Past and present research
My research has mostly dealt with classical and quantum field theory on black hole spacetimes, with particular focus on rotating black holes and also on asymptotically anti-de Sitter (AdS) black holes. Namely, I worked on the questions of classical instabilities, superradiance and formulation of classical and quantum field theories (QFTs) in these backgrounds. Below, I present a summary of my past and recent research.
Black hole superradiance
The phenomenon of superradiance in rotating black holes and their resulting instabilities are by now reasonably well-understood [1], especially in the case of asymptotically flat spacetimes such as the Kerr black hole and higher-dimensional analogues. Some work has also been done for asymptotically AdS black holes, usually motivated by the AdS/CFT correspondence, showing that superradiance instabilities exist for small (relative to the AdS radius) black holes [2].
However, there is still much left to study on the topic of black hole superradiance and, in my work, I obtained novel results which add pieces to the current understanding of superradiance, some of them not explored yet in asymptotically flat black holes. Most notably, by considering a more general set of Robin boundary conditions at the conformal boundary of asymptotically AdS black holes (instead of the usually considered Dirichlet boundary conditions), I found that not only does the superradiance effect can be amplified or reduced but also that it competes with an intrinsic, bulk instability caused by the AdS asymptotics. For some Robin boundary conditions, the instability is caused mainly by the superradiance effect, whereas for some other Robin boundary conditions the AdS bulk instability is dominant. These new features were shown explicitly for the simple case of a massive scalar field in the (2+1)-dimensional BTZ black hole, in collaboration with Carlos Herdeiro and Claudio Dappiaggi [3], while also showing that this black hole solution can have classical superradiance, contrarily to the previous claims in the literature. Even though we considered a simplified setting, numerical methods were necessary to analyse this problem. I am currently finalising work that extends these results to the Kerr-AdS black hole.
Moreover, in a separate article with Carlos Herdeiro [4], I established the existence of stationary clouds of massive scalar fields around BTZ black holes, which exist at the threshold of the superradiant instabilities described above. For this, it was also essential to consider more general boundary conditions than those commonly used in previous works.
This research shows that the intuition derived from the study of superradiance in asymptotically flat spacetimes is not always valid for black holes with different asymptotics. Another example of this was provided in an earlier work [5] where I considered a rotating black hole with a “squashed AdS” asymptotics, called the warped AdS black hole. Surprisingly, there is no superradiant instability, showing once more that rotation by itself does not necessarily render a black hole unstable and that the asymptotic structure plays a key role.
Quantum field theory on rotating black holes
Additionally, in the past I have also investigated the behaviour of quantum matter fields on rotating black holes, a largely unexplored topic.
One of the more important tasks when studying quantum matter fields propagating on black hole spacetimes is the computation of local observables of interest, such as the renormalised stress-energy tensor. The knowledge of this quantity is essential as a starting point of semiclassical gravity and to obtain the back-reaction of the metric.
In collaboration with Jorma Louko [6], I developed a novel renormalisation implementation to obtain the renormalised vacuum polarization for a quantised scalar field in a rotating black hole. This provided, for the first time, a general, explicit method to numerically compute these quantities for a stationary black hole. This generalised the standard techniques used previously for static black holes and is sufficiently general to be applicable to an arbitrary stationary black hole spacetime, such as Kerr.
Classical and quantum field theory on AdS spacetimes
As for QFT on AdS and asymptotically AdS spacetimes in general, many of their basic features are still poorly understood and my work provided a significant contribution to the field. Given that these spacetimes are not globally hyperbolic, the classical dynamics of matter fields is not completely determined by suitable initial data on a spacelike hypersurface and boundary conditions need to be specified at infinity in order to have a well-posed system. Moreover, the standard formulation of QFT is only applicable to globally hyperbolic spacetimes and, failing this condition, there is no universally accepted replacement. My work with Claudio Dappiaggi [7,8] has analysed the role of the boundary conditions on the classical and quantum theory of scalar fields in pure AdS and AdS black holes, which was essential for the study of superradiance in AdS black holes, as mentioned above. Furthermore, we proposed a natural way to define and construct physically relevant quantum states in these spacetimes, something that was missing in the literature.
References
[1] R. Brito, V. Cardoso and P. Pani, Superradiance, Lect. Notes Phys. 906, pp.1 (2015), arXiv:1501.06570 [gr-qc].
[2] V. Cardoso and O. J. C. Dias, Small Kerr-AdS black holes are unstable, Phys. Rev. D 70 (2004) 084011, arXiv:0405006 [hep-th].
[3] C. Dappiaggi, H. R. C. Ferreira and C. A. R. Herdeiro, Superradiance in BTZ black hole with Robin boundary conditions (2017), arXiv:1710.08039 [gr-qc].
[4] H. R. C. Ferreira and C. A. R. Herdeiro, Stationary scalar clouds around a BTZ black hole, Phys. Lett. B 773, 129 (2017), arXiv:1707.08133 [gr-qc].
[5] H. R. C. Ferreira, Stability of warped AdS3 black holes in Topologically Massive Gravity under scalar perturbations, Phys. Rev. D 87, 124013 (2013), arXiv:1304.6131 [gr-qc].
[6] H. R. C. Ferreira, J. Louko, Renormalized vacuum polarization on rotating warped AdS3 black holes, Phys.Rev.D91 (2015), 024038, arXiv:1410.5983 [gr-qc].
[7] C. Dappiaggi, H. R. C. Ferreira, Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions, Phys. Rev. D 94 12, 125016 (2016), arXiv:1610.01049 [gr-qc].
[8] C. Dappiaggi and H. R. C. Ferreira, On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime, Rev. Math. Phys. (2017), arXiv:1701.07215 [math-ph].
[9] F. Bussola, C. Dappiaggi, H. R. C. Ferreira and I. Khavkine, Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions, Phys. Rev. D 96, 105016 (2017), arXiv:1708.00271 [gr-qc].
Last updated November 2017
Black hole superradiance
The phenomenon of superradiance in rotating black holes and their resulting instabilities are by now reasonably well-understood [1], especially in the case of asymptotically flat spacetimes such as the Kerr black hole and higher-dimensional analogues. Some work has also been done for asymptotically AdS black holes, usually motivated by the AdS/CFT correspondence, showing that superradiance instabilities exist for small (relative to the AdS radius) black holes [2].
However, there is still much left to study on the topic of black hole superradiance and, in my work, I obtained novel results which add pieces to the current understanding of superradiance, some of them not explored yet in asymptotically flat black holes. Most notably, by considering a more general set of Robin boundary conditions at the conformal boundary of asymptotically AdS black holes (instead of the usually considered Dirichlet boundary conditions), I found that not only does the superradiance effect can be amplified or reduced but also that it competes with an intrinsic, bulk instability caused by the AdS asymptotics. For some Robin boundary conditions, the instability is caused mainly by the superradiance effect, whereas for some other Robin boundary conditions the AdS bulk instability is dominant. These new features were shown explicitly for the simple case of a massive scalar field in the (2+1)-dimensional BTZ black hole, in collaboration with Carlos Herdeiro and Claudio Dappiaggi [3], while also showing that this black hole solution can have classical superradiance, contrarily to the previous claims in the literature. Even though we considered a simplified setting, numerical methods were necessary to analyse this problem. I am currently finalising work that extends these results to the Kerr-AdS black hole.
Moreover, in a separate article with Carlos Herdeiro [4], I established the existence of stationary clouds of massive scalar fields around BTZ black holes, which exist at the threshold of the superradiant instabilities described above. For this, it was also essential to consider more general boundary conditions than those commonly used in previous works.
This research shows that the intuition derived from the study of superradiance in asymptotically flat spacetimes is not always valid for black holes with different asymptotics. Another example of this was provided in an earlier work [5] where I considered a rotating black hole with a “squashed AdS” asymptotics, called the warped AdS black hole. Surprisingly, there is no superradiant instability, showing once more that rotation by itself does not necessarily render a black hole unstable and that the asymptotic structure plays a key role.
Quantum field theory on rotating black holes
Additionally, in the past I have also investigated the behaviour of quantum matter fields on rotating black holes, a largely unexplored topic.
One of the more important tasks when studying quantum matter fields propagating on black hole spacetimes is the computation of local observables of interest, such as the renormalised stress-energy tensor. The knowledge of this quantity is essential as a starting point of semiclassical gravity and to obtain the back-reaction of the metric.
In collaboration with Jorma Louko [6], I developed a novel renormalisation implementation to obtain the renormalised vacuum polarization for a quantised scalar field in a rotating black hole. This provided, for the first time, a general, explicit method to numerically compute these quantities for a stationary black hole. This generalised the standard techniques used previously for static black holes and is sufficiently general to be applicable to an arbitrary stationary black hole spacetime, such as Kerr.
Classical and quantum field theory on AdS spacetimes
As for QFT on AdS and asymptotically AdS spacetimes in general, many of their basic features are still poorly understood and my work provided a significant contribution to the field. Given that these spacetimes are not globally hyperbolic, the classical dynamics of matter fields is not completely determined by suitable initial data on a spacelike hypersurface and boundary conditions need to be specified at infinity in order to have a well-posed system. Moreover, the standard formulation of QFT is only applicable to globally hyperbolic spacetimes and, failing this condition, there is no universally accepted replacement. My work with Claudio Dappiaggi [7,8] has analysed the role of the boundary conditions on the classical and quantum theory of scalar fields in pure AdS and AdS black holes, which was essential for the study of superradiance in AdS black holes, as mentioned above. Furthermore, we proposed a natural way to define and construct physically relevant quantum states in these spacetimes, something that was missing in the literature.
References
[1] R. Brito, V. Cardoso and P. Pani, Superradiance, Lect. Notes Phys. 906, pp.1 (2015), arXiv:1501.06570 [gr-qc].
[2] V. Cardoso and O. J. C. Dias, Small Kerr-AdS black holes are unstable, Phys. Rev. D 70 (2004) 084011, arXiv:0405006 [hep-th].
[3] C. Dappiaggi, H. R. C. Ferreira and C. A. R. Herdeiro, Superradiance in BTZ black hole with Robin boundary conditions (2017), arXiv:1710.08039 [gr-qc].
[4] H. R. C. Ferreira and C. A. R. Herdeiro, Stationary scalar clouds around a BTZ black hole, Phys. Lett. B 773, 129 (2017), arXiv:1707.08133 [gr-qc].
[5] H. R. C. Ferreira, Stability of warped AdS3 black holes in Topologically Massive Gravity under scalar perturbations, Phys. Rev. D 87, 124013 (2013), arXiv:1304.6131 [gr-qc].
[6] H. R. C. Ferreira, J. Louko, Renormalized vacuum polarization on rotating warped AdS3 black holes, Phys.Rev.D91 (2015), 024038, arXiv:1410.5983 [gr-qc].
[7] C. Dappiaggi, H. R. C. Ferreira, Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions, Phys. Rev. D 94 12, 125016 (2016), arXiv:1610.01049 [gr-qc].
[8] C. Dappiaggi and H. R. C. Ferreira, On the algebraic quantization of a massive scalar field in anti-de-Sitter spacetime, Rev. Math. Phys. (2017), arXiv:1701.07215 [math-ph].
[9] F. Bussola, C. Dappiaggi, H. R. C. Ferreira and I. Khavkine, Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions, Phys. Rev. D 96, 105016 (2017), arXiv:1708.00271 [gr-qc].
Last updated November 2017