Open Access

High-energy astrophysics plays an increasingly important role in the understanding of our universe. On one hand, this is due to ground-breaking observations, like the gravitational-wave detections of the LIGO and Virgo network or the black-hole shadow observations of the EHT collaboration. On the other hand, the field of numerical relativity has reached a level of sophistication that allows for realistic simulations that include all four fundamental forces of nature. A prime example of how observations and theory complement each other can be seen in the studies following GW170817, the first detection of gravitational waves from a binary neutron-star merger. The same detection is also the chronological starting point of this Thesis. The plethora of information and constraints on nuclear physics derived from GW170817 in conjunction with theoretical computations will be presented in the first part of this Thesis. The second part goes beyond this detection and prepares for future observations when also the high-frequency postmerger signal will become detectable. Specifically, signatures of a quark-hadron phase transition are discussed and the specific case of a delayed phase transition is analyzed in detail. Finally, the third part of this Thesis focuses on the inclusion of radiative transport in numerical astrophysics. In the context of binary neutron-star mergers, radiation in the form of neutrinos is crucial for realistic long-term simulations. Two methods are introduced for treating radiation: the approximate state-of-the-art two-moment method (M1) and the recently developed radiative Lattice-Boltzmann method. The latter promises to be more accurate than M1 at a comparable computational cost. Given that most methods for radiative transport or either inaccurate or unfeasible, the derivation of this new method represents a novel and possibly paradigm-changing contribution to an accurate inclusion of radiation in numerical astrophysics.

In this thesis I develop a new technique of the use of tracers to study problems in the micro- and macroscopic aspects of post-merger dynamics in binary neutron star mergers, with particular attention to the dynamical ejecta and resulting r-process nucleosynthesis.

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.

This thesis investigates second-order relativistic hydrodynamics and transport coefficients in strongly correlated systems. Our focus is mainly on the physical conditions relevant to heavy-ion collisions, as well as compact dense stellar objects at nonzero temperatures and in strong magnetic fields. Chapter 1 provides a brief introduction to the area of research covered by this thesis, specifically relativistic hydrodynamics and transport in hot and dense media, which occur in heavy-ion collisions and heated stellar matter. In Chapter 2 we give a new formulation of second-order dissipative hydrodynamics for relativistic systems using Zubarev's non-equilibrium statistical operator approach. We first solve the quantum Liouville equation with an infinitesimal source term to construct a non-equilibrium statistical operator which is a non-local functional of the thermodynamic parameters and their space-time gradients. Exploiting then the gradient expansion of the statistical operator we derive transport equations for the shear stress tensor, the bulk viscous pressure and the flavour diffusion currents up to the second order in hydrodynamic gradients. We show that the second-order corrections to the dissipative fluxes arise from (i) the quadratic terms of the Taylor expansion of the statistical operator; and (ii) the linear terms which are nonlocal in space and time. These non-local corrections generate finite relaxation time scales in the evolution of the dissipative quantities. We derive the most generic form of the transport equations which involve gradients of the dissipative fluxes, as well as products of two first-order quantities (i.e., either thermodynamic forces or dissipative fluxes). We then go on to express the first- and the second-order transport coefficients, which appear in these equations, via certain two- and three-point equilibrium correlation functions. Finally, we express the relaxation times for the dissipative fluxes via the frequency-derivatives of the corresponding first-order transport coefficients. In Chapter 3 we compute the transport coefficients of quark matter in the strong coupling regime within the two-flavor Nambu-Jona-Lasinio model. We apply the Kubo-Zubarev formalism to obtain the thermal and the electrical conductivities as well as the shear and the bulk viscosities by evaluating the corresponding equilibrium two-point correlation functions at the leading order in the 1/N_c expansion. In this approximation the conductivities and the shear viscosity are given by single-loop skeleton diagrams, whereas the bulk viscosity includes an infinite geometrical series of multi-loop diagrams. The dispersive effects that lead to nonzero transport coefficients arise from quark-meson fluctuations above the Mott transition temperature T_M, where meson decay into two on-mass-shell quarks is kinematically allowed. We find that the conductivities and the shear viscosity are decreasing functions of temperature and density above T_M. We also show that the Wiedemann-Franz law does not hold. The ratio of the shear viscosity to the entropy density is larger than unity close to the Mott temperature and approaches the AdS/CFT bound at higher temperatures. We conjecture on the basis of the uncertainty principle that the ratio of the thermal conductivity to the heat capacity per unit volume is bounded from below by 1/18. The case of the bulk viscosity turns out to be special, because the multi-loop contributions dominate the single-loop contribution close to the Mott line in the case where the chiral symmetry is explicitly broken. We find that in this case only at high temperatures the one-loop contribution becomes dominant. The resulting bulk viscosity exceeds the shear viscosity close to the Mott temperature by factors 5-20 when multi-loop contributions are included. In the high-temperature domain the bulk viscosity is negligible compared to the shear viscosity. For practical applications we provide simple, but accurate fits to the transport coefficients, which can facilitate the implementation of our results in hydrodynamics codes. In Chapter 4 we compute the electrical conductivity of finite temperature, strongly magnetized crust of a compact star which may be formed in the aftermath of a supernova explosion, binary neutron star merger, or during accretion processes in X-ray binaries. We focus on the temperature-density regime where plasma is in the liquid state and, therefore, the conductivity is dominated by the electron scattering off correlated nuclei. The dynamical screening of electron-ion interaction is implemented in terms of the polarization tensor computed in the hard-thermal-loop (HTL) effective field theory of QED plasma. The correlations of the background ionic component are accounted for via a structure factor derived from Monte Carlo simulations of one-component plasma. With this input we solve the Boltzmann kinetic equation in relaxation time approximation taking into account the anisotropy of transport due to the magnetic field. The electrical conductivity tensor is studied numerically as a function of temperature, density, magnetic field and the crust composition in a broad parameter range. We find that the conductivity as a function of temperature attains a minimum at the transition from the degenerate to the nondegenerate regime of electrons. We also provide accurate fit formulas to our numerical results for three components of the conductivity tensor. In addition, we provide supplemental tables which can be used in dissipative magneto-hydrodynamics(MHD) simulations of warm compact stars. We summarize our results and discuss the perspectives in Chapter 5.

Binary neutron star mergers represent unique observational phenomena because all four fundamental interactions play an important role at various stages of their evolution by leaving imprints in astronomical observables. This makes their accurate numerical modeling a challenging multiphysics problem that promises to increase our understanding of the high-energy astrophysics at play, thereby providing constraints for the underlying fundamental theories such as the gravitational interaction or the strong interaction of dense matter. For example, the first and so far only multi-messenger observation of the binary neutron star merger GW170817 resulted in numerous bounds on the parameters of isolated non-rotating neutron stars, e.g., their maximum mass or their distribution in radii, which can be directly used to constrain the equation of state of cold nuclear matter. While many of these results stem from the observation of the inspiral gravitational-wave signal, the postmerger phase of binary neutron star mergers encodes even more details about the extreme physics of hot and dense neutron star matter. In this Thesis we focus on the exploration of dissipative and shearing effects in binary neutron star mergers in order to identify novel approaches to constrain hot and dense neutron star matter. The first effect is the well-motivated dissipation of energy due to the bulk viscosity which arises from violations of weak chemical equilibrium. We start by exploring the impact of bulk viscosity on black-hole accretion. This simplified problem gives us the opportunity to develop a test case for future codes taking into account the effects of dissipation in a fully general-relativistic setup and build intuition in the physics of relativistic dissipation. Next, we move on to isolated neutron stars and binary neutron star mergers by developing a robust implementation of bulk-viscous dissipation for numerical relativity simulations. We test our implementation by calculating the damping of eigenmodes of isolated neutron stars and the violent migration scenario. Finally, we present the first results on the impact of bulk viscosity on binary neutron star mergers. We identify a number of ways how bulk viscosity impacts the postmerger phase, out of which the suppression of gravitational-wave emission and dynamical mass ejection are the most notable ones. In the last part of this Thesis we investigate how the shearing dynamics at the beginning of the merger affects the amplification of different initial magnetic-field topologies. We explore the hypothesis that magnetic fields which are located only in a small region near the stellar surface prior to merger lead to a weaker magnetic-field amplification. We show first evidence which confirms this hypothesis and discuss possible implications for constraining the physics of superconduction in cold neutron stars.