Intrinsic and extrinsic geometries of a tidally deformed black hole

A description of the event horizon of a perturbed Schwarzschild black hole is provided in terms of the intrinsic and extrinsic geometries of the null hypersurface. This description relies on a Gauss-Codazzi theory of null hypersurfaces embedded in spacetime, which extends the standard theory of spacelike and timelike hypersurfaces involving the first and second fundamental forms. We show that the intrinsic geometry of the event horizon is invariant under a reparameterization of the null generators, and that the extrinsic geometry depends on the parameterization. Stated differently, we show that while the extrinsic geometry depends on the choice of gauge, the intrinsic geometry is gauge invariant. We apply the formalism to solutions to the vacuum field equations that describe a tidally deformed black hole. In a first instance we consider a slowly-varying, quadrupolar tidal field imposed on the black hole, and in a second instance we examine the tide raised during a close parabolic encounter between the black hole and a small orbiting body.Comment: 27 pages, 4 figure

Transient resonances in the inspirals of point particles into black holes

We show that transient resonances occur in the two body problem in general relativity, in the highly relativistic, extreme mass-ratio regime for spinning black holes. These resonances occur when the ratio of polar and radial orbital frequencies, which is slowly evolving under the influence of gravitational radiation reaction, passes through a low order rational number. At such points, the adiabatic approximation to the orbital evolution breaks down, and there is a brief but order unity correction to the inspiral rate. Corrections to the gravitational wave signal's phase due to resonance effects scale as the square root of the inverse of mass of the small body, and thus become large in the extreme-mass-ratio limit, dominating over all other post-adiabatic effects. The resonances make orbits more sensitive to changes in initial data (though not quite chaotic), and are genuine non-perturbative effects that are not seen at any order in a standard post-Newtonian expansion. Our results apply to an important potential source of gravitational waves, the gradual inspiral of white dwarfs, neutron stars, or black holes into much more massive black holes. It is hoped to exploit observations of these sources to map the spacetime geometry of black holes. However, such mapping will require accurate models of binary dynamics, which is a computational challenge whose difficulty is significantly increased by resonance effects. We estimate that the resonance phase shifts will be of order a few tens of cycles for mass ratios $\sim 10^{-6}$, by numerically evolving fully relativistic orbital dynamics supplemented with an approximate, post-Newtonian self-force.Comment: 4 pages, 1 figure, minor correction

MONTE CARLO CALCULATIONS: DIFFUSION IN ZEOLITES

The objective of this study is to estimate the diffusivities of single and multicomponent systems as a function of temperature, concentration and parameters of the zeolite frame- work

Tidal response from scattering and the role of analytic continuation

The tidal response of a compact object is a key gravitational-wave observable encoding information about its interior. This link is subtle due to the nonlinearities of general relativity. We show that considering a scattering process bypasses challenges with potential ambiguities, as the tidal response is determined by the asymptotic in- and outgoing waves at null infinity. As an application of the general method, we analyze scalar waves scattering off a nonspinning black hole and demonstrate that the frequency-dependent tidal response calculated for arbitrary dimensions and multipoles reproduces known results for the Love number and absorption in limiting cases. In addition, we discuss the definition of the response based on gauge-invariant observables obtained from an effective action description, and clarify the role of analytic continuation for robustly (i) extracting the response and the physical information it contains, and (ii) distinguishing high-order post-Newtonian corrections from finite-size effects in a binary system. Our work is important for interpreting upcoming gravitational-wave data for subatomic physics of ultradense matter in neutron stars, probing black holes and gravity, and looking for beyond standard model fields

Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by tidal effects during a binary inspiral, leading to a potentially measurable effect in the gravitational wave signal. We take an important step towards incorporating these effects in waveform models by developing a relativistic effective action for the gravitomagnetic dynamics that clarifies a number of subtleties. Working in the slow-rotation limit, we first consider the post-Newtonian approximation and explicitly derive the effective action from the equations of motion. We demonstrate that this formulation opens a novel way to compute mode frequencies, yields insights into the relevant matter variables, and elucidates the role of a shift symmetry of the fluid properties under a displacement of the gravitomagnetic mode amplitudes. We then construct a fully relativistic action based on the symmetries and a power counting scheme. This action involves four coupling coefficients that depend on the internal structure of the neutron star and characterize the key matter parameters imprinted in the gravitational waves. We show that, after fixing one of the coefficients by normalization, the other three directly involve the two kinds of gravitomagnetic Love numbers (static and irrotational), and the mode frequencies. We discuss several interesting features and dynamical consequences of this action. Our results provide the foundation for deriving precision predictions of gravitomagnetic effects, and the nuclear physics they encode, for gravitational-wave astronomy

Serodiagnosis of infectious mononucleosis by using recombinant Epstein-Barr virus antigens and enzyme-linked immunosorbent assay technology

Four recombinant, diagnostically useful Epstein-Barr virus (EBV) proteins representative of the viral capsid antigen (p150), diffuse early antigen (p54), the major DNA-binding protein (p138), and the EBV nuclear antigen (p72) (W. Hinderer, H. Nebel-Schickel, H.H. Sonneborn, M. Motz, R. Kühbeck, and H. Wolf, J. Exp. Clin. Cancer Res. 7[Suppl.]:132, 1988) were used to set up individual enzyme-linked immunosorbent assays (ELISAs) for the qualitative and quantitative detection of immunoglobulin M (IgM) and IgG antibodies. In direct comparison with results obtained by standard immunofluorescence or immunoperoxidase assays, it was then shown that the recombinant EBV ELISAs provide the means for specific and sensitive serodiagnosis of infectious mononucleosis (IM) caused by EBV. The most useful markers in sera from such patients proved to be IgM antibodies against p54, p138, and p150. Additional positive markers for recent or ongoing IM apparently were IgG antibodies against p54 and p138. In contrast, anti-p72 IgG had a high preference for sera from healthy blood donors and, therefore, can be considered indicative of past exposure to the virus. Altogether, the individual ELISAs proved to be as specific and at least as sensitive for the diagnosis of IM as the currently available standard techniques are. Moreover, our findings suggest that, by combining individual test antigens, a workable ELISA system consisting of three assays (IgM against p54, p138, and p150; IgG against p54 and p138; and IgG against p72) can be established for the standardized rapid diagnosis of acute EBV infections

Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions

We study the collision of two highly boosted equal mass, nonrotating black holes with generic impact parameter. We find such systems to exhibit zoom-whirl behavior when fine tuning the impact parameter. Near the threshold of immediate merger the remnant black hole Kerr parameter can be near maximal (a/M about 0.95) and the radiated energy can be as large as 35% of the center-of-mass energy.Comment: Rearranged results section; accepted for publication in Phys. Rev. Let

The potential of ground gravity measurements to validate GRACE data

New satellite missions are returning high precision, time-varying, satellite measurements of the Earth’s gravity field. The GRACE mission is now in its calibration/- validation phase and first results of the gravity field solutions are imminent. We consider here the possibility of external validation using data from the superconducting gravimeters in the European sub-array of the Global Geodynamics Project (GGP) as ‘ground truth’ for comparison with GRACE. This is a pilot study in which we use 14 months of 1-hour data from the beginning of GGP (1 July 1997) to 30 August 1998, when the Potsdam instrument was relocated to South Africa. There are 7 stations clustered in west central Europe, and one station, Metsahovi in Finland. We remove local tides, polar motion, local and global air pressure, and instrument drift and then decimate to 6-hour samples. We see large variations in the time series of 5–10<i>µ</i>gal between even some neighboring stations, but there are also common features that correlate well over the 427-day period. The 8 stations are used to interpolate a minimum curvature (gridded) surface that extends over the geographical region. This surface shows time and spatial coherency at the level of 2– 4<i>µ</i>gal over the first half of the data and 1–2<i>µ</i>gal over the latter half. The mean value of the surface clearly shows a rise in European gravity of about 3µgal over the first 150 days and a fairly constant value for the rest of the data. The accuracy of this mean is estimated at 1<i>µ</i>gal, which compares favorably with GRACE predictions for wavelengths of 500 km or less. Preliminary studies of hydrology loading over Western Europe shows the difficulty of correlating the local hydrology, which can be highly variable, with large-scale gravity variations.<br><br><b>Key words. </b>GRACE, satellite gravity, superconducting gravimeter, GGP, ground trut

On the calibration of a superconducting gravimeter using absolute gravity measurements

International audienceA 24 hr continuous parallel registration between an absolute free-fall gravimeter and a relative cryogenic gravimeter is analysed. Different adjustment procedures (L,, L2 norms) are applied to the sets of absolute and relative readings in order to estimate the value of the calibration factor of the superconducting meter, as well as its uncertainty. In addition, a sensitivity test is performed to investigate the influence of some parameters (like the laser frequency and its short-term drift) upon this factor. The precision in the calibration factor is found to be better than 1 per cent, but systematic effects related to the short time interval may add another one and half per cent uncertainty. From preliminary results, it appears that this calibration experiment leads to a close agreement between the values of the gravimetric factor for the reference tidal wave O1 observed with the superconducting meter and the theoretical value (Dehant-Wahr body tide + ocean loading)