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José Natário

Publications and source records attributed to José Natário.

At least 37 records · Page 2Linked to original sources
arXiv2024

Reference frames in General Relativity and the galactic rotation curves

The physical interpretation of the exact solutions of the Einstein field equations is, in general, a challenging task, part of the difficulties lying in the significance of the coordinate system. We discuss the extension of the International Astronomical Union (IAU) reference system to the exact theory. It is seen that such an extension, retaining some of its crucial properties, can be achieved in a special class of spacetimes, admitting nonshearing congruences of observers which, at infinity, have zero vorticity and acceleration. As applications, we consider the Friedmann-Lemaître-Robertson-Walker (FLRW), Kerr and Newman-Unti-Tamburino (NUT) spacetimes, the van Stockum rotating dust cylinder, spinning cosmic strings and, finally, we debunk the so-called Balasin-Grumiller (BG) model, and the claims that the galaxies' rotation curves can be explained through gravitomagnetic effects without the need for dark matter. The BG spacetime is shown to be completely inappropriate as a galactic model: its dust is actually static with respect to the asymptotic inertial frame, its gravitomagnetic effects arise from unphysical singularities along the axis (a pair of NUT rods, combined with a spinning cosmic string), and the rotation curves obtained are merely down to an invalid choice of reference frame -- the congruence of zero angular momentum observers, which are being dragged by the singularities.

gr-qc↗
arXiv2023

Message in a bottle: energy extraction from bouncing geometries

Quantum gravity phenomenology suggests the interesting possibility that black holes are not eternal. Collapse could be halted by some unknown mechanism, or Hawking radiation might leave behind a regular spacetime. Here we investigate a simple bouncing geometry, with (outer and inner) apparent horizons but no event horizon. We show that the inner horizon blueshifts radiation, which can lead to a gigantic amplification of energy observable from far away regions. Thus, if such phenomena exists in our universe, they can power high-energy bursts at late stages in their lives, when the horizons disappear and spacetime bounces back to a flat geometry.

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arXiv2022

Curvature and dynamical spacetimes: can we peer into the quantum regime?

Stationary compact astrophysical objects such as black holes and neutron stars behave as classical systems from the gravitational point of view. Their (observable) curvature is everywhere "small". Here we investigate whether mergers of such objects, or other strongly dynamical spacetimes such as collapsing configurations, may probe the strong-curvature regime of General Relativity. Our results indicate that dynamical black hole spacetimes always result in a modest increase $\sim 3$ in the Kretschmann scalar, relative to the stationary state. Our results show that the Kretschmann scalar can dynamically increase by orders of magnitude, during the gravitational collapse of scalar fields, and that the (normalized) peak curvature does not correspond to that of the critical solution. Nevertheless, without fine tuning of initial data, this increase lies far below that needed to render quantum-gravity corrections important.

gr-qc↗
arXiv2022

Compactness bounds in General Relativity

A foundational theorem due to Buchdahl states that, within General Relativity (GR), the maximum compactness $\mathcal{C}\equiv GM/(Rc^2)$ of a static, spherically symmetric, perfect fluid object of mass $M$ and radius $R$ is $\mathcal{C}=4/9$. As a corollary, there exists a compactness gap between perfect fluid stars and black holes (where $\mathcal{C}=1/2$). Here we generalize Buchdahl's result by introducing the most general equation of state for elastic matter with constant longitudinal wave speeds and apply it to compute the maximum compactness of regular, self-gravitating objects in GR. We show that: (i) the maximum compactness grows monotonically with the longitudinal wave speed; (ii) elastic matter can exceed Buchdahl's bound and reach the black hole compactness $\mathcal{C}=1/2$ continuously; (iii) however, imposing subluminal wave propagation lowers the maximum compactness bound to $\mathcal{C}\approx0.462$, which we conjecture to be the maximum compactness of \emph{any} static elastic object satisfying causality; (iv) imposing also radial stability further decreases the maximum compactness to $\mathcal{C}\approx 0.389$. Therefore, although anisotropies are often invoked as a mechanism for supporting horizonless ultracompact objects, we argue that the black hole compactness cannot be reached with physically reasonable matter within GR and that true black hole mimickers require either exotic matter or beyond-GR effects.

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arXiv2022

Compact elastic objects in general relativity

We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to $\approx 22\%$, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^2R)\approx 0.35$ while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically realizable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to build consistent models of exotic ultracompact objects and black-hole mimickers, and can also be relevant for a more accurate modelling of the interior of neutron stars.

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arXiv2021

Spinning cylinders in general relativity: a canonical form for the Lewis metrics of the Weyl class

In the main article [CQG 38 (2021) 055003], a new "canonical" form for the Lewis metrics of the Weyl class has been obtained, depending only on three parameters -- Komar mass and angular momentum per unit length, plus the angle deficit -- corresponding to a coordinate system fixed to the "distant stars" and an everywhere timelike Killing vector field. Such form evinces the local but non-global static character of the spacetime, and striking parallelisms with the electromagnetic analogue. We discuss here its generality, main physical features and important limits (the Levi-Civita static cylinder, and spinning cosmic strings). We contrast it on geometric and physical grounds with the Kerr spacetime -- as an example of a metric which is locally non-static.

gr-qc↗
arXiv2021

Frame-dragging: meaning, myths, and misconceptions

Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two analogies commonly employed, the analogy with magnetism holds strong where it applies, whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the first level) is, in general, misleading. Common misconceptions (such as viscous-type "body-dragging") are debunked. Applications considered include rotating cylinders (Lewis-Weyl metrics), Kerr, Kerr-Newman and Kerr-dS spacetimes, black holes surrounded by disks/rings, and binary systems.

gr-qc↗
arXiv2021

Reply to the comment on "Frame-dragging: meaning, myths, and misconceptions" by A. Deriglazov

It has been claimed in [arXiv:2110.09522] that the expression for the Sagnac coordinate time delay given in [arXiv:2109.14641] "differs from the standard interpretation described in the book by Landau-Lifshitz (LL)". We note that: 1) the Sagnac effect is not even discussed in LL; 2) the expression in [arXiv:2109.14641] is standard, given in countless papers and even textbooks; 3) the expression by LL quoted by the author consists of the (infinitesimal) two-way trip travel time for a light signal, which the author confuses with the Sagnac time delay (when they are actually very different things); 4) such confusion would negate the existence, both in special and general relativity, of the well-known and experimentally tested Sagnac effect; 5) the claims that it sheds doubt in any of the assertions made in [arXiv:2109.14641] are completely unfounded.

gr-qc↗
arXiv2021

Extrinsic black hole uniqueness in pure Lovelock gravity

We define a notion of extrinsic black hole in pure Lovelock gravity of degree $k$ which captures the essential features of the so-called Lovelock-Schwarzschild solutions, viewed as rotationally invariant hypersurfaces with null $2k$-mean curvature in Euclidean space $\mathbb R^{n+1}$, $2\leq 2k\leq n-1$. We then combine a regularity argument with a rigidity result by Araújo-Leite to prove, under a natural ellipticity condition, a global uniqueness theorem for this class of black holes. As a consequence we obtain, in the context of the corresponding Penrose inequality for graphs established by Ge-Wang-Wu, a local rigidity result for the Lovelock-Schwarzschild solutions.

math.DG↗
arXiv2021

Gravitomagnetism and the significance of the curvature scalar invariants

The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a fundamental difference between the gravitomagnetic fields arising from the translational and rotational motions of the sources (which have been subject of observational and experimental tests, including the dedicated Gravity Probe-B and LARES space missions). In this work we clarify both the algebraic and physical meaning of the curvature invariants and their electromagnetic counterparts. They are seen to yield conditions for the existence of observers measuring vanishing electric/magnetic fields and gravitoelectric/gravitomagnetic tidal tensors, respectively. We determine these observers (in the gravitational sector and in the presence of sources, for the more relevant gravitomagnetic case) obtaining their velocities explicitly in terms of the fields/tidal tensors as measured by an arbitrary observer. The structure of the invariants of the astrophysical setups of interest is studied in detail, and its relationship with the gravitomagnetic effects is dissected. Finally, a new classification for intrinsic/extrinsic gravitomagnetism is proposed.

gr-qc↗
arXiv2021

Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity

In electromagnetism, the concept of Poynting vector as measured by an observer is well known. A mathematical analogue in general relativity is the super-Poynting vector of the Weyl tensor. Observers for which the (super-)Poynting vector vanishes are called principal. When, at a given point, the electromagnetic field is non-null, or the gravitational field is of Weyl-Petrov type I or D, principal observers instantaneously passing through that point always exist. We survey characterizations of such observers and study their relation to arbitrary observers. In the non-null electromagnetic case it is known that, given any observer, there is a principal observer which moves relative to the first in the direction of his Poynting vector. Replacing Poynting by super-Poynting yields a possible gravitational analogue; we show that this analogy indeed holds for any observer when the Petrov type is D, but only for a one-dimensional variety of observers when the Petrov type is I. We provide algorithms to obtain the principal observers directly from the electric and magnetic fields (in the electromagnetic case) or electric and magnetic parts of the Weyl tensor (in the gravitational case) relative to an arbitrary observer. It is found that in Petrov type D doubly aligned non-null Einstein-Maxwell fields (which include all classical charged black hole solutions) the Poynting and super-Poynting vectors are aligned, at each point and for each observer, and the principal observers coincide. Our results are illustrated in simple examples.

gr-qc↗
arXiv2021

Addendum to "Strong cosmic censorship: The nonlinear story"

We clarify a number of issues that arise when extending the analysis of Strong Cosmic Censorship (SCC) to perturbations of highly charged Reissner-Nordström de Sitter (RNdS) spacetimes. The linear stability of the Cauchy horizon can be determined from the spectral gap of quasinormal modes, thus giving a clear idea of the ranges of parameters that are likely to lead to SCC violations for infinitesimally small perturbations. However, the situation becomes much more subtle once nonlinear backreaction is taken into account. These subtleties have created a considerable amount of confusion in the literature regarding the conclusions one is able to derive about SCC from the available numerical simulations. Here we present new numerical results concerning charged self-gravitating scalar fields in spherical symmetry, correct some previous claims concerning the neutral case, and argue that the existing numerical codes are insufficient to draw conclusions about the potential failure of SCC for near extremal RNdS black hole spacetimes.

gr-qc↗
arXiv2021

Gravitomagnetism in the Lewis cylindrical metrics

The Lewis solutions describe the exterior gravitational field produced by infinitely long rotating cylinders, and are useful models for global gravitational effects. When the metric parameters are real (Weyl class), the exterior metrics of rotating and static cylinders are locally indistinguishable, but known to globally differ. The significance of this difference, both in terms of physical effects (gravitomagnetism) and of the mathematical invariants that detect the rotation, remain open problems in the literature. In this work we show that, by a rigid coordinate rotation, the Weyl class metric can be put into a "canonical" form where the Killing vector field $\partial_{t}$ is time-like everywhere, and which depends explicitly only on three parameters with a clear physical significance: the Komar mass and angular momentum per unit length, plus the angle deficit. This new form of the metric reveals that the two settings differ only at the level of the gravitomagnetic vector potential which, for a rotating cylinder, cannot be eliminated by any global coordinate transformation. It manifests itself in the Sagnac and gravitomagnetic clock effects. The situation is seen to mirror the electromagnetic field of a rotating charged cylinder, which likewise differs from the static case only in the vector potential, responsible for the Aharonov-Bohm effect, formally analogous to the Sagnac effect. The geometrical distinction between the two solutions is also discussed, and the notions of local and global staticity revisited. The matching in canonical form to the van Stockum interior cylinder is also addressed.

gr-qc↗
arXiv2020

Riemannian manifolds dual to static spacetimes

We establish a one-to-one correspondence between static spacetimes and Riemannian manifolds that maps causal geodesics to geodesics, as suggested by L. C. Epstein. We then explore constant curvature spacetimes - such as the de Sitter and the anti-de Sitter universes - and find that they map to constant curvature Riemannian manifolds, namely the Euclidean space, the sphere and the hyperbolic space. By imposing the conditions required to map to the sphere, we obtain the spherically symmetric metrics for which there is radial oscillatory motion with a period independent of the amplitude. We then consider the case of a perfect fluid and an Einstein cluster and determine the pressure and density profiles required to find this type of motion. Finally, we give examples of surfaces corresponding to certain types of motion for metrics that do not exhibit constant curvature, such as the Schwarzschild, Schwarzschild de Sitter and Schwarzschild anti-de Sitter solutions, and even for a simplified model of a wormhole.

gr-qc↗
arXiv2020

Decay of solutions of the wave equation in expanding cosmological spacetimes

We study the decay of solutions of the wave equation in some expanding cosmological spacetimes, namely flat Friedmann-Lemaître-Robertson-Walker (FLRW) models and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) solution. By introducing a partial energy and using an iteration scheme, we find that, for initial data with finite higher order energies, the decay rate of the time derivative is faster than previously existing estimates. For models undergoing accelerated expansion, our decay rate appears to be (almost) sharp.

gr-qc↗
arXiv2020

Rigid elastic solids in relativity

After briefly reviewing the theory of relativistic elasticity, we expand a general elastic Lagrangian to quadratic order and compute the main parameters for the linear elasticity of relativistic solids: the longitudinal and transverse speeds of sound, the Poisson ratio, and the bulk, shear and Young moduli. Using these, we discuss which Lagrangian is the best choice to model a relativistic rigid elastic solid.

gr-qc↗
arXiv2020

Mathematical relativity

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

gr-qc↗