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The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into "fast and slow" degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlevé transcendents are a smoking gun of integrable structures, we propose the Painlevé-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward's conjecture relating integrable and (anti-)self-dual solutions can provide the avenue to encode background binary black hole data in (nonlocal) twistor structures. [ABSTRACT FROM AUTHOR]

Partial differential equations with distributional sources—in particular, involving (derivatives of) delta distributions—have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of considerable interest to obtain numerical solutions for such equations, but any singular ("particle"-like) source modeling invariably introduces nontrivial computational obstacles. A common method to circumvent these is through some form of delta function approximation procedure on the computational grid; however, this often carries significant limitations on the efficiency of the numerical convergence rates, or sometimes even the resolvability of the problem at all. In this paper, we present an alternative technique for tackling such equations which avoids the singular behavior entirely: the "Particle-without-Particle" method. Previously introduced in the context of the self-force problem in gravitational physics, the idea is to discretize the computational domain into two (or more) disjoint pseudospectral (Chebyshev–Lobatto) grids such that the "particle" is always at the interface between them; thus, one only needs to solve homogeneous equations in each domain, with the source effectively replaced by jump (boundary) conditions thereon. We prove here that this method yields solutions to any linear PDE the source of which is any linear combination of delta distributions and derivatives thereof supported on a one-dimensional subspace of the problem domain. We then implement it to numerically solve a variety of relevant PDEs: hyperbolic (with applications to neuroscience and acoustics), parabolic (with applications to finance), and elliptic. We generically obtain improved convergence rates relative to typical past implementations relying on delta function approximations. [ABSTRACT FROM AUTHOR]

We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized. We also explore the rapidity distribution of the energy density at hydrodynamization. This is far from boost-invariant and its width decreases as the non-conformality increases. Nevertheless, the velocity field at hydrodynamization is almost exactly boost-invariant regardless of the non-conformality. This result may be used to constrain the initialization of hydrodynamic fields in heavy ion collisions. [ABSTRACT FROM AUTHOR]

Neutron stars and black holes are the most compact astrophysical objects we can think of and as a consequence they are the main sources of gravitational waves. There are many astrophysically relevant scenarios in which these objects are immersed in or endowed with strong magnetic fields, in such a way that gravitational perturbations can couple to electromagnetic ones and can potentially trigger synergistic electromagnetic signatures. In a recent paper we derived the main equations for gravito-electromagnetic perturbations and studied in detail the case of polar electromagnetic perturbations driven by axial gravitational perturbations. In this paper we deal with the case of axial electromagnetic perturbations driven by polar black-hole or neutron stars oscillations, in which the energy emitted in case is considerably larger than in the previous case. In the case of neutron stars the phenomenon lasts considerably longer since the fluid acts as an energy reservoir that shakes the magnetic field for a timescale of the order of secs. [ABSTRACT FROM AUTHOR]

One of the main channels of interactions in galactic nuclei between stars and the central massive black hole (MBH) is the gradual inspiral of compact remnants into the MBH due to the emission of gravitational radiation. This process is known as an ‘extreme mass ratio inspiral’ (EMRI). Previous works about the estimation of how many events space observatories such as LISA will be able to observe during its operational time differ in orders of magnitude, due to the complexity of the problem. Nevertheless, a common result to all investigations is that the possibility that a compact object merges with the MBH after only one intense burst of gravitational waves is much more likely than a slow adiabatic inspiral, an EMRI. The latter is referred to as a ‘plunge’ because the compact object dives into the MBH, crosses the horizon and is lost as a probe of strong gravity for evolved Laser Interferometer Space Antenna (eLISA). The event rates for plunges are orders of magnitude larger than slow inspirals. On the other hand, nature MBH's are most likely Kerr and the magnitude of the spin has been sized up to be high. We calculate the number of periapsis passages that a compact object set on to an extremely radial orbit goes through before being actually swallowed by the Kerr MBH and we then translate it into an event rate for a LISA-like observatory, such as the proposed European Space Agency mission eLISA/New Gravitational wave Observatory. We prove that a ‘plunging’ compact object is conceptually indistinguishable from an adiabatic, slow inspiral; plunges spend on average up to hundred of thousands of cycles in the bandwidth of the detector for a 2 yr mission. This has an important impact on the event rate, enhancing in some cases significantly, depending on the spin of the MBH and the inclination. If the orbit of the EMRI is prograde, the effective size of the MBH becomes smaller for larger spin, whilst if retrograde, it becomes bigger. However, this situation is not symmetric, resulting in an effective enhancement of the rates. The effect of vectorial resonant relaxation on the sense of the orbit does not affect the enhancement. Moreover, it has been recently proved that the production of low-eccentricity EMRIs is severely blocked by the presence of a blockade in the rate at which orbital angular momentum change takes place. This is the result of relativistic precession on to the stellar potential torques and hence affects EMRIs originating via resonant relaxation at distances of about ∼10−2 pc from the MBH. Since high-eccentricity EMRIs are a result of two-body relaxation, they are not affected by this phenomenon. Therefore, we predict that eLISA EMRI event rates will be dominated by high-eccentricity binaries, as we present here. [ABSTRACT FROM AUTHOR]

Physic in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high-energy physics (HEP). The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong-field astrophysical processes, could prove extremely useful to understand HEP processes such as trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with a roadmap for the next years. [ABSTRACT FROM AUTHOR]

We report results on the construction of cosmological braneworld models in the context of the Einstein-Gauss-Bonnet gravity, which include the leading correction to the Einstein-Hilbert action suggested by superstring theory. We obtain and study the equations governing the dynamics of the standard cosmological models. We find that they can be written in the same form as in the case of the Randall-Sundrum model but with time-varying four-dimensional gravitational and cosmological constants. Finally, we discuss the cosmological evolution predicted by these models and their compatibility with observational data. [ABSTRACT FROM AUTHOR]

Constructs a four-index tensor with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space-times with vanishing scalar curvature. Long history of the investigation of conservation laws in general relativity; Friedman-Lemaitre-Robertson-Walker models with an energy-momentum content of incoherent radiation.

In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear. [ABSTRACT FROM AUTHOR]

Examines the application of generalized Kerr-Schild (GKS) transformation for stationary perfect-fluid solution analysis of the Einstein field equations. Combination of Null and timelike vector field techniques; Establishment of wide family for stationary perfect-fluid spacetimes; Appearance of symmetries on GKS spacetimes.