International Journal of Modern Physics D

We review recent work on the theory of tidal deformability and the tidal Love numbers of a slowly spinning compact object within general relativity. Angular momentum introduces couplings between distortions of different parity and new classes of spin-induced, tidal Love numbers emerge. Due to spin-tidal effects, a rotating object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second-order in the spin. The tidal Love numbers depend strongly on the object’s internal structure. All tidal Love numbers of a Kerr black hole (BH) were proved to be exactly zero to first-order in the spin and also to second-order in the spin, at least in the axisymmetric case. For a binary system close to the merger, various components of the tidal field become relevant. Preliminary results suggest that spin-tidal couplings can introduce important corrections to the gravitational waveforms of spinning neutron star (NS) binaries approaching the merger.

We report the visit to Amazonia of the British astronomers Crommelin and Davidson, in their way to the Brazilian city Sobral to perform the measurements related to the total solar eclipse of 29th May 1919, as an experimental test of the Theory of General Relativity.

In this paper, we have investigated the arising of geometric quantum phases in a relativistic quantum dynamics of a Dirac neutral particle from the spontaneous Lorentz symmetry violation effects in the cosmic string spacetime. We started by the Dirac equation in an effective metric, and we have observed a relativistic geometric phase which stems from the topology of the cosmic string spacetime and an intrinsic Lorentz symmetry breaking effects. It is shown that both Lorentz symmetry breaking effects and the topology of the defect yields a phase shift in the wave function of the nonrelativistic spin-$1/2$ particle.

We study wave propagation in a draining bathtub: a black hole analogue in fluid mechanics whose perturbations are governed by a Klein–Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possesses an (effective) horizon, an ergosphere and null circular orbits. We propose here that a ‘pulse’ disturbance may be used to map out the light-cone of the effective geometry. First, we apply the eikonal approximation to elucidate the link between wavefronts, null geodesic congruences and the Raychaudhuri equation. Next, we solve the wave equation numerically in the time domain using the method of lines. Starting with Gaussian initial data, we demonstrate that a pulse will propagate along a null congruence and thus trace out the light-cone of the effective geometry. Our new results reveal features, such as wavefront intersections, frame-dragging, winding and interference effects, that are closely associated with the presence of null circular orbits and the ergosphere.

We review some properties of black hole structures appearing in gravity with a massless scalar field, with both minimal and nonminimal coupling. The main properties of the resulting cold black holes are described. The study of black holes in scalar-gravity systems is extended to $k$-essence theories, and some examples are explicitly worked out. In these cases, even while the existence of horizons is possible, the metric regularity requirement on the horizon implies either a cold black type structure or a singular behavior of the scalar field.

Horndeski gravity holds a special position as the most general extension of Einstein’s theory of general relativity (GR) with a single scalar degree of freedom and second-order field equations. Because of these features, Horndeski gravity is an attractive phenomenological playground to investigate the consequences of modifications of GR in cosmology and astrophysics. We present a review of the progress made so far in the study of compact objects (black holes (BHs) and neutron stars (NSs)) within Horndeski gravity. In particular, we review our recent work on slowly rotating BHs and present some new results on slowly rotating NSs.

In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.

We discuss the phenomenology of massless scalar fields around a regular Bardeen black hole, namely absorption cross-section, scattering cross-section and quasinormal modes. We compare the Bardeen and Reissner–Nordström black holes, showing limiting cases for which their properties are similar.

A self-gravitating Skyrmion is an analytic and globally regular solution of the Einstein–Skyrme system with nonvanishing topological charge. The spacetime is the direct product $R\times S^3$ and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX and, through an analytic continuation, it can also be turned into a transversable asymptotically AdS Lorentzian wormhole. The stress–energy of this wormhole satisfies physically realistic energy conditions and the only “exotic matter” required by it is a negative cosmological constant.

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two $D$-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

Scalar fields can form real bound states around black holes for a specific frequency. In this work, we review the case of a charged and massive scalar field around a charged rotating black hole, in order to find these bound states. We analyze the behavior of these solutions for different parameters and also comment on analytic solutions for certain regimes.

We present in detail the Einstein equations in the Baumgarte–Shapiro–Shibata–Nakamura formulation for the case of $D$-dimensional spacetimes with $\mathrm{\text{SO}}(D-d)$ isometry based on a method originally introduced in Ref. 1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value $d=D-2$, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in $D=7$ spacetime dimensions with $\mathrm{\text{SO}}(4)$ symmetry.

Self-interacting boson stars (BSs) have been shown to alleviate the astrophysically low maximal mass of their nonself-interacting counterparts. We report some physical features of spinning self-interacting BSs, namely their compactness, the occurrence of ergo-regions and the scalar field profiles, for a sample of values of the coupling parameter. The results agree with the general picture that these BSs are comparatively less compact than the nonself-interacting ones. We also briefly discuss the effect of scalar self-interactions on the properties of Kerr black holes with scalar hair.

The inspiral of a stellar-mass astrophysical object into a massive black hole may be modeled within perturbation theory of General Relativity via the so-called self-force. In this paper, we present a novel method for the calculation of the self-force which is based on the Green function (GF) of the wave equation satisfied by the field created by the smaller object. We review the results in [M. Casals, S. Dolan, A. C. Ottewill and B. Wardell, Phys. Rev. D 88 (2013) 044022; B. Wardell, C. R. Galley, A. Zenginoğlu, M. Casals, S. R. Dolan and A. C. Ottewill, Phys. Rev. D 89 (2014) 084021] on the GF and the self-force on a scalar charge (as a model for the gravitational case) moving on a Schwarzschild black hole spacetime. This GF method offers an appealing geometrical insight into the origin of the self-force and is a promising candidate for practical self-force calculations.

In [R. P. Bernar, L. C. B. Crispino and A. Higuchi, Phys. Rev. D 90 (2014) 024045.] we investigated gravitational perturbations in the background of de Sitter spacetime in arbitrary dimensions. More specifically, we used a gauge-invariant formalism to describe the perturbations inside the cosmological horizon, i.e. in the static patch of de Sitter spacetime. After a gauge-fixed quantization procedure, the two-point function in the Bunch–Davies-like vacuum state was shown to be infrared finite and invariant under time-translation. In this work, we give details of the calculations to obtain the graviton two-point function in 3 + 1 dimensions.

In this work, we study the influence of the gravitational field induced by the presence of a cosmological constant $\mathrm{\Lambda }$ on the Casimir energy density. We consider two metrics with the presence of the $\mathrm{\Lambda }$-term, namely de Sitter and Schwarzschild-de Sitter (SdS). In the former case, we consider a conformal de Sitter spacetime and in the last one, a weak gravitational SdS spacetime.

We consider the Casimir effect, by calculating the Casimir energy and its corrections for nonzero temperatures, of a massless scalar field in the spacetime with topology $S^3\times R^1$ (Einstein universe) containing an idealized cosmic string. The obtained results confirm the role played by the identifications imposed on the quantum field by boundary conditions arising from the topology of the gravitational field under consideration and illustrate a realization of a gravitational analogue of the Casimir effect. In this backgorund, we show that the vacuum energy can be written as a term which corresponds to the vacuum energy of the massless scalar field in the Einstein universe added by another term that formally corresponds to the vacuum energy of the electromagnetic field in the Einstein universe, multiplied by a parameter associated with the presence of the cosmic string, namely, $\lambda =(1/\alpha )-1$, where $\alpha$ is a constant related to the cosmic string tension, $G\mu$.

We show that a purely circulating and compressible system, in an adiabatic regime of acoustic propagation, presents superresonant instabilities. To show the existence these instabilities, we compute the quasinormal mode frequencies of this system numerically using two different frequency domain methods.

We describe a few unexpected features of de Sitter quantum field theory (QFT) that have no Minkowskian counterparts. These phenomena show that even when the cosmological constant is tiny a Minkowskian way of fast thinking about de Sitter can lead to mistakes and that de Sitter QFT is essentially different from standard relativistic (Minkowskian) QFT.

For an observer, the Black Hole (BH) shadow is the BHs apparent image in the sky due to the gravitational lensing of nearby radiation, emitted by an external source. A recent class of solutions dubbed Kerr BHs with scalar hair possess smaller shadows than the corresponding Kerr BHs and, under some conditions, novel exotic shadow shapes can arise. Thus, these hairy BHs could potentially provide new shadow templates for future experiments such as the Event Horizon Telescope. In order to obtain the shadows, the backward ray-tracing algorithm is briefly introduced, followed by numerical examples of shadows of Kerr BHs with scalar hair contrasting with the Kerr analogues. Additionally, an analytical solution for the Kerr shadow is derived in closed form for a ZAMO observer at an arbitrary position.

We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on recent developments regarding the spin evolution in black hole binaries, high-energy black hole collisions, compact object solutions in scalar–tensor gravity, superradiant instabilities, hairy black hole solutions in Einstein’s gravity coupled to fundamental fields, and the possibility to gain insight into these phenomena using analog gravity models.

We introduce an alternate method for gravitational radiation extraction for binary black hole mergers where we do not use a single extraction radius at the intermediate field region but instead use a whole spherical shell of three-dimensional (3D) data and continue its evolution using the linearized (Teukolsky) evolution to a final distant radiation extraction radius. We implement this using the Hahndol code for the 3D evolution, and use the “Lazarus” procedure to convert the numerical data into the linearized data. The final waveform is compatible with the ones obtained from the full 3D evolutions with some minor variations that require further study. In the process, we tested the “Lazarus” method with our numerical 3D implementation and gauges showing that even with the advanced gauges suitable for 3D rotating binary evolutions, we recover the same type of limited results obtained in the original work.

We compute the absorption cross-section of the Kerr black holes (BH) for the massless scalar field, and present a selection of numerical results, to complement the results of Ref.[C. F. B. Macedo, L. C. S. Leite, E. S. Oliveria, S. R. Dolan and L. C. B. Crispino, Phys. Rev. D 88 (2013) 064033.] We show that, in the high-frequency regime, the cross-section approaches the geodesic capture cross-section. We split the absorption cross-section into corotating and counterrotating contributions, and we show that the counterrotating contribution exceeds the corotating one.

The anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are a class of pulsars understood as neutron stars (NSs) with super strong surface magnetic fields, namely $B\gtrsim 10^{14}$G, and for that reason are known as magnetars. However, in the last years, some SGRs/AXPs with low surface magnetic fields $B\sim (10^{12}$–$10^{13})$G have been detected, challenging the magnetar description. Moreover, some fast and very magnetic white dwarfs (WDs) have also been observed, and at least one showed X-ray energy emission as an ordinary pulsar. Following this fact, an alternative model based on WDs pulsars has been proposed to explain this special class of pulsars. In this model, AXPs and SGRs as dense and magnetized WDs can have surface magnetic field $B\sim 10^7$–$10^{10}$ G and rotate very fast with frequencies $\mathrm{\Omega }\sim 1$rad/s, consistent with the observed rotation periods $P\sim (2$–12)s.