Marc Casals

I am a researcher in General Relativity and Quantum Field Theory in curved spacetimes. I am particularly interested in applications to black hole binary inspirals and gravitational waves, black hole stability properties and quantum black hole physics. There follows a brief description of these different areas of research interests.

Gravitational Waves and Black Hole Inspirals

According to General Relativity, gravitational waves (‘ripples in space-time’) are emitted during the inspiral of compact objects such as black holes or neutron stars. In a historical accomplishment, the Laser Interferometer Gravitational-Wave Observatory (LIGO) achieved the first direct detection of gravitational waves [1]. The source of these waves was a binary of stellar-mass black holes. While LIGO targets inspirals of at most an intermediate mass-ratio (i.e, up to a mass ratio of 1 - 10^4), the European Space Agency, in collaboration with NASA, has planned a space-based interferometer (LISA [2]), expected to launch in the near future, that will target inspirals in the extreme mass-ratio (between 1-104 and 1-108). An extreme -and even intermediate- mass-ratio inspiral can be modelled within perturbation theory of General Relativity as the smaller compact object deviating from a geodesic of the background created by the more massive black hole; the deviation being due to a self-force [3].

I take part in a worldwide effort towards the calculation of the self-force in different settings, as is important for both theoretical and experimental reasons. From a theoretical viewpoint, the understanding of the two-body motion is one of the few outstanding fundamental problems in General Relativity. From an experimental viewpoint, the calculation of the self-force is key to the obtention of accurate gravitational waveforms for extreme -and intermediate- mass-ratio inspirals within this new era of gravitational wave astronomy!

Spectroscopy of Black Holes: Stability Properties and Late-time Waveform

    The Green function of the wave equation satisfied by field perturbations of black hole spacetimes is of central physical importance in classical and quantum gravity. Classically, the Green function is useful, for example, for calculating the self-force [4], studying the stability properties of black holes and fully determining the evolution of some initial data for the field. Quantum-mechanically, the Green function may also be used for calculating quantum correlations in Hawking radiation or investigating the communication between quantum particle detectors.

    The Green function is made up of different analytical contributions from its Fourier-modes [5]. For example, poles of the Fourier modes (quasi-normal modes, QNMs) are useful for modelling the late (‘ringdown’) stage of a gravitational waveform corresponding to the inspiral of two black holes. Furthermore, the potential existence of such poles on the upper complex-frequency plane would lead to instabilities of the spacetime (rotating Kerr black holes do not have such instabilities thanks to a 'hidden' symmetry [6]) and, even if they lie on the lower plane, they may determine the regularity properties of the inner (Cauchy) horizon of black holes. The regularity of the Cauchy horizon would imply that General Relativity ceases to be deterministic inside black holes, thus violating Penrose's Strong Cosmic Censorship hypothesis. There is newly-found evidence [7] of the regularity under classical field perturbations of the Cauchy horizon of some charged, rotating black holes in a de Sitter Universe (i.e., Kerr-Newman-de Sitter), thus violating Strong Cosmic Censorship. In its turn, a new branch cut of the Fourier modes in the complex-frequency plane in the case of maximally-rotating Kerr yields blow-up of derivatives of the field on the event horizon [8] (the so-called Aretakis phenomenon).

Quantum Black Holes: from Conceptual Foundations to CERN

In the absence of a full theory of Quantum Gravity, one may gain a revealing insight into such a theory when the scales of the physical system are much larger than the Planck scales by quantizing the 'matter' fields and treating the gravitational field classically. Such framework has led to many important discoveries, such as the emission of quantum, thermal (Hawking) radiation by astrophysical black holes, and has posed fundamental unresolved challenges, such as the black hole information paradox (that is, emission of Hawking radiation seems to imply that the system evolves from a pure to a mixed state, in apparent contradiction with the unitarity property of quantum physics). It is known that, in the case of a Kerr black hole, there is no quantum state that models the black hole in thermal equilibrium with its own Hawking bosonic radiation [9]. Interestingly, however, such a thermal state is well-defined (up to a finite distance from the event horizon) for fermions [10]. Such quantum state is the relevant one for studying the thermodynamical properties of black holes and for the 'gauge-gravity' duality (a conjectured correspondence between gravity in a certain space-time and a Quantum Field Theory on its boundary).

It is important to investigate how quantum effects backreact on classical black holes. The first quantum-backreacted metric on a rotating black hole was obtained in [11], where the backgrounds were a rotating (BTZ) black hole and a ‘naked’ singularity (i.e., a spacetime singularity which is not ‘hidden’ by an event horizon) in (2+1)-dimensions. There, it was found that quantum effects render the Cauchy horizon of the black hole irregular and that, in the case of the naked singularity, they turn it into a black hole. These results support the role of quantum physics as a Cosmic Censor! In the astrophysically-relevant case of Kerr, semiclassical effects on its Cauchy horizon also render it irregular [12].

On a different semiclassical setting, high-energy Physics models suggest that our 4-dimensional world may be embedded in a higher-dimensional spacetime. I have worked on the thrilling prospect of such models leading to the creation of miniature black holes in the Large Hadron Collider at CERN [13]. Finally, as of recently I have started working on the new thriving field of relativistic quantum information, where communication between quantum particle detectors on a curved spacetime are studied as well as the possibility of their harvesting correlations from a quantum field.
    [1] Abbott et al., Phys. Rev. Lett. 116, 061102 (2016).
    [2] P. Amaro-Seoane et al., arXiv:1702.00786. [3] Poisson, Pound and Vega, Living Rev. Rel. 14, 7 (2011).
    [4] Casals, Dolan, Ottewill and Wardell, Phys. Rev. D 88, 044022 (2013). ArXiv: 1306.0884 [gr-qc].
    [5] Casals and Ottewill, Phys. Rev. Lett. 109, 111101 (2012). ArXiv: 1205.6592 [gr-qc].
    [6] Casals and Teixeira da Costa. Commun. Math. Phys. 394, 797 (2022). ArXiv:2105.13329 [gr-qc].
    [7] Casals and Marinho, Phys. Rev. D 106, 044060 (2022). ArXiv:2006.06483 [gr-qc].
    [8] Casals, Gralla and Zimmerman, Phys. Rev. D 94, 064003 (2016). ArXiv: 1606.08505 [gr-qc].
    [9] Kay and Wald, Physics Reports 207, 49 (1991).
    [10] Casals, Dolan, Nolan, Ottewill and Winstanley, Phys. Rev. D 87, 064027 (2013). ArXiv: 1207.7089 [gr-qc].
    [11] Casals, Fabbri, Martinez and Zanelli, Phys. Rev. Lett. 118, 131102 (2017). ArXiv: 1608.05366 [gr-qc].
    [12] Zilberman, Casals, Ori and Ottewill. Phys. Rev. Lett. 129, 261102-1/6 (2022). ArXiv:2203.08502 [gr-qc].
    [13] Frost, Gaunt, Sampaio, Casals, Dolan, Parker and Webber, JHEP 10, 014 (2009). ArXiv: 0904.0979 [hep-ph].