Table of contents

Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [1, 2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the nonlinear level. We confirm this expectation and explicitly construct examples of such Kerr BHs with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [3] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr–Newman BHs with a real, massless vector field.

We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza–Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss–Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories.

We investigate solutions $({\mathcal{M}},g)$ to Einstein's vacuum field equations with positive cosmological constant Λ which admit a smooth past null infinity ${{\mathcal{I}}}^{-}$ à la Penrose and a Killing vector field whose associated Mars–Simon tensor (MST) vanishes. The main purpose of this work is to provide a characterization of these spacetimes in terms of their Cauchy data on ${{\mathcal{I}}}^{-}$. Along the way, we also study spacetimes for which the MST does not vanish. In that case there is an ambiguity in its definition which is captured by a scalar function Q. We analyze properties of the MST for different choices of Q. In doing so, we are led to a definition of 'asymptotically Kerr–de Sitter-like spacetimes', which we also characterize in terms of their asymptotic data on ${{\mathcal{I}}}^{-}$.

We model the inspiral of a compact object into a more massive black hole rotating very near the theoretical maximum. We find that once the body enters the near-horizon regime the gravitational radiation is characterized by a constant frequency, equal to (twice) the horizon frequency, with an exponentially damped profile. This contrasts with the usual 'chirping' behavior and, if detected, would constitute a 'smoking gun' for a near-extremal black hole in nature.

We argue that the event horizon of a binary black hole merger, in the extreme-mass-ratio limit where one of the black holes is much smaller than the other, can be described in an exact analytic way. This is done by tracing in the Schwarzschild geometry a congruence of null geodesics that approaches a null plane at infinity. Its form can be given explicitly in terms of elliptic functions, and we use it to analyze and illustrate the time-evolution of the horizon along the merger. We identify features such as the line of caustics at which light rays enter the horizon, and the critical point at which the horizons touch. We also compute several quantities that characterize these aspects of the merger.

We discuss the cosmological implications of an extended Brans–Dicke theory presented recently, in which there is an energy exchange between the scalar field and ordinary matter, determined by the theory. A new mass scale is generated in the theory which modifies the Friedmann equations with field-dependent corrected kinetic terms. In a radiation Universe the general solutions are found and there are branches with complete removal of the initial singularity, while at the same time a transient accelerating period can occur within deceleration. Entropy production is also possible in the early Universe. In the dust era, late-times acceleration has been found numerically in agreement with the correct behavior of the density parameters and the dark energy equation of state, while the gravitational constant has only a slight variation over a large redshift interval in agreement with observational bounds.

We critically discuss current research on black hole (BH) solutions in f (R) gravity and shed light on its geometrical and physical significance. We also investigate the meaning, existence or lack thereof of Birkhoff's theorem (BT) in this kind of modified gravity. We then focus on the analysis and search for non-trivial (i.e. hairy) asymptotically flat (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does not vanish identically in the domain of outer communication. To do so, we provide and enforce regularity conditions at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of f (R) models like those proposed recently for explaining the accelerated expansion in the Universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the absence of geometric hair in AFSSSBH solutions in those f (R) models. First, we submit the models to the available no-hair theorems (NHTs), and in the cases where the theorems apply, the absence of hair is demonstrated analytically. In the cases where the theorems do not apply, we resort to a numerical analysis due to the complexity of the non-linear differential equations. With that aim, a code to solve the equations numerically was built and tested using well-known exact solutions. In a future investigation we plan to analyze the problem of hair in de Sitter and anti-de Sitter backgrounds.

We first make a Killing spinor analysis for a general three-dimensional off-shell $N=(2,0)$ supergravity and find conditions for a bosonic background to preserve at least one real supercharge. We then consider a particular model, namely $N=(2,0)$ topologically massive supergravity and impose its field equations. By making a suitable ansatz on metric functions we find a large class of solutions that include spacelike, timelike and null warped AdS₃ among others. Isometric quotients of spacelike and timelike squashed AdS₃ solutions yield extremal black holes without closed causal curves.

Pulsars orbiting around the black hole (BH) at our galactic center provide us with a unique testing site for gravity. In this work, we propose an approach to probe the gravity around the BH introducing two phenomenological parameters which characterize deviation from the vacuum Einstein theory. The two phenomenological parameters are associated with the energy–momentum tensor in the framework of the Einstein theory. Therefore, our approach can be regarded as the complement to the parametrized post-Newtonian framework in which phenomenological parameters are introduced for deviation of gravitational theories from general relativity. In our formulation, we take into account the possibility of existence of a relativistic and exotic matter component. Since the pulsars can be regarded as test particles, as the first step, we consider geodesic motion in the system composed of a central BH and a perfect fluid whose distribution is static and spherically symmetric. It is found that the mass density of the fluid and a parameter of the equation of state can be determined with precision with $0.1 \%$ if the density on the pulsar orbit is larger than ${10}^{-9}\;{\rm{g}}\;{\mathrm{cm}}^{-3}$.

Axisymmetric and stationary solutions are constructed to the Einstein–Vlasov and Vlasov–Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein–Vlasov system which contain ergoregions.

In de Sitter (dS) gravity, where gravity is a gauge field introduced to realize the local dS invariance of the matter field, two kinds of conservation laws are derived. The first kind is a differential equation for a dS-covariant current, which unites the canonical energy-momentum (EM) and angular momentum (AM) tensors. The second kind presents a dS-invariant current which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current unites the total (matter plus gravity) EM and AM currents. It is well known that the AM current contains an inherent part, called the spin current. Here it is shown that the EM tensor also contains an inherent part, which might be observed by its contribution to the deviation of the dust particle's world line from a geodesic. All the results are compared to the ordinary Lorentz gravity.

In the close vicinity of a compact object strong gravity imprints its signature onto matter. Systems that contain at least one compact object are observed to exhibit extreme physical properties and typically emit highly energetic radiation. The nature of the compact objects that produce the strongest gravitational fields is to date not settled. General relativistic numerical simulations of fluid dynamics around black holes, neutron stars, and other compact objects such as boson stars (BSs) may give invaluable insights into this fundamental question. In order to study the behavior of fluid in the strong gravity regime of an arbitrary compact object we develop a new general relativistic hydrodynamics code. To this end we extend the existing versatile adaptive mesh refinement code MPI-AMRVAC into a general relativistic hydrodynamics framework and adapt it for the use of numerically given spacetime metrics. In the present article we study accretion flows in the vicinity of various types of BSs whose numerical metrics are calculated by the KADATH spectral solver library. We design specific tests to check the reliability of any code intending to study BSs and compare the solutions with those obtained in the context of Schwarzschild black holes. We perform the first ever general relativistic hydrodynamical simulations of gas accretion by a BS. The behavior of matter at small distances from the center of a BS differs notably from the black hole case. In particular we demonstrate that in the context of Bondi spherical accretion the mass accretion rate onto non-rotating BSs remains constant whereas it increases for Schwarzschild black holes. We also address the scenario of non-spherical accretion onto BSs and show that this may trigger mass ejection from the interior of the BS. This striking feature opens the door to forthcoming investigations regarding accretion-ejection flows around such types of compact objects.

Based on spin weighted spherical harmonic decomposition, the $(2,\pm 2)$ modes dominate the gravitational waveforms generated by binary black holes. Several recent works found that other modes including $(l,0)$ ones are also important to gravitational wave data analysis. For aligned-spin binaries, these $(l,0)$ modes are related to the memory effect of gravitational wave. Based on the post-Newtonian analysis, quasi-normal modes analysis and the results of numerical relativity simulations, we present a full inspiral-merger-ringdown gravitational waveform model for the $(2,0)$ mode generated by binary black holes. Our model includes the quasinormal ringing part and includes the effect of a black hole's spin. It is complementary to the previous results.

In four space–time dimensions General Relativity can be non-trivially deformed. Deformed theories continue to describe two propagating degrees of freedom, as GR. We study Euclidean black hole thermodynamics of these deformations. We use the recently developed formulation that works with ${\rm{SO}}(3)$ connections as well as certain matrices M of auxiliary fields. We show that the black hole entropy is given by one quarter of the horizon area as measured by the Lie algebra valued two-form MF, where F is the connection curvature. This coincides with the horizon area as measured by the metric only for the case of General Relativity.

We extend the conjectured Kerr/CFT correspondence to the case of extremal Kerr black holes immersed by a magnetic field, namely the extremal Melvin–Kerr black holes. We compute the central charge which appears in the associated Virasoro algebra generated by a class of diffeomorphisms that satisfies a set of boundary conditions in the near horizon of an extremal Melvin–Kerr black hole. Our results support the Kerr/CFT conjecture, where the macroscopic Bekenstein–Hawking entropy for an extremal Melvin–Kerr black hole matches the result obtained from a dual 2D CFT microscopic computation using Cardy formula. Interestingly, the dual CFT description could be non-unitary, due to the possibility of negative central charge.

Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing us to make direct contact with previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is discussed, as well as an embedding of reduced quantum states to a subsector of the quantum symmetry reduced full theory states. On this full theory subsector, the quantum algebra of the mentioned observables is computed and shown to qualitatively reproduce the quantum algebra of the reduced variables in the large quantum number limit for a specific choice of regularisation. Insufficiencies in recovering the reduced algebra quantitatively from the full theory are attributed to the oversimplified full theory quantum states we use.

In this work, we examine cosmological constraints on models of composite inflation based on the slow-roll approximation by using the recent Planck measurement. We compare the spectral index of curvature perturbation (and its running) and the tensor-to-scalar ratio predicted by such models with Planck 2015 data. We find that the predictions of technicolor inflation are nicely consistent with the Planck analysis. Moreover, the predictions from the second model, glueball inflation, are in good agreement with the Planck data at 2σC.L. However, the final two models, super glueball inflation and orientifold inflation, favor only the rather large value of the tensor-to-scalar ratio of which the predictions are in tension with the Planck analysis.