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Register a new userNumerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
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Mark A. Scheel
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We describe a numerical code that solves Einsteins equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.
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The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases of the evolution of black hole binary systems, providing a qualitative physical interpretation of each one of them. I will also briefly describe how these phases would be modified if gravitation were described by a theory extending or deforming General Relativity, or if the binary components turned out to be more exotic compact objects than black holes.
In this work, new solutions for regular black holes that have multihorizons are proposed. These are formed by the direct product of solutions already published in the literature, which are described through the coupling of gravity with nonlinear electrodynamics. We analyze the regularity of the spacetime, the electric field, and the energy conditions of each solution. The strong energy condition is always violated within the event horizon in all solutions, while other energy conditions depend on the ratio between extreme charges of isolated solutions. For solutions with four horizons, we present two examples, Bardeen-Culetu and Balart-Culetu. Both solutions are regular, but the first do not satisfy all the energy conditions, except the strong, because it has an extreme charge ratio of 1.57581, great value. The second solution, on the other hand, can satisfy all other energy conditions, except the SEC, and has an extreme charge ratio of 1.09915, a value that allows this feature. Its also proposed a regular solution with up to six horizons, Balart-Culetu-Dymnikova, where, for a given charge value, we can verify that it satisfies all energy conditions, except the strong one. This was possible due to the ratio between extreme charges that are neither too high nor too close. We propose solutions with any number of horizons. We show that points where $-F(r)$ has a non null minimum represent a cusp in the Lagrangian $-L(F)$. We also show an example of multihorizon solution with magnetic charge. Multihorizon solutions may exhibit exotic properties, such as negative energy density, or violation of energy conditions, but which can be circumvented with a selected choice of customized solutions and extreme charge values, resulting in regular black hole solutions that satisfy all energy conditions, less the strong.
We consider the thermodynamic properties of the constant curvature black hole solution recently found by Banados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton.
Binary black holes with spins that are aligned with the orbital angular momentum do not precess. However, post-Newtonian calculations predict that up-down binaries, in which the spin of the heavier (lighter) black hole is aligned (antialigned) with the orbital angular momentum, are unstable when the spins are slightly perturbed from perfect alignment. This instability provides a possible mechanism for the formation of precessing binaries in environments where sources are preferentially formed with (anti) aligned spins. In this paper, we present the first full numerical relativity simulations capturing this instability. These simulations span $sim 100$ orbits and $sim 3$-$5$ precession cycles before merger, making them some of the longest numerical relativity simulations to date. Initialized with a small perturbation of $1^{circ}$-$10^{circ}$, the instability causes a dramatic growth of the spin misalignments, which can reach $sim 90^{circ}$ near merger. We show that this leaves a strong imprint on the subdominant modes of the gravitational wave signal, which can potentially be used to distinguish up-down binaries from other sources. Finally, we show that post-Newtonian and effective-one-body approximants are able to reproduce the unstable dynamics of up-down binaries extracted from numerical relativity.
We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $gtrsim 180-240$, with the precise value depending on the dimension of the GR waveform family used in data analysis.
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