Showing papers in "Classical and Quantum Gravity in 2007"
TL;DR: In this article, the authors explore the influence that density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity and show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions.
Abstract: Using the concept of cracking we explore the influence that density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity. This concept, conceived to describe the behavior of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of self-gravitating compact objects. We show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found that these regions could occur when, at a particular point within the distribution, the tangential speed of sound is greater than the radial one.
488 citations
TL;DR: In this paper, a review of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed is provided, based on discussions at a workshop hosted by the Albert Einstein Institute in Golm, Germany.
Abstract: Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany.
425 citations
TL;DR: The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an Abelian ideal of supertranslations as mentioned in this paper.
Abstract: The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an Abelian ideal of supertranslations. The associated charge algebra is shown to admit a non-trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.
349 citations
TL;DR: In this paper, the existence of an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2,1) symmetry was shown to be valid for a general two-derivative theory coupled to abelian vectors and uncharged scalars.
Abstract: Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2,1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravity coupled to abelian vectors and uncharged scalars, allowing for a non-trivial scalar potential. We prove that it remains valid in the presence of higher-derivative corrections. We show that SO(2,1)-symmetric near-horizon solutions can be analytically continued to give SU(2)-symmetric black hole solutions. For example, the near-horizon limit of an extremal 5D Myers-Perry black hole is related by analytic continuation to a non-extremal cohomogeneity-1 Myers-Perry solution.
346 citations
TL;DR: In this article, a general formalism in the metric framework is developed considering a point-like f(R) Lagrangian where spherical symmetry is required, and examples of exact solutions are given.
Abstract: We search for spherically symmetric solutions of f(R) theories of gravity via the Noether symmetry approach. A general formalism in the metric framework is developed considering a point-like f(R) Lagrangian where spherical symmetry is required. Examples of exact solutions are given.
317 citations
TL;DR: In this paper, the subject of spontaneous supersymmetry breaking in a semiclassical theory is discussed, and the authors illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetric breaking.
Abstract: We review the subject of spontaneous supersymmetry breaking. First we consider supersymmetry breaking in a semiclassical theory. We illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetry breaking. Then we give a brief review of the dynamics of supersymmetric gauge theories. Finally, we use this dynamics to present various mechanisms for dynamical supersymmetry breaking. This paper is based on lectures given by the authors in 2007, at various schools.
295 citations
TL;DR: In this article, the authors reviewed the asymptotic safety scenario in quantum gravity, according to which a renormalizable quantum theory of the gravitational field is feasible and argued that the self-interactions appear two dimensional in the extreme ultraviolet.
Abstract: The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. All presently known evidence is surveyed: (a) from the 2 + expansion, (b) from the perturbation theory of higher derivative gravity theories and a 'large N' expansion in the number of matter fields, (c) from the 2-Killing vector reduction and (d) from truncated flow equations for the effective average action. Special emphasis is given to the role of perturbation theory as a guide to 'asymptotic safety'. Furthermore it is argued that as a consequence of the scenario the self-interactions appear two dimensional in the extreme ultraviolet. Two appendices discuss the distinct roles of the ultraviolet renormalization in perturbation theory and in the flow equation formalism.
261 citations
TL;DR: In this paper, a general class of gravastars were constructed and conditions for their existence as equilibrium solutions of the Einstein equations were determined. But their quasi-normal modes differ from those of a black hole of the same mass.
Abstract: Gravastars have been recently proposed as potential alternatives to explain the astrophysical phenomenology traditionally associated with black holes, raising the question of whether the two objects can be distinguished at all. Leaving aside the debate about the processes that would lead to the formation of a gravastar and the astronomical evidence in their support, here we address two basic questions: is a gravastar stable against generic perturbations? If it is stable, can an observer distinguish it from a black hole of the same mass? To answer these questions we construct a general class of gravastars and determine the conditions they must satisfy in order to exist as equilibrium solutions of the Einstein equations. For such models we perform a systematic stability analysis against axial perturbations, computing the real and imaginary parts of the eigenfrequencies. Overall, we find that gravastars are stable to axial perturbations, but also that their quasi-normal modes differ from those of a black hole of the same mass and thus can be used to discern, beyond dispute, a gravastar from a black hole.
247 citations
TL;DR: In this article, a phenomenological family of waveforms which can model the inspiral, merger and ring-down stages of black-hole coalescence was proposed, and a template bank was constructed using this waveform family.
Abstract: Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger and ring-down stages of black-hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.
224 citations
TL;DR: In this paper, the authors showed that adding TiO2 to Ta2O5 in TaO5/SiO2 coatings reduces the internal friction and in addition present data confirming it reduces thermal noise.
Abstract: Reducing thermal noise from optical coatings is crucial to reaching the required sensitivity in next generation interferometric gravitational-wave detectors. Here we show that adding TiO2 to Ta2O5 in Ta2O5/SiO2 coatings reduces the internal friction and in addition present data confirming it reduces thermal noise. We also show that TiO2-doped Ta2O5/SiO2 coatings are close to satisfying the optical absorption requirements of second generation gravitational-wave detectors.
221 citations
TL;DR: In this paper, the authors provide a detailed discussion of the classical gravitational instability of the neutral uniform black string in higher-dimensional gravity, and the connection between classical and thermodynamic stability, known as the correlated stability conjecture, is discussed.
Abstract: We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory We focus mainly on Gregory–Laflamme instabilities In the first part of the review, we provide a detailed discussion of the classical gravitational instability of the neutral uniform black string in higher-dimensional gravity The uniform black string is part of a larger phase diagram of Kaluza–Klein black holes which will be discussed thoroughly This phase diagram exhibits many interesting features including new phases, non-uniqueness and horizon-topology changing transitions In the second part, we turn to charged black branes in supergravity and show how the Gregory–Laflamme instability of the neutral black string implies via a boost/U-duality map similar instabilities for non- and near-extremal smeared branes in string theory We also comment on instabilities of D-brane bound states The connection between classical and thermodynamic stability, known as the correlated stability conjecture, is also reviewed and illustrated with examples Finally, we examine the holographic implications of the Gregory–Laflamme instability for a number of non-gravitational theories including Yang–Mills theories and little string theory
TL;DR: In this paper, the authors extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background.
Abstract: We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.
TL;DR: In this article, the authors show that the requirements on the spacetime in the classical definition of causal simplicity (i.e. to be distinguishing plus the closedness of J+(p), J−(q)) can be weakened by requiring only to be causal instead of distinguishing.
Abstract: The classical definition of global hyperbolicity for a spacetime (M, g) comprises two conditions: (A) compactness of the diamonds J+(p)J−(q), and (B) strong causality. Here we show that condition (B) can be replaced just by causality. In fact, we show first that the requirements on the spacetime in the classical definition of causal simplicity (i.e. to be distinguishing plus the closedness of J+(p), J−(q)) can be weakened by requiring only to be causal instead of distinguishing. So, the full consistency of the causal ladder (recently proved by the authors in a definitive way) yields directly the result.
TL;DR: In this paper, the authors derived a formula for the black hole entropy in theories with gravitational Chern-Simons terms, by generalizing Wald's argument which uses the Noether charge.
Abstract: We derive a formula for the black hole entropy in theories with gravitational Chern–Simons terms, by generalizing Wald's argument which uses the Noether charge. It correctly reproduces the entropy of three-dimensional black holes in the presence of the Chern–Simons term, which was previously obtained via indirect methods.
TL;DR: In this article, a brief introduction to hot big bang cosmology and cosmic inflation, together with a selection of some recent attempts to embed inflation into string theory, is presented, aimed at graduate students with a working knowledge of quantum field theory, but who are unfamiliar with the details of cosmology or string theory.
Abstract: These notes present a brief introduction to hot big bang cosmology and cosmic inflation, together with a selection of some recent attempts to embed inflation into string theory. They provide a partial description of lectures presented at the RTN Winter School at CERN in January 2007, as well as in courses at Dubrovnik in August 2006 and at Cargese in August 2007. Given the substantial overlap between these three courses, the same paper will also appear as part of the proceedings of the latter two schools. It is aimed at graduate students with a working knowledge of quantum field theory, but who are unfamiliar with the details of cosmology or string theory.
TL;DR: Algebraic quantum gravity (AQG) as discussed by the authors is a top-down approach to canonical quantum gravity, where the quantum kinematics of AQG are determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph.
Abstract: We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single master constraint operator. While AQG is inspired by loop quantum gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of general relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken. There simply is no lattice regulator that must be sent to zero.
TL;DR: In this article, it was shown that a transition from decelerated to accelerated cosmic expansion arises as a pure interaction phenomenon if pressureless dark matter is coupled to holographic dark energy whose infrared cutoff scale is set by the Hubble length.
Abstract: We demonstrate that a transition from decelerated to accelerated cosmic expansion arises as a pure interaction phenomenon if pressureless dark matter is coupled to holographic dark energy whose infrared cutoff scale is set by the Hubble length. In a spatially flat universe the ratio of the energy densities of both components remains constant through this transition, while it is subject to slow variations for non-zero spatial curvature. The coincidence problem is dynamized and reformulated in terms of the interaction rate. An early matter era is recovered since for negligible interaction at high redshifts the dark energy itself behaves as matter. A simple model for this dynamics is shown to fit the SN Ia data. The constant background energy density ratio simplifies the perturbation analysis which is characterized by non-adiabatic features.
TL;DR: In this paper, the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality is discussed, focusing on conciseness and conceptual aspects rather than on technical details.
Abstract: I review recent progress on the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics covered include the large- limit of gauge theories, the gravitational description of gauge theory thermodynamics and hydrodynamics, and confinement/deconfinement thermal phase transitions.
TL;DR: In this article, a new numerical code was developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements.
Abstract: The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of γ-ray bursts, requires the solution of the Einstein equations together with those of general-relativistic magnetohydrodynamics. We present a new numerical code developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code and assess its accuracy. Such tests range from the solution of relativistic Riemann problems in flat spacetime, over to the stationary accretion onto a Schwarzschild black hole and up to the evolution of oscillating magnetized stars in equilibrium and constructed as consistent solutions of the coupled Einstein–Maxwell equations.
TL;DR: In this paper, the quasi-equilibrium initial-data method is extended to allow nonzero radial velocities to be specified in binary black hole initial data, and new low-eccentricity initial data are obtained by adjusting the orbital frequency and radial veloities to minimize the orbital eccentricity, and the resulting (~5 orbit) evolutions are compared with those of quasi-circular initial data.
Abstract: Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but nonzero orbital eccentricities. In this paper, the quasi-equilibrium initial-data method is extended to allow nonzero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting (~5 orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964 Phys. Rev. 136 1224–32). The gravitational waveforms, which contain ~8 cycles in the dominant l = m = 2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.
TL;DR: In this article, a combination of mathematical and physical reasonings is used to argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z > 1, corresponding to a universe less than half of its current size.
Abstract: In cosmography, cosmokinetics and cosmology, it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available; for instance, we have supernova data at least back to redshift z ≈ 1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift. Based on a combination of mathematical and physical reasonings, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z > 1, corresponding to a universe less than half of its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parametrization y = z/(1 + z). In terms of the y-redshift, we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang (y = 1), but that y-based expansions must break down for y < −1, now corresponding to a universe more than twice its current size.
TL;DR: In this article, a pedagogical review of nongeometric flux compactifications is presented based on lectures given at the 2007 RTN Winter School at CERN, where the authors argue that one must include non-geometric 'fluxes' in order to have a superpotential which is invariant under T-duality.
Abstract: These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric 'fluxes' in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.
TL;DR: In this paper, the von Neumann and linear entropy of the fluctuations were derived from the Lindblad equation and the Wigner function was shown to be positive everywhere for super-Hubble modes during inflation.
Abstract: Primordial fluctuations in inflationary cosmology acquire classical properties through decoherence when their wavelengths become larger than the Hubble scale. Although decoherence is effective, it is not complete, so a significant part of primordial correlations remains up to the present moment. We address the issue of the pointer states which provide a classical basis for the fluctuations with respect to the influence by an environment (other fields). Applying methods from the quantum theory of open systems (the Lindblad equation), we show that this basis is given by narrow Gaussians that approximate eigenstates of field amplitudes. We calculate both the von Neumann and linear entropy of the fluctuations. Their ratio to the maximal entropy per field mode defines a degree of partial decoherence in the entropy sense. We also determine the time of partial decoherence making the Wigner function positive everywhere which, for super-Hubble modes during inflation, is virtually independent of coupling to the environment and is only slightly larger than the Hubble time. On the other hand, assuming a representative environment (a photon bath), the decoherence time for sub-Hubble modes is finite only if some real dissipation exists.
TL;DR: In this article, the authors present a model of millimetre and sub-millimetre emission from Sagittarius A* (Sgr A*) based on relativistic numerical simulations of the accretion flow.
Abstract: The radio source Sagittarius A* (Sgr A*) is believed to be a hot, inhomogeneous, magnetized plasma flowing near the event horizon of the 3.6 × 106 M⊙ black hole at the galactic centre. At a distance of 8 kpc ( 2.5 × 1022 cm) the black hole would be among the largest black holes as judged by angular size. Recent observations are consistent with the idea that the millimetre and sub-millimetre photons are dominated by optically thin, thermal synchrotron emission. Anticipating future Very Long Baseline Interferometry (VLBI) observations of Sgr A* at these wavelengths, we present here the first dynamically self-consistent models of millimetre and sub-millimetre emission from Sgr A* based on general relativistic numerical simulations of the accretion flow. Angle-dependent spectra are calculated assuming a thermal distribution of electrons at the baryonic temperature dictated by the simulation and the accretion rate, which acts as a free parameter in our model. The effects of varying model parameters (black hole spin and inclination of the spin to the line of sight) and source variability on the spectrum are shown. We find that the accretion rate value needed to match our calculated millimetre flux to the observed flux is consistent with constraints on the accretion rate inferred from detections of the rotation measure. We also describe the relativistic jet that is launched along the black hole spin axis by the accretion disc and evolves to scales of ~103GMc−2, where M is the mass of the black hole.
TL;DR: In this paper, a new LQC model of the spatially closed, homogeneous, isotropic universe is constructed, where the topology of the spacelike section of the universe is assumed to be SU(2) or SO(3).
Abstract: The basic idea of loop quantum cosmology (LQC) applies to every spatially homogeneous cosmological model; however only the spatially flat (so-called k = 0) case has been understood in detail in the literature thus far. In the closed (so-called k = 1) case certain technical difficulties have been the obstacle to development. In this work the difficulties are overcome, and a new LQC model of the spatially closed, homogeneous, isotropic universe is constructed. The topology of the spacelike section of the universe is assumed to be that of SU(2) or SO(3). Surprisingly, according to the new results achieved in this paper, the two cases can be distinguished from each other just by the local properties of the quantum geometry of the universe! The quantum Hamiltonian operator of the gravitational field takes the form of a difference operator, where the elementary step is the quantum of the 3-volume derived in the flat case by Ashtekar, Pawlowski and Singh. The mathematical properties of the operator are studied: it is essentially self-adjoint, bounded from above by 0, the 0 itself is not an eigenvalue, the eigenvectors form a basis. An estimate on the dimension of the spectral projection on any finite interval is provided.
TL;DR: In this article, the authors present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q ≡ M1/M2 = {1, 0.85, 0., 0.78, 0, 55, 0.32}, or equivalently, with reduced mass parameters η ≡ M 1M2/(M 1 + M 2)2 ={0.25, 0..25,0.34, 0.34,
Abstract: We present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q ≡ M1/M2 = {1, 0.85, 0.78, 0.55, 0.32}, or equivalently, with reduced mass parameters η ≡ M1M2/(M1 + M2)2 = {0.25, 0.248, 0.246, 0.229, 0.183}. For each case, the initial binary orbital parameters are chosen from the Cook–Baumgarte equal-mass ISCO configuration. We show waveforms of the dominant l = 2, 3 modes and compute estimates of energy and angular momentum radiated. For the plunges from the close separations considered, we measure kick velocities from gravitational radiation recoil in the range 25–82 km s−1. Due to the initial close separations our kick velocity estimates should be understood as a lower bound. The close configurations considered are also likely to contain significant eccentricities influencing the recoil velocity.
TL;DR: In this article, a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics.
Abstract: We show that a class of background-independent models of quantum spacetime have local excitations that can be mapped to the first-generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics (Kribs and Markopoulou 2005 Preprint gr-qc/0510052, Markopoulou and Poulin unpublished). These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by Bilson-Thompson (2005 Preprint hep-ph/0503213). These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.
TL;DR: In this paper, a higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension n.
Abstract: A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension n. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in n − 4 spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers–Perry metric as an explicit example of a vacuum type D spacetime to show that principal geodesic null congruences in vacuum type D spacetimes do not share this property.
TL;DR: In this article, the authors describe the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity, and show that with appropriate fine tuning of the initial conditions one can reach a region of parameter space, which they denote the threshold of immediate merger, and illustrate how this information can be used to estimate the cross section and energy emitted in the ultrarelativistic black hole scattering problem.
Abstract: We describe recent numerical simulations of the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity. We show that with appropriate fine tuning of the initial conditions one can reach a region of parameter space we denote the threshold of immediate merger. Here, the binary enters a phase of close interaction in a near-circular orbit, stays there for an amount of time proportional to the logarithmic distance from the threshold in parameter space, then either separates or merges to form a single Kerr black hole. To gain a better understanding of this phenomenon, we study an analogous problem in the evolution of equatorial geodesics about a central Kerr black hole. A similar threshold of capture exists for appropriate classes of initial conditions, and tuning to threshold the geodesics approach one of the unstable circular geodesics of the Kerr spacetime. Remarkably, with a natural mapping of the parameters of the geodesic to that of the equal mass system, the scaling exponents describing the whirl phase of each system turn out to be quite similar. Armed with this lone piece of evidence that an approximate correspondence might exist between near-threshold evolution of geodesics and generic binary mergers, we illustrate how this information can be used to estimate the cross section and energy emitted in the ultra-relativistic black hole scattering problem. This could eventually be of use in providing estimates for the related problem of parton collisions at the large hadron collider in extra dimension scenarios where black holes are produced.
TL;DR: In this article, an initial configuration for primordial black hole (PBH) formation was defined in terms of a curvature profile, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann-Robertson-Walker model.
Abstract: This work is part of an ongoing research programme to study possible primordial black hole (PBH) formation during the radiation-dominated era of the early universe. Working within spherical symmetry, we specify an initial configuration in terms of a curvature profile, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann–Robertson–Walker model, which are required for PBH formation. Using an asymptotic quasi-homogeneous solution, we relate the curvature profile with the density and velocity fields, which at an early enough time, when the length scale of the configuration is much larger than the cosmological horizon, can be treated as small perturbations of the background values. We present general analytic solutions for the density and velocity profiles. These solutions enable us to consider in a self-consistent way the formation of PBHs in a wide variety of cosmological situations with the cosmological fluid being treated as an arbitrary mixture of different components with different equations of state. We obtain the analytical solutions for the density and velocity profiles as functions of the initial time. We then use two different parametrizations for the curvature profile and follow numerically the evolution of initial configurations.