59 research outputs found
Pollney, Denis (Assoc Prof)
No full textDepartment of Mathematics Denis Pollney ORCID 0000-0001-9110-9033 </a
Algebraic and numerical techniques in general relativity The classification of spacetimes via the Cartan-Karlhede method, and Cauchy-characteristic matching for numerically generated spacetimes
No full textAvailable from British Library Document Supply Centre-DSC:DXN051456 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo
Recoil velocities from equal-mass binary-black-hole mergers
No full textThe final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning binaries with unequal masses have pointed out that kick velocities ~175 km/s can be reached for a mass ratio ~=0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as ~440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum
Excision without excision
No full textWe analyze and apply an alternative to black hole excision based on smoothing the interior of black holes with arbitrary -- possibly constraint violating -- initial data, and solving the vacuum Einstein evolution equations everywhere. By deriving the constraint propagation system for our hyperbolic formulation of the BSSN evolution system we rigorously prove that the constraints propagate causally and so any constraint violations introduced inside the black holes cannot affect the exterior spacetime. (This does not follow from the causal structure of the spacetime as is often assumed.) We present numerical evolutions of Cook-Pfeiffer binary black hole initial configurations showing that these techniques appear to work robustly for generic data. We also present numerical evidence from spherically symmetric evolutions that for the gauge conditions used the same stationary end-state is approached irrespective of the choice of initial data and smoothing procedure
GRAVITATIONAL MEMORY IN BINARY BLACK HOLE MERGERS
No full textIn addition to the dominant oscillatory gravitational wave signals produced during binary inspirals, a non-oscillatory component arises from the nonlinear "memory" effect, sourced by the emitted gravitational radiation. The memory grows significantly during the late-inspiral and merger, modifying the signal by an almost step-function profile, and making it difficult to model by approximate methods. We use numerical evolutions of binary black holes (BHs) to evaluate the nonlinear memory during late-inspiral, merger, and ringdown. We identify two main components of the signal: the monotonically growing portion corresponding to the memory, and an oscillatory part which sets in roughly at the time of merger and is due to the BH ringdown. Counterintuitively, the ringdown is most prominent for models with the lowest total spin. Thus, the case of maximally spinning BHs anti-aligned to the orbital angular momentum exhibits the highest signal-to-noise ratio (S/N) for interferometric detectors. The largest memory offset, however, occurs for highly spinning BHs, with an estimated value of h^(tot)_(20) ≃ 0.24 in the maximally spinning case. These results are central to determining the detectability of nonlinear memory through pulsar timing array measurements
Final spin from the coalescence of two black holes
No full textWe provide a compact analytic formula to compute the spin of the black hole produced by the coalescence of two black holes following a quasicircular inspiral. Without additional fits than those already available for binaries with aligned or antialigned spins, but with a minimal set of assumptions, we derive an expression that can model generic initial spin configurations and mass ratios, thus covering all of the 7-dimensional space of parameters. A comparison with simulations already shows very accurate agreements with all of the numerical data available to date, but we also suggest a number of ways in which our predictions can be further improved
Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes
No full textIn this thesis, we study gravitational theories for which the natural choice of an affine connection is metric compatible while not being symmetric. More specifically, we study gravitational theories constructed on the Riemann-Cartan and Weitzenböck space-times. Firstly, we outline the mathematical notions needed to construct a definition of space-time. Following this, we introduce the space-time definitions to be made use of throughout this thesis. We then discuss the notions of extremal and auto-parallel curves on the Riemann-Cartan space-time. It is noted that test particles follow extremal curves which are auto-parallel curves of the LeviCivita connection. Therefore, one must turn to the standard, torsion-free Raychaudhuri equation when studying the focusing conditions that arise in theories constructed on the Riemann-Cartan or Weitzenböck space-times. Once we have introduced the definitions of the relevant space-times, we move on to review some of the gravitational theories that involve non-vanishing torsion. We first review the Einstein-Cartan theory and two of its modifications. We then review the so-called f(T) theories of gravity before discussing the focusing conditions that arise in this context. By making use of the f(T) field equations together with the torsion-free Raychaudhuri equation, we derive for the first time the f(T) focusing conditions for a one-parameter dependent congruence of timelike auto-parallel curves of the LeviCivita connection. We then study these focusing conditions for three bi-parametric cosmological models. Finally, we turn our attention back to the Einstein-Cartan theory and derive the Arnowitt-DeserMisner formulation of this theory. By making use of this formulation, we derive for the first time the Generalised-Baumgarte-Shapiro-Shibata-Nakamura formulation of the Einstein-Cartan theory. We then consider the case of a vacuum in spherical symmetry and construct a 1-dimensional code to evolve the system numerically. We leave the inclusion of torsion into this code as the subject for future work
Notes on the integration of numerical relativity waveforms
No full textThe primary goal of numerical relativity is to provide estimates of the wave strain, h, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, ψ_4. Assuming Bondi gauge, transforming to the strain h reduces to integration of ψ_4 twice in time. Integrations performed in either the time or frequency domain, however, lead to secular nonlinear drifts in the resulting strain h. These nonlinear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular nonlinear drifts in the resulting strain
Dynamical evolution of quasi-circular binary black hole data
No full textWe study the fully nonlinear dynamical evolution of binary black hole data, whose orbital parameters are specified via the effective potential method for determining quasicircular orbits. The cases studied range from the Cook-Baumgarte innermost stable circular orbit (ISCO) to significantly beyond that separation. In all cases we find the black holes to coalesce (as determined by the appearance of a common apparent horizon) in less than half an orbital period. The results of the numerical simulations indicate that the initial holes are not actually in quasicircular orbits, but that they are in fact nearly plunging together. The dynamics of the final horizon are studied to determine physical parameters of the final black hole, such as its spin, mass, and oscillation frequency, revealing information about the inspiral process. We show that considerable resolution is required to extract accurate physical information from the final black hole formed in the merger process, and that the quasinormal modes of the final hole are strongly excited in the merger process. For the ISCO case, by comparing physical measurements of the final black hole formed to the initial data, we estimate that less than 3% of the total energy is radiated in the merger process
Classical, quantum and numerical aspects of modified theories of gravity
No full textIn this thesis, we examine some specific aspects of two classes of modified gravity theories: ghostfree infinite-derivative gravity and so-called f(R) gravity. Regarding the former, we consider the four-dimensional theory at the level of the quadratic action and study the single graviton exchange of two massive spin-0 particles. We derive the corresponding gravitational potential energy for the non-static case and show that the quantum correction of the local theory, which is in the form of a Dirac delta function, is smeared out in the non-local theory. It is also shown that the gravitational potential energy associated with the self-interaction of the individual particles is finite. We then examine the quantumgravitational entanglement of two test masses that undergo a spatial splitting that is orthogonal to their separation. For such a set-up, we compute the concurrence and von Neumann entropy for the entanglement and show that an increase in the length scale of nonlocality leads to a decrease in both of the aforementioned quantities. Our attention is then turned to two specific two-dimensional dilaton gravity models; namely the Spherically-Reduced Gravity (SRG) and the Callan-Giddings-Harvey-Strominger (CGHS) theories. The quadratic action for each theory is derived and diagonalised in order to construct ghost-free infinite-derivative modifications. In the case of the SRG theory, we make use of the Schwarzschild-type gauge whereas, for the CGHS theory, we impose the conformal gauge. For each of the two local theories, we construct appropriate source actions that can be used to generate their respective linearised black-hole solutions. We then make use of the same source actions in the linearised non-local theories and obtain non-local modifications to the aforesaid solutions. Lastly, we consider the application of numerical relativity techniques to f(R) gravity models. It is well-known that the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) modification of the Arnowitt-Deser-Misner formulation of General Relativity is suitable for the construction of numerical relativity codes. While a BSSN-like formulation for f(R) gravity exists, it is constructed with Cartesian coordinates in mind. In this thesis, we generalise the formalism to accommodate arbitrary coordinates and then impose spherical symmetry. The description of a numerical relativity code for the Starobinsky gravity model based on this formalism is given before considering a number of scenarios. We first perform the evolution of Schwarzschild Einstein-Rosen bridge initial data using the fourth-order Runge-Kutta method as well as the evolution of a gauge pulse in flat space using the Partially-Implicit-Runge-Kutta scheme. These two cases serve as tests for our code and our results are compared with those presented in the literature. Then, we perform the evolution of a massless scalar field in the context of the Starobinsky gravity model and show that damped oscillations arise for subcritical simulations
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