The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

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We analytically compute time domain gravitational waveforms produced in the final stages of extreme mass ratio inspirals of non-spinning compact objects into supermassive nearly extremal Kerr black holes. Conformal symmetry relates all corotating equatorial orbits in the geodesic approximation to circular orbits through complex conformal transformations. We use this to obtain the time domain Teukolsky perturbations for generic equatorial corotating plunges in closed form. The resulting gravitational waveforms consist of an intermediate polynomial ringdown phase in which the decay rate depends on the impact parameters, followed by an exponential quasi-normal mode decay. The waveform amplitude exhibits critical behavior when the orbital angular momentum tends to a minimal value determined by the innermost stable circular orbit. We show that either near-critical or large angular momentum leads to a significant extension of the LISA observable volume of gravitational wave sources of this kind.

We compute scalar quasinormal mode (QNM) frequencies in rotating black hole solutions of the most general class of higher-derivative gravity theories, to quartic order in the curvature, that reduce to General Relativity for weak fields and are compatible with its symmetries. The wave operator governing the QNMs is not separable, but we show one can extract the QNM frequencies by a projection onto the set of spheroidal harmonics. We have obtained accurate results for the quasinormal frequency corrections relative to Kerr for rotating black holes with dimensionless spins up to ∼ 0.7. We also discuss to what extent our results carry over to the phenomenologically more relevant case of gravitational QNMs. Finally we provide an ancillary computational package that allows one to generalize our calculations to any effective energy-momentum tensor arising from higher-derivative terms in the effective action.

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.

We extend the Ori-Thorne-Kesden procedure to consistently describe the non-quasi-circular transition around the ISCO from inspiral to plunge into a black hole of arbitrary spin, including nearextremal. We identify that for moderate or high spins the transition is governed by the Painlevé transcendent equation of the first kind while for extremely high spins it is governed by a self-similar solution to the Korteweg-de Vries equation. We match the transition solution at leading order in the high spin limit with the analytical quasi-circular inspiral in the near-horizon region. We also show that the central black hole of an extreme mass ratio binary has a near-extremality parameter that scales at least as the mass ratio due to superradiant gravitational wave emission, which excludes extremely high spins.A theoretical modeling effort is required in order to produce a database of accurate and faithful templates for extreme mass ratio inspirals (EMRIs) for the LISA mission [1,2] or its proposed extension [3]. In addition to the main science objectives of the mission, intermediate mass ratio coalescences (IMRACs) which consist in intermediate mass black holes plunging into supermassive black holes constitute a potential source for LISA [4]. Such sources require an accurate modeling of the transition from inspiral to plunge since the number of cycles spent in that latter phase is observationally significant.The transition from inspiral to plunge was modeled for quasi-circular inspirals in the equatorial plane by Ori and Thorne [5] within black hole perturbation theory under some simplifying assumptions (see also the EOB framework [6] and [7-14] for extensions). Such a transition occurs around the innermost stable circular orbit (ISCO). One of the original assumptions of [5] was that the orbit is quasi-circular around the transition. However, such an assumption was shown to lead to mathematical inconsistencies by Kesden [11], though its analysis has been overlooked in the subsequent literature. It is therefore required to relax that hypothesis and consider a non-circular transition motion. The Ori-Thorne-Kesden model applies for all moderate spins but becomes inconsistent in the high spin regime where λ ≡ 1 − J 2 /M 4 → 0 [11]. The main purpose of this paper is to complete the Ori-Thorne-Kesden analysis to cover the high spin regime where new qualitative features arise.Geometrically thin disks allow to spin up black holes only up to the Thorne bound λ ≥ 0.06 [15]. Other accretion models might however by-pass this bound since no fundamental limitation exists on how fast accretion can spin up a black hole [16]. More fundamentally, the high spin limit λ → 0 can be viewed as the leading order result of a perturbative expansion for small λ. In the high spin regime, the ISCO lies within the near-horizon region of Kerr which is described by the near-horizon FIG. 1: Evolution of the near-horizon radius R N in terms of proper time τ during the inspiral (solid black line) and transition to plunge (dotted-dashed red line) for a bina...

We study gravitational perturbations of slowly-rotating black holes in a general effective-fieldtheory extension of general relativity that includes up to eight-derivative terms. We show that two Schrödinger-like equations with spin-dependent effective potentials govern the odd -and even-parity master variables. These equations are coupled for parity-violating corrections, and this coupling affects the quasinormal modes even at linear order in the higher-derivative corrections, due to their isospectrality in general relativity. We provide results for the shifts in the fundamental quasinormal mode frequencies at linear order in the spin, which we expect to be valuable for high-precision phenomenology through future gravitational wave observations.

We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' highercurvature corrections that yield second-order Friedmann-Lemaître equations and second-order-intime linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation r = −8nT . Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.