General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is ...in systems that contain one or more black holes. Black holes are the most compact objects in the Universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is four-dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar-tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory.
Black hole spacetimes, like the Kerr spacetime, admit both stable and plunging orbits, separated in parameter space by the separatrix. Determining the location of the separatrix is of fundamental ...interest in understanding black holes, and is of crucial importance for modeling extreme-mass-ratio inspirals. Previous numerical approaches to locating the Kerr separatrix were not always efficient or stable across all of parameter space. In this paper we show that the Kerr separatrix is the zero set of a single polynomial in parameter space. This gives two main results. First, we thoroughly analyze special cases (extreme Kerr, polar orbits, etc.), finding strict bounds on the limits of roots, and unifying a number of results in the literature. Second, we pose a stable numerical method which is guaranteed to quickly and robustly converge to the separatrix. This new approach is implemented in the Black Hole Perturbation Toolkit, and results in a ∼45× speedup over the prior robust approach.
We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to ...interpolate the remnant mass, spin, and recoil velocity in the seven-dimensional parameter space of precessing black-hole binaries with mass ratios q≤2, and spin magnitudes χ_{1}, χ_{2}≤0.8. For precessing systems, our errors in estimating the remnant mass, spin magnitude, and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude (improvement is also reported in the extrapolated region at high mass ratios and spins). In addition, we also model the remnant spin and kick directions. Being trained directly on precessing simulations, our fits are free from ambiguities regarding the initial frequency at which precessing quantities are defined. We also construct a model for remnant properties of aligned-spin systems with mass ratios q≤8, and spin magnitudes χ_{1}, χ_{2}≤0.8. As a byproduct, we also provide error estimates for all fitted quantities, which can be consistently incorporated into current and future gravitational-wave parameter-estimation analyses. Our model(s) are made publicly available through a fast and easy-to-use Python module called surfinBH.
In theories of gravity that include a scalar field, a compact object’s scalar charge is a crucial quantity since it controls dipole radiation, which can be strongly constrained by pulsar timing and ...gravitational wave observations. However, in most such theories, computing the scalar charge requires simultaneously solving the coupled, nonlinear metric and scalar field equations of motion. In this article, we prove that in linearly coupled Einstein-dilaton-Gauss-Bonnet gravity, a black hole’s scalar charge is completely determined by the horizon surface gravity times the Euler characteristic of the bifurcation surface, without solving any equations of motion. Within this theory, black holes announce their horizon topology and surface gravity to the rest of the Universe through the dilaton field. In our proof, a four-dimensional topological density descends to a two-dimensional topological density on the bifurcation surface of a Killing horizon. We also comment on how our proof can be generalized to other topological densities on general G-bundles, and to theories where the dilaton is nonlinearly coupled to the Euler density.
Corrections to general relativity that introduce long-ranged scalar fields which are nonminimally coupled to curvature typically predict that neutron stars possess a nontrivial scalar field profile ...anchored to the star. An observer far from a star is most sensitive to the spherically symmetric piece of this profile that decays linearly with the inverse of the distance to the source, the so-called scalar monopole charge, which is related to the emission of dipolar radiation from compact binary systems. The presence of dipolar radiation has the potential to rule out or very strongly constrain extended theories of gravity. The best constraints on Gauss-Bonnet gravity will thus come from accurate black hole observations, for example through gravitational waves from inspiraling binaries or the timing of pulsar-black hole binaries with radio telescopes. We estimate these constraints to be a factor of 10 better than the current estimated bound, and also include estimated constraints on generic quadratic gravity theories from pulsar timing.
Gravity theories beyond general relativity (GR) can change the properties of gravitational waves: their polarizations, dispersion, speed, and, importantly, energy content are all heavily theory ...dependent. All these corrections can potentially be probed by measuring the stochastic gravitational-wave background. However, most existing treatments of this background beyond GR overlook modifications to the energy carried by gravitational waves, or rely on GR assumptions that are invalid in other theories. This may lead to mistranslation between the observable cross-correlation of detector outputs and gravitational-wave energy density, and thus to errors when deriving observational constraints on theories. In this article, we lay out a generic formalism for stochastic gravitational-wave searches, applicable to a large family of theories beyond GR. We explicitly state the (often tacit) assumptions that go into these searches, evaluating their generic applicability, or lack thereof. Examples of problematic assumptions are as follows: statistical independence of linear polarization amplitudes; which polarizations satisfy equipartition; and which polarizations have well-defined phase velocities. We also show how to correctly infer the value of the stochastic energy density in the context of any given theory. We demonstrate with specific theories in which some of the traditional assumptions break down: Chern-Simons gravity, scalar-tensor theory, and Fierz-Pauli massive gravity. In each theory, we show how to properly include the beyond-GR corrections, and how to interpret observational results.
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 quasinormal mode spectrum of the final black hole. We thus compute the leading-order dynamical Chern-Simons modifications to the complex frequencies of the postmerger 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 quasinormal 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.
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 quasinormal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio ≳ 180 – 240 , with the precise value depending on the dimension of the GR waveform family used in data analysis.
Testing general relativity in the nonlinear, 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 ℓ≲O(10) km.
Black holes are a powerful setting for studying general relativity and theories beyond GR. However, analytical solutions for rotating black holes in beyond-GR theories are difficult to find because ...of the complexity of such theories. In this paper, we solve for the deformation to the near-horizon extremal Kerr metric due to two example string-inspired beyond-GR theories: Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons theory. We accomplish this by making use of the enhanced symmetry group of NHEK and the weak-coupling limit of EdGB and dCS. We find that the EdGB metric deformation has a curvature singularity, while the dCS metric is regular. From these solutions, we compute orbital frequencies, horizon areas, and entropies. This sets the stage for analytically understanding the microscopic origin of black hole entropy in beyond-GR theories.
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