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An exact and analytical solution of four dimensional vacuum General Relativity representing a system of two static black holes at equilibrium is presented. The metric is completely regular outside the event horizons, both from curvature and conical singularities. The balance between the two Schwarzschild sources is granted by an external gravitational field, without the need of extra matter fields besides gravity, nor strings or struts. The geometry of the solution is analysed. The Smarr law, the first and the second law of black hole thermodynamics are discussed.
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Ambient magnetic fields are thought to play a critical role in black hole jet formation. Furthermore, dual electromagnetic signals could be produced during the inspiral and merger of binary black hole systems. However, due to the absence of theoretical models, the physical status of binary black hole arrays with dual jets has remained unresolved. In this paper, we derive the exact solution for the electromagnetic field occurring when a static, axisymmetric binary black hole system is placed in the field of two magnetic or electric monopoles. As a by-product of this derivation, we also find the exact solution of the binary black hole configuration in a magnetic or electric dipole field. The presence of conical singularities in the static black hole binaries represent the gravitational attraction between the black holes that also drag the external two monopole field. We show that these off-balance configurations generate no energy outflows.
We produce the first numerical relativity binary black hole gravitational waveforms in a higher-curvature theory beyond general relativity. In particular, we study head-on collisions of binary black holes in order-reduced dynamical Chern-Simons gravity. This is a precursor to producing beyond-general-relativity waveforms for inspiraling binary black hole systems that are useful for gravitational wave detection. Head-on collisions are interesting in their own right, however, as they cleanly probe the quasi-normal mode spectrum of the final black hole. We thus compute the leading-order dynamical Chern-Simons modifications to the complex frequencies of the post-merger gravitational radiation. We consider equal-mass systems, with equal spins oriented along the axis of collision, resulting in remnant black holes with spin. We find modifications to the complex frequencies of the quasi-normal mode spectrum that behave as a power law with the spin of the remnant, and that are not degenerate with the frequencies associated with a Kerr black hole of any mass and spin. We discuss these results in the context of testing general relativity with gravitational wave observations.
Testing general relativity in the non-linear, dynamical, strong-field regime of gravity is one of the major goals of gravitational wave astrophysics. Performing precision tests of general relativity (GR) requires numerical inspiral, merger, and ringdown waveforms for binary black hole (BBH) systems in theories beyond GR. Currently, GR and scalar-tensor gravity are the only theories amenable to numerical simulations. In this article, we present a well-posed perturbation scheme for numerically integrating beyond-GR theories that have a continuous limit to GR. We demonstrate this scheme by simulating BBH mergers in dynamical Chern-Simons gravity (dCS), to linear order in the perturbation parameter. We present mode waveforms and energy fluxes of the dCS pseudoscalar field from our numerical simulations. We find good agreement with analytic predictions at early times, including the absence of pseudoscalar dipole radiation. We discover new phenomenology only accessible through numerics: a burst of dipole radiation during merger. We also quantify the self-consistency of the perturbation scheme. Finally, we estimate bounds that GR-consistent LIGO detections could place on the new dCS length scale, approximately $ell lesssim mathcal{O}(10)~mathrm{km}$.
In General Relativity, the spacetimes of black holes have three fundamental properties: (i) they are the same, to lowest order in spin, as the metrics of stellar objects; (ii) they are independent of mass, when expressed in geometric units; and (iii) they are described by the Kerr metric. In this paper, we quantify the upper bounds on potential black-hole metric deviations imposed by observations of black-hole shadows and of binary black-hole inspirals in order to explore the current experimental limits on possible violations of the last two predictions. We find that both types of experiments provide correlated constraints on deviation parameters that are primarily in the tt-components of the spacetimes, when expressed in areal coordinates. We conclude that, currently, there is no evidence for a deviations from the Kerr metric across the 8 orders of magnitudes in masses and 16 orders in curvatures spanned by the two types of black holes. Moreover, because of the particular masses of black holes in the current sample of gravitational-wave sources, the correlations imposed by the two experiments are aligned and of similar magnitudes when expressed in terms of the far field, post-Newtonian predictions of the metrics. If a future coalescing black-hole binary with two low-mass (e.g., ~3 Msun) components is discovered, the degeneracy between the deviation parameters can be broken by combining the inspiral constraints with those from the black-hole shadow measurements.
Determining the conditions under which a black hole can be produced is a long-standing and fundamental problem in general relativity. We use numerical simulations of colliding selfgravitating fluid objects to study the conditions of black-hole formation when the objects are boosted to ultrarelativistic speeds. Expanding on previous work, we show that the collision is characterized by a type-I critical behaviour, with a black hole being produced for masses above a critical value, M_c, and a partially bound object for masses below the critical one. More importantly, we show for the first time that the critical mass varies with the initial effective Lorentz factor <gamma> following a simple scaling of the type M_c ~ K <gamma>^{-1.0}, thus indicating that a black hole of infinitesimal mass is produced in the limit of a diverging Lorentz factor. Furthermore, because a scaling is present also in terms of the initial stellar compactness, we provide a condition for black-hole formation in the spirit of the hoop conjecture.
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