COSMO

Marc Casals

I am a researcher in General Relativity and in Quantum Field Theory in curved spacetimes. I am particularly interested in applications to black hole binary inspirals and gravitational waves, classical and quantum black hole physics, and to higher-dimensional spacetimes. 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 two compact objects such as black holes or neutron stars. The Laser Interferometer Gravitational-Wave Observatory (LIGO) recently announced [1] the first direct detection of gravitational waves. 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 has planned a space-based interferometer (eLISA), expected to launch in the near future, that will target inspirals in the extreme mass-ratio (between 1 -10^4 and 1 - 10^8). A typical extreme mass-ratio inspiral is that of a stellar-mass compact object orbiting around a supermassive black hole, which is believed to exist at the centre of most galaxies. Such binary inspiral can be modelled within perturbation theory of General Relativity as the smaller object deviating from a geodesic of the background created by the massive black hole; the deviation being due to a self-force [2]. The calculation of the self-force [3] is important for both purely 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. Furthermore, the self-force may be crucial in ensuring that a small object does not 'destroy' a black hole, thus avoiding the formation of a 'naked' singularity ('Cosmic Censorship' hypothesis). From an experimental viewpoint, the calculation of the self-force is key to the obtention of accurate gravitational waveforms and, with the recent LIGO detection, the era of gravitational wave astronomy has just begun!

Spectroscopy of Black Holes

    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 [3], studying the stability properties of black holes and fully determining the evolution of some initial data for the field [4]. Quantum-mechanically, the Green function may also be used to calculate quantum correlations in Hawking radiation. The Green function is made up of different analytical contributions from its Fourier-modes. For example, poles of the Fourier modes (quasi-normal modes) [5] have proved useful on many settings, most notably as LIGO matched [1] their recently-detected gravitational wave data to a QNM ‘ringdown’ at the late stage of the inspiral of the two black holes. In its turn, a branch cut of the Fourier modes in the complex-frequency plan has been shown to yield a power-law tail decay and a following logarithmic behaviour at late times of a field perturbation [6]. Importantly, a new branch cut in the case of extreme Kerr yields a horizon instability [7].

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 in the limit 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 astrophysically-relevant case of a rotating (Kerr) black hole, there is no quantum state that models the black hole in thermal equilibrium with its own Hawking bosonic radiation [8,9]. 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 conformal Quantum Field Theory on its boundary, with one dimension less).

In recent years, there has been growing interest in extending Einstein's General Relativity to a number of space-time dimensions different from four. The motivation has mainly come from high-energy Physics models but it is also of interest in order to obtain a better understanding of General Relativity itself. I am interested in investigating higher-dimensional space-times, both its quantum properties, such as black hole evaporation (it has been suggested that, if higher dimensions exist in Nature, 'mini' black holes could be produced in the Large Hadron Collider at CERN, which would evaporate in only fractions of a second via the emission of Hawking radiation [11,12]), or the 'gauge-gravity' duality conjecture, as well as its classical properties, such as topology and stability. I am also particularly interested in investigating quantum backreaction effects. A calculation in 2+1-dimensions has shown that the backreaction on a 'naked singularity' can turn it into a black hole, thus preserving the Cosmic Censorship hypothesis [13]. In the case of backreaction on a rotating 2+1-dimensional black hole, backreaction produces a curvature singularity at the inner horizon.
    [1] Abbott et al., Phys. Rev. Lett. 116, 061102 (2016).
    [2] Poisson, Pound and Vega, Living Rev. Rel. 14, 7 (2011).
    [3] Casals, Dolan, Ottewill and Wardell, Phys. Rev. D 88, 044022 (2013).
    [4] Yang and Casals, Phys. Rev. D 90, 023014 (2014).
    [5] Berti, Cardoso and Starinets, Class. Quant. Grav. 26, 163001 (2009).
    [6] Casals and Ottewill, Phys. Rev. Lett. 109, 111101 (2012).
    [7] Casals, Gralla and Zimmerman, Phys. Rev. D 94, 064003 (2016); ArXiv: 1606.08505 [gr-qc].
    [8] Kay and Wald, Physics Reports 207, 49 (1991).
    [9] Ottewill and Winstanley, Phys. Rev. D 62, 084018 (2000).
    [10] Casals, Dolan, Nolan, Ottewill and Winstanley, Phys. Rev. D 87, 064027 (2013).
    [11] Casals, Kanti and Winstanley, JHEP 02, 051 (2006).
    [12] Frost, Gaunt, Sampaio, Casals, Dolan, Parker and Webber, JHEP 10, 014 (2009).
    [13] Casals, Fabbri, Martinez and Zanelli, accepted for publication in Phys. Rev. Lett. (2017); arXiv: 1608.05366 [gr-qc].