound on black holes, and lead to black hole area quantization and applications in the gravitational entropic force. As a result, gravity can be derived as emergent phenomenon from thermodynamics.
The thesis contains an overview about recent quantum gravity black hole approaches and concludes with the derivation of nonlocal operators that modify the Einstein equations to ultraviolet complete field equations.
In thesis I investigate the possibility that at the smallest length scale (Planck scale) the very notion of "dimension" needs to be revisited. Due to "quantum effects" spacetime might become very turbulent at these scales and properties like those of "fractals" emerge, including a "scale dependent dimension". It seems that this "spontaneous dimensional reduction" and the appearance of a minimal physical length are very general effects that most approaches to quantum gravity share. Main emphasis is given to the"spectral dimension" and its calculation for strings and p-branes.
The Generalized Uncertainty Principle (GUP) arises from Quantum Gravity thought experiments and contains a minimal lenght. In this thesis I calculate Schwarzschild Black Holes that are modified by the GUP. These Black Holes have the property, that their temperature does not diverge for small masses, although they still posses a curvature singularity. I calculate analytically that in more than 3+1 dimensions the temperature diverges again.
This thesis is a summary of existing and upcoming publications, with a focus on high order methods in numerical relativity and general relativistic flows. The text is structed in five chapters. In the first three ones, the ADER-DG technique and its application to the Einstein-Euler equations is introduced. Novel formulations for both the Einstein equations in the 3+1 split as well as the general relativistic magnetohydrodynamics (GRMHD) had to be derived. The first order conformal and covariant Z4 formulation of Einstein equations (FO-CCZ4) is proposed and proven to be strongly hyperbolic. Together with the fluid equations of general relativistic magnetohydodynamics (GRMHD), a number of benchmark scenarios is presented to show both the correctness of the PDEs as well as the applicability of the numerical scheme.
As an application in astrophysics, a general-relativistic study of the treshold mass for a prompt-collapse of a binary neutron star merger with realistic nuclear equation of states has been carried out. A nonlinear universal relation between the treshold mass and the maximum compactness is found. Furthermore, by taking recent measurements of GW170817 into account, lower limits on the stellar radii for any mass can be given.
Furthermore, an (unpaired) work in quantum mechanical black hole engineering is presented. Higher dimensional extensions of generalized Heisenberg’s uncertainty principle (GUP) are studied. A number of new phenomenology is found, such as the existence of a conical singularity which mimics the effect of a gravitational monopole on short scale and that of a Schwarzschild black hole at a large scale, as well as oscillating Hawking temperatures which we call "lighthouse effect". All results are consistent with the self complete paradigm and a cold evaporation endpoint remnant.
