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Register a new userFrame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
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When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an electric part E_{jk} that describes tidal gravity and a magnetic part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizons (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.
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When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free (STF) tensors: (i) the Weyl tensors so-called electric part or tidal field, and (ii) the Weyl tensors so-called magnetic part or frame-drag field. Being STF, the tidal field and frame-drag field each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of the tidal fields eigenvectors tendex lines, we call each tendex lines eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for the frame-drag field are vortex lines, their vorticities, and vortexes. We build up physical intuition into these concepts by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side by side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. [Abstract is abbreviated; full abstract also mentions additional results.]
Binary black holes emit gravitational radiation with net linear momentum leading to a retreat of the final remnant black hole that can reach up to $sim5,000$ km/s. Full numerical relativity simulations are the only tool to accurately compute these recoils since they are largely produced when the black hole horizons are about to merge and they are strongly dependent on their spin orientations at that moment. We present eight new numerical simulations of BBH in the hangup-kick configuration family, leading to the maximum recoil. Black holes are equal mass and near maximally spinning ($|vec{S}_{1,2}|/m_{1,2}^2=0.97$). Depending on their phase at merger, this family leads to $simpm4,700$ km/s and all intermediate values of the recoil along the orbital angular momentum of the binary system. We introduce a new invariant method to evaluate the recoil dependence on the merger phase via the waveform peak amplitude used as a reference phase angle and compare it with previous definitions. We also compute the mismatch between these hangup-kick waveforms to infer their observable differentiability by gravitational wave detectors, such as advanced LIGO, finding currently reachable signal-to-noise ratios, hence allowing for the identification of highly recoiling black holes having otherwise essentially the same binary parameters.
We show that rotating black holes do not experience any tidal deformation when they are perturbed by a weak and adiabatic gravitational field. The tidal deformability of an object is quantified by the so-called Love numbers, which describe the objects linear response to its external tidal field. In this work, we compute the Love numbers of Kerr black holes and find that they vanish identically. We also compute the dissipative part of the black holes tidal response, which is non-vanishing due to the absorptive nature of the event horizon. Our results hold for arbitrary values of black hole spin, for both the electric-type and magnetic-type perturbations, and to all orders in the multipole expansion of the tidal field. The boundary conditions at the event horizon and at asymptotic infinity are incorporated in our study, as they are crucial for understanding the way in which these tidal effects are mapped onto gravitational-wave observables. In closing, we address the ambiguity issue of Love numbers in General Relativity, which we argue is resolved when those boundary conditions are taken into account. Our findings provide essential inputs for current efforts to probe the nature of compact objects through the gravitational waves emitted by binary systems.
With the advent of gravitational wave astronomy, searching for gravitational wave echoes from black holes (BHs) is becoming an interesting probe of their quantum nature near their horizons. Newborn BHs may be strong emitters of echoes, as they accompany large perturbations in the surrounding spacetime upon formation. Utilizing the Quantum Black Hole Seismology framework (Oshita et al. 2020), we study the expected echoes upon BH formation resulting from neutron star mergers and failed supernovae. For BH remnants from neutron star mergers, we evaluate the consistency of these models with the recent claim on the existence of echoes following the neutron star merger event GW170817. We find that the claimed echoes in GW170817, if real, suggest that overtones contribute a significant amount of energy in the ringdown of the remnant BH. We finally discuss the detectability of echoes from failed supernovae by second and third-generation gravitational wave detectors, and find that current (future) detectors constrain physical reflectivity models for events occurring within a few Mpc (a few x 10 Mpc). Detecting such echo signals may significantly constrain the maximum mass and equation of state of neutron stars.
Slightly more than two years ago the Event Horizon Telescope (EHT) team presented the first image reconstruction around shadow for the supermassive black hole in centre of M87. It gives an opportunity to evaluate the shadow size. Recently, the EHT team constrained parameters (charges) of spherical symmetrical metrics of black holes from an estimated allowed interval for shadow radius from observations of M87*. In our papers we obtained analytical expressions for shadow radius as a function of charge (including a tidal one) in the case of the case of Reissner -- Nordstrom metric. Some time ago Bin-Nun proposed to apply Reissner -- Nordstrom metric with a tidal charge as an alternative to the Schwarzschild metric in Sgr A*. If we assume that Reissner -- Nordstrom black hole with a tidal charge exists in M87*, therefore, based on results of shadow evaluation for M87* done by the EHT team we constrain a tidal charge. Similarly, we evaluate a tidal charge from shadow size estimates for Sgr A*.
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