We study the ultraviolet properties of quantum gravity and its consequences for black hole physics using the functional renormalisation group (RG). In particular we concentrate on the asymptotic safety scenario for quantum gravity put forward by S. Weinberg. This approach relies on the existence of an ultraviolet fixed point in the renormalisation group flow. In chapter 2 we review the functional renormalisation group formalism that is used in order to search for the existence of a fixed point with the properties required for asymptotic safety. Following this introduction, in chapter 3 we use these methods to find ultraviolet fixed points in four-dimensional quantum gravity to high order in a polynomial approximation in the Ricci scalar. In the following three chapters we concentrate on the implications of the renormalisation group for black hole physics. In chapter 4 we study quantum gravitational corrections to black holes in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short distance physics is characterised by a weakening of gravity due to the nontrivial fixed point. Furthermore, mini-black hole production in particle collisions, such as those at the Large Hadron Collider (LHC), is analysed within low-scale quantum gravity models. In chapter 5 we investigate the thermodynamical properties of the RG improved metrics in detail and study their evaporation process. In chapter 6 we study renormalisation group improved black hole thermodynamics in a metric free approach. Conditions are formulated under which the thermodynamic properties of four dimensional Kerr-Newman type black holes persist under the RG evolution of couplings. We show that the RG scale must be set by the horizon area of the black hole which acts as a diffeomorphism invariant cut-off for the underlying Wilsonian action.

The scale of quantum gravity could be as low as a few TeV in the existence of extra spatial dimensions or if the Planck scale runs fast due to a large number of particles in a hidden sector. One of the most striking features of low-scale quantum gravity models would be the creation of quantum black holes, i.e. non-thermal black holes with masses around a few TeV, in high energy collisions. This thesis deals with the production and decay mechanisms of quantum black holes at current colliders, such as the Large Hadron Collider (LHC). Firstly, a review of models with low-scale gravity is given. We will present an overview of production and decay mechanism of classical and semi-classical black holes, including the Hoop conjecture criterion, closed trapped surfaces and thermal decay via Hawking radiation. We will then introduce a phenomenological approach of black holes, very differently from the (semi-)classical counterparts, which covers a substantially model independent and specifically established field theory, describing the production of quantum black holes. This is done by matching the amplitude of the quantum black hole processes to the extrapolated semi-classical cross section. All possible decay channels and their probabilities are found for quantum black holes with a continuous and discrete mass spectrum, respectively, by considering different symmetry conservation restrictions for a quantum gravitational theory. In conjunction with these branching ratios, we developed a Monte Carlo integration algorithm to determine the cross sections of specific final states. We extended the algorithm to investigate the enhancement of supersymmetric particle production via quantum black hole processes. Studying such objects proves very important, since it provides new possible insights and restrictions on the quantum black hole model and likewise on the low-scale quantum gravity scenarios.

Inflation is the leading candidate to explain the initial conditions for the Universe we see today. It consists of an epoch of accelerated expansion, and regularly solves many problems with the Big Bang theory. Non-Gaussianity of the primordial curvature perturbation can potentially be used to discriminate between competing models and provide an understanding of the mechanism of inflation. Whilst inflation is believed to have lasted at least 50 - 60 e-folds, constraints from sources such as the cosmic microwave background (CMB) or large-scale structure of the Universe (LSS) only span the largest 6 - 10 e-folds inside today's Hubble horizon, limiting our ability to constrain the early universe. Strong constraints on the non-Gaussianity on smaller scales. Primordial black holes (PBHs) represent a unique probe to study the small-scale early Universe, placing an upper limit on the primordial power spectrum spanning around 40 e-folds smaller than those visible in the CMB. PBHs are also a viable dark matter candidate. In this thesis, the effect of non-Gaussianity upon the abundance of PBHs, and the implications of such an effect are considered. It is shown that even smaller non-Gaussianity parameters can have a large effect on the constraints that can be placed on the primordial curvature perturbation power spectrum - which can become stronger or weaker by an order of magnitude. The effects of super-horizon curvature perturbation modes at the time of PBH formation are considered, and it is shown that these have little effect on the formation of a PBH, but can have an indirect effect on the abundance of PBHs due to modal coupling to horizon-scale modes in the presence of non-Gaussianity. By taking into account the effect of modal coupling to CMB-scale modes, many models can be ruled out as a mechanism to produce enough PBHs to constitute dark matter.

Master of Science / General Relativity (GR) is founded on the revolutionary idea that space and time are merely parts of a greater, unified whole: spacetime. Furthermore, the force we know as gravity results from the bending and stretching of the geometry of spacetime by its energetic contents. GR is notorious for its mathematical complexity and subtlety, meaning that an intuitive understanding of a spacetime is difficult. One of the best approaches to studying the properties of a given spacetime is to consider its geodesic structure—that is, to consider the motion of unaccelerated, “free-falling” particles. This report presents the results of such a study into two important spacetimes — the Kerr solution for a rotating black hole, and the Robertson-Walker solution for a homogeneous universe.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Binary black hole mergers are the strongest expected producers of graviational radiation in the universe. Ground-based and proposed space-based gravitational wave detectors will benefit from simulations modeling the mergers and extracting the resulting gravitational waveforms. Producing templates of waveforms will both aid the likelihood of detection and the estimation of parameters (mass ratio, spin, etc.). openGR is modular, open framework development to carry out simulations of binary black hole mergers. While designed with the two-body problem in mind, openGR will evolve most general spacetimes. This work overviews the capabilities of openGR and the corresponding physics involved. openGR supports both excision and puncture methods. When excising the black hole, to date we have used only the weakly hyperbolic ADM formulation of the Einstein’s equations. As expected from a weakly hyperbolic system, instabilites arise and crash the code when simulating even just a single boosted black hole in Kerr-Schild coordinates. In contrast, successful mergers of two black holes have been achieved using the puncture method. We demonstrate such a simulation in Ch 8. In this case, we make use of a BSSN formulation of Einstein’s equations (a strongly hyperbolic system). / text

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Master of Science / General Relativity (GR) is founded on the revolutionary idea that space and time are merely parts of a greater, unified whole: spacetime. Furthermore, the force we know as gravity results from the bending and stretching of the geometry of spacetime by its energetic contents. GR is notorious for its mathematical complexity and subtlety, meaning that an intuitive understanding of a spacetime is difficult. One of the best approaches to studying the properties of a given spacetime is to consider its geodesic structure—that is, to consider the motion of unaccelerated, “free-falling” particles. This report presents the results of such a study into two important spacetimes — the Kerr solution for a rotating black hole, and the Robertson-Walker solution for a homogeneous universe.

Thesis (M.Sc.). / Written for the Dept. of Mathematics and Statistics. Title from title page of PDF (viewed 2008/01/15). Includes bibliographical references.

First observed as early as redshift z = 7 and now thought to be found at the centre of every massive galaxy in the local Universe, the evolution history of supermassive black holes (SMBHs) spans over 13 billion years. In this thesis, the coevolution between SMBHs and their host galaxies is studied using a set of hydrodynamical simulations to isolate different components of the interaction between black holes and cosmic gas. The simulations range from black hole accretion in an idealised context to the impact of feedback in the cosmological simulations of the HORIZON suite. The origin of SMBHs during the first billion years of the Universe is a highly non-linear problem, where small-scale behaviour influences large- scale behaviour and vice versa. Gas fuelling a black hole flows from the cosmic web, through its host galaxy and into the black hole's gravitational potential, before eventually reaching its event horizon. Even discounting the complex physical processes at play, resolving the 19 orders of magni- tude in spatial scale involved is beyond the capabilities of current simula- tions. Some of the length scales therefore have to be covered by sub-grid algorithms which need to be able to handle a wide range of environments. Idealised accretion simulations presented in this thesis show that the Bondi-Hoyle-Lyttleton (BHL) accretion algorithm is sufficiently versatile. It automatically determines the accretion rate onto the black hole by the mass flux into its accretion region when the black hole's gravitational po- tential becomes resolved. The accretion rate onto the black hole therefore naturally converges to the correct solution once the size of the accretion region approaches the physical size of the black hole. A drag force algo- rithm that compensates for unresolved dynamical friction, on the other hand, produces a force on the black hole that can unphysically accelerate it relative to the bulk flow of the gas. It needs to be switched off when gas properties are measured within the black hole's gravitational potential. A study of black hole accretion within an isolated cooling halo confirms that the accretion algorithm is able to handle the flow configurations en- countered within an evolving galaxy. To ensure gas is always accreted within the black hole's gravitational potential, a refinement algorithm called "zoom-within-zoom" is introduced in this thesis. It allows the black hole environment to be resolved by orders of magnitude above that of its host galaxy. A low mass seed black hole with a strong drag force early on takes advantage of this extra information during the black hole's early evolution. In the longer term, resolving gas clouds in the black hole vicin- ity to sub-pc scales has a lasting impact on both the mass evolution and duty cycle of massive black holes. Sub-pc size clumps also play a deciding role in the first 200 Myr of evo- lution of a SMBH progenitor in a full cosmological context: 90% of its mass is gained through interactions with dense clumps, which fuel super- Eddington accretion bursts. Once the gas within the host galaxy settles into a rotationally supported disc, star formation and black hole accre- tion slow down. As both primarily occur within the central 30 pc of the compact host galaxy, star formation in proto-galaxies has a major impact on black hole accretion even in the absence of feedback. At low redshift, on the other hand, feedback becomes the crucial link between a SMBH and its host galaxy. A comparison of two simulations from the HORIZON suite, run with and without active galactic nuclei (AGN) feedback respectively, shows that AGN feedback is able to prevent as much as 90% of the stellar mass from forming in the most massive galaxies. Quenching proceeds via a combination of AGN driven outflows and reduced inflows and evolves with redshift as the M_SMBH - M_* relation flattens from z = 5 to z = 0. In conclusion, neither the evolution of galaxies nor that of black holes can be understood without the context of the other. At high redshift, the competition between star formation and black hole accretion inside the compact host galaxy intrinsically links the origin of SMBHs to the early evolution of galaxies. At low redshift, AGN feedback modulates the gas supply of the host galaxy, which has a lasting impact on star formation. The coevolution of black holes and galaxies therefore spans their entire history.