Elementos del riesgo de crédito y de liquidez

NR plays an important role in GW astrophysics and data analysis. The semi- analytical waveform models employed to search for BBHs (see Sec. 6 below) model the complete radiative evolution from the early inspiral, through the merger and to the final ringdown stage, with the later stages calibrated to BBH simulations [1111,1112]. These models and more sophisticated ones incorporating more physical effects, for example precession [1113, 1114], are used to determine the fundamental properties of the GW source, i.e. its masses and spin angular momenta as well as extrinsic quantities such as the orbital orientation relative to the observatories [1115, 1116].

Alternatively, pure NR waveforms may be used directly [1117,1118] or by the means of surrogate models [1119–1121]. But due to the computational cost of simulations, these have only been attempted so far on a very restricted portion of the parameter space. Despite this restriction, pure NR surrogate models have the advantage of incorporating more physical effects that may be limited or entirely neglected in currently available semi-analytic models.

The ringdown phase after the merger may be described by perturbation theory (see e.g. [1122] for a review), but the amplitudes of the excited quasi-normal modes can only be obtained from numerical simulations. These are of particular interest as measuring the amplitudes of individual quasinormal modes would allow to map the final state of the merger to the properties of the progenitor BHs [1123, 1124] and to test the BH nature of the source [1125] (see also Sections4.1 and 4.2).

In order to estimate the mass and spin angular momentum of the remnant BH, fits to NR simulations are essential [1092–1094, 1126–1133]. Independent measurements of the binary properties from the inspiral portion of the GW signal and from the later stages of the binary evolution using fits from NR allow, when combined, to test the predictions from GR [17, 1134]. While the phenomenological fit formulae have seen much improvement in recent years, modelling the final state of precessing BH binaries from numerical simulations still remains an open challenge.

Generically, when BHs merge, anisotropic emission of GWs leads to the build up of a net linear momentum. Due to the conservation of momentum, once the GW emission subsides, the remnant BH recoils (“kick”). While the recoil builds up during the entire binary evolution, it is largest during the non-linear merger phase. Kick velocities can be as high as several thousands km/s, with astrophysical consequences: a BH whose recoil velocity is larger than the escape velocity of its galaxy may leave its host. Numerical simulations are necessary to predict the recoil velocities [1135–1138] (a convenient surrogate model for these velocities was constructed recently in [1139]). It has been suggested that it may be possible to directly measure the recoil speed from the GW signal by observing the induced differential Doppler shift throughout the inspiral, merger and ringdown [1140].

Numerical simulations of the strong field regime are also crucial for exploring other spin-related phenomena such as “spin-flips” [1141] caused by spin-spin coupling, whose

signatures may be observable. Understanding the spin evolution and correctly modelling spin effects is crucial for mapping out the spin distribution of astrophysical BHs from GW observations.

Waveform models as well as fitting formulae for remnant properties are prone to systematic modelling errors. For GW observations with low SNR, the statistical uncertainty dominates over the systematic modelling error in the parameter measurement accuracy. Improved sensitivities for current and future GW observatories (including, especially, LISA [1142,1143]) will allow for high SNR observations reaching into the regime where systematic errors are accuracy limiting. This includes strongly inclined systems, higher-order modes, eccentricity, precession and kicks, all of which can be modelled more accurately through the inclusion of results from NR (see [1025] for a detailed discussion in the context of the first BBH observation GW150914).

5. Numerical relativity in fundamental physics

Contributor: U. Sperhake

The standard model of particle physics and Einstein’s theory of GR provide us with an exquisite theoretical framework to understand much of what we observe in the Universe. From high-energy collisions at particle colliders to planetary motion, the GW symphony of NS and BH binaries and the cosmological evolution of the Universe at large, the theoretical models give us remarkably accurate descriptions. And yet, there are gaps in this picture that prompt us to believe that something is wrong or incomplete. Galactic rotation curves, strong gravitational lensing effects, X-ray observations of galactic halos and the cosmic microwave background cannot be explained in terms of the expected gravitational effects of the visible matter [283]. Either we are prepared to accept the need to modify the laws of gravity, or there exists a form of dark matter (DM) that at present we can not explain satisfactorily with the SM (or both). Different DM candidates and their status are reviewed in Section 5.1. Likewise, the accelerated expansion of the Universe [1144] calls for an exotic form of matter dubbed dark energy or (mathematically equivalently) the introduction of a cosmological constant with a value many orders of magnitude below the zero-point energy estimated by quantum field theory—the cosmological constant problem. Further chinks in the armor of the SM+GR model of the universe include the hierarchy problem, i.e. the extreme weakness of gravity relative to the other forces, and the seeming irreconcilability of GR with quantum theory.

Clearly, gravity is at the center of some of the most profound contemporary puzzles in physics. But it has now also given us a new observational handle on these puzzles, in the form of GWs [1]. Furthermore, the aforementioned 2005 breakthrough in NR [1039– 1041] has given us the tools needed to systematically explore the non-linear strong- field regime of gravity. For much of its history, NR was motivated by the modeling of astrophysical sources of GWs, as we have described in Sec.4. As early as 1992, however, Choptuik’s milestone discovery of critical behaviour in gravitational collapse [1145] has

demonstrated the enormous potential of NR as a tool for exploring a much wider range of gravitational phenomena. In this section we review the discoveries made in this field and highlight the key challenges and goals for future work.

5.1. Particle laboratories in outer space

DM, by its very definition, generates little if any electromagnetic radiation; rather, it interacts with its environment through gravity. Many DM candidates have been suggested (see also Section5), ranging from primordial BH clouds to weakly interacting massive particles (WIMPs) and ultralight bosonic fields [283, 284,1146]. The latter are a particularly attractive candidate in the context of BH and GW physics due to their specific interaction with BHs. Ultralight fields, also referred to as weakly interacting slim particles (WISPs), typically have mass parameters orders of magnitude below an electron volt and arise in extensions of the SM of particle physics or extra dimensions in string theory. These include axions or axion-like particles, dark photons, non-topological solitons (so-called Q-balls) and condensations of bosonic states [283, 1147–1149]. For reference, we note that a mass 10−10eV (10−20eV) corresponds to a Compton wavelength of O(1) km (O(102) AU) which covers the range of Schwarzschild radii of astrophysical BHs.

At first glance, one might think the interaction between such fundamental fields and BHs is simple; stationary states are constrained by the no-hair theorems and the field either falls into the BH or disperses away. In practice, however, the situation is more complex—and more exciting. NR simulations have illustrated the existence of long-lived, nearly periodic states of single, massive scalar or Proca (i.e. vector) fields around BHs [1150–1152]. Intriguingly, these configurations are able to extract rotational energy from spinning BHs through superradiance [1153–1156], an effect akin to the Penrose process [1156, 1157]. Further details on this process are provided in Section 5.7. In the presence of a confining mechanism that prevents the field from escaping to infinity, this may even lead to a runaway instability dubbed the BH bomb [1158, 1159]. Another peculiar consequence arising in the same context is the possibility of floating orbits where dissipation of energy through GW emission is compensated by energy gain through superradiance [1160, 1161].

Naturally, non-linear effects will limit the growth of the field amplitude or the lifetime of floating orbits, and recent years have seen the first numerical studies to explore the role of non-linearities in superradiance. These simulations have shown that massive, real scalar fields around BHs can become trapped inside a potential barrier outside the horizon, form a bound state and may grow due to superradiance [1150]. Furthermore, beating phenomena result in a more complex structure in the evolution of the scalar field. These findings were confirmed in [1151], which also demonstrated that the scalar clouds can source GW emission over long timescales. The amplification of GWs through superradiance around a BH spinning close to extremality has been modeled in Ref. [1162] and found to be maximal if the peak frequency of the wave

is above the superradiant threshold but close to the dominant quasi-normal mode frequency of the BH. The generation of GW templates for the inspiral and merger of hairy BHs and the identification of possible smoking gun effects distinguishing them from their vacuum counterparts remains a key challenge for future NR simulations.

Numerical studies of the non-linear saturation of superradiance are very challenging due to the long time scales involved. A particularly convenient example of superradiance in spherical symmetry arises through the interaction of charged, massless scalar fields with Reissner-Nordström BHs in asymptotically anti-de Sitter spacetime or in a cavity; here energy is extracted from the BH charge rather than its rotation. The scalar field initially grows in accordance with superradiance, but eventually saturates, leaving behind a stable hairy BH [1163,1164]. Recently the instability of spinning BHs in AdS backgrounds was studied in full generality [1165]. The system displays extremely rich dynamics and it is unclear if there is a stationary final state.

The superradiant growth of a complex, massive vector field around a near-extremal Kerr BH has recently been modeled in axisymmetry [1166]. Over 9 % of the BH mass can be extracted until the process gradually saturates. Massive scalar fields can also pile up at the center of “normal” stars. Due to gravitational cooling, this pile-up does not lead to BH formation but stable configurations composed of the star with a “breathing” scalar field [1167].

The hairy BH configurations considered so far are long-lived but not strictly stationary. A class of genuinely stationary hairy BH spacetimes with scalar or vector fields has been identified in a series of papers [1168–1172]. The main characteristic of these systems is that the scalar field is not stationary—thus bypassing the no-hair theorems—but the spacetime metric and energy-momentum are. A subclass of these solutions smoothly interpolates between the Kerr metric and boson stars. A major challenge for numerical explorations is to evaluate whether these solutions are non- linearly stable and might thus be astrophysically viable. A recent study of linearized perturbations around the hairy BH solution of [1168] has found unstable modes with characteristic growth rates similar to or larger than those of a massive scalar field on a fixed Kerr background. However, such solution may still be of some astrophysical relevance [1173]. See also Sec. 4.2.1 of Chapter III for a related discussion.