arXiv subjects

C. A. R. Herdeiro

Publications and source records attributed to C. A. R. Herdeiro.

12 recordsLinked to original sources

arXiv2023

The non-spherical ground state of Proca stars

Spherical Proca Stars (PSs) are regarded as the ground state amongst the family of PSs. In accordance, spherical PSs are thought to have a fundamental branch of stable solutions. In this Letter, we provide energetic, morphological and dynamical evidence that spherical PSs are actually excited states. The ground state is shown to be a family of static, non-spherical, in fact prolate, PSs. The spherical stars in the fundamental branch, albeit stable against spherical perturbations, turn out to succumb to non-spherical dynamics, undergoing an isometry breaking into prolate PSs. We also provide evidence for the dynamical formation of prolate PSs, starting from spherical dilute initial data, via gravitational cooling. Consequently, PSs provide a remarkable example of (possibly compact) relativistic stars, in General Relativity minimally coupled to a simple, physical, field theory model, where staticity plus stability implies non-sphericity.

gr-qc↗

arXiv2021

Chains of Boson Stars

We study axially symmetric multi-soliton solutions of a complex scalar field theory with a sextic potential, minimally coupled to Einstein's gravity. These solutions carry no angular momentum and can be classified by the number of nodes of the scalar field, $k_z$, along the symmetry axis; they are interpreted as chains with $k_z+1$ boson stars, bound by gravity, but kept apart by repulsive scalar interactions. Chains with an odd number of constituents show a spiraling behavior for their ADM mass (and Noether charge) in terms of their angular frequency, similarly to a single fundamental boson star, as long as the gravitational coupling is small; for larger coupling, however, the inner part of the spiral is replaced by a merging with the fundamental branch of radially excited spherical boson stars. Chains with an even number of constituents exhibit a truncated spiral pattern, with only two or three branches, ending at a limiting solution with finite values of ADM mass and Noether charge.

gr-qc↗

arXiv2020

Multipolar boson stars: macroscopic Bose-Einstein condensates akin to hydrogen orbitals

Boson stars are often described as macroscopic Bose-Einstein condensates. By accommodating large numbers of bosons in the same quantum state, they materialize macroscopically the intangible probability density cloud of a single particle in the quantum world. We take this interpretation of boson stars one step further. We show, by explicitly constructing the fully non-linear solutions, that static (in terms of their spacetime metric, $g_{μν}$) boson stars, composed of a single complex scalar field, $Φ$, can have a non-trivial multipolar structure, yielding the same morphologies for their energy density as those that elementary hydrogen atomic orbitals have for their probability density. This provides a close analogy between the elementary solutions of the non-linear Einstein--Klein-Gordon theory, denoted $Φ_{(N,\ell,m)}$, which could be realized in the macrocosmos, and those of the linear Schrödinger equation in a Coulomb potential, denoted $Ψ_{(N,\ell,m)}$, that describe the microcosmos. In both cases, the solutions are classified by a triplet of quantum numbers $(N,\ell,m)$. In the gravitational theory, multipolar boson stars can be interpreted as individual bosonic lumps in equilibrium; remarkably, the (generic) solutions with $m\neq 0$ describe gravitating solitons $[g_{μν},Φ_{(N,\ell,m)}]$ without any continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are also constructed.

gr-qc↗

arXiv2011

Mass inflation in a D dimensional Reissner-Nordstrom black hole: a hierarchy of particle accelerators ?

We study the geometry inside the event horizon of perturbed D dimensional Reissner-Nordstrom-(A)dS type black holes showing that, similarly to the four dimensional case, mass inflation also occurs for D>4. First, using the homogeneous approximation, we show that an increase of the number of spatial dimensions contributes to a steeper variation of the metric coefficients with the areal radius and that the phenomenon is insensitive to the cosmological constant in leading order. Then, using the code reported in arXiv:0904.2669 [gr-qc] adapted to D dimensions, we perform fully non-linear numerical simulations. We perturb the black hole with a compact pulse adapting the pulse amplitude such that the relative variation of the black hole mass is the same in all dimensions, and determine how the black hole interior evolves under the perturbation. We qualitatively confirm that the phenomenon is similar to four dimensions as well as the behaviour observed in the homogeneous approximation. We speculate about the formation of black holes inside black holes triggered by mass inflation, and about possible consequences of this scenario.

gr-qc↗

arXiv2009

Global embedding of the Kerr black hole event horizon into hyperbolic 3-space

An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H^3, for arbitrary values of the angular momentum. For this example, considering a quotient of H^3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding which cannot be made global.

gr-qc↗

arXiv2009

Mass Inflation in Brans-Dicke gravity

A detailed non-linear analysis of the internal structure of spherical, charged black holes that are accreting scalar matter is performed in the framework of the Brans-Dicke theory of gravity. We choose the lowest value of the Brans-Dicke parameter that is compatible with observational constraints. First, the homogeneous approximation is used. It indicates that mass inflation occurs and that the variations of the Brans-Dicke scalar inside the black hole, which could in principle be large in the absence of mass inflation, become small when mass inflation does occur. Then, a full non-linear numerical study of the black hole interior perturbed by a self-gravitating massless uncharged scalar-field is performed. We use an algorithm with adaptive mesh refinement capabilities. In this way, the changes in the internal structure of the black hole caused by mass inflation are determined, as well as the induced variations of the Brans-Dicke scalar, confirming, qualitatively, the indications given by the homogeneous approximation.

gr-qc↗

arXiv2008

Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry

We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalisation of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo-surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.

gr-qc↗

arXiv2003

The Kerr-Newman-Godel Black Hole

By applying a set of Hassan-Sen transformations and string dualities to the Kerr-Godel solution of minimal D=5 supergravity we derive a four parameter family of five dimensional solutions in type II string theory. They describe rotating, charged black holes in a rotating background. For zero background rotation, the solution is D=5 Kerr-Newman; for zero charge it is Kerr-Godel. In a particular extremal limit the solution describes an asymptotically Godel BMPV black hole.

hep-th↗

arXiv2001

The Melvin Universe in Born-Infeld Theory and other Theories of Non-Linear Electrodynamics

We derive a Melvin Universe type solution describing a magnetic field permeating the whole Universe in gravity minimally coupled to any non-linear electromagnetic theory, including Born-Infeld Theory. For a large set of non-linear electrodynamics theories, our solution is complete and non-singular, as long as the magnetic field is sub-critical. We examine some properties of the solution; in particular there is a shift of the symmetry axis and a non-standard period along the orbits of the U(1) symmetry to avoid a conical singularity. We show these are consistent with the usual Dirac quantization condition for the magnetic flux. We find exact solutions describing propagation of waves in the `generalized Melvin Universe' along the principal null directions of the electromagnetic field, where the Boillat and Einstein light-cone touch. By electric-magnetic duality we show that similar Melvin electric and dyonic universes can be obtained.

hep-th↗

arXiv2000

Born-Infeld Theory and Stringy Causality

Fluctuations around a non-trivial solution of Born-Infeld theory have a limiting speed given not by the Einstein metric but the Boillat metric. The Boillat metric is S-duality invariant and conformal to the open string metric. It also governs the propagation of scalars and spinors in Born-Infeld theory. We discuss the potential clash between causality determined by the closed string and open string light cones and find that the latter never lie outside the former. Both cones touch along the principal null directions of the background Born-Infeld field. We consider black hole solutions in situations in which the distinction between bulk and brane is not sharp such as space filling branes and find that the location of the event horizon and the thermodynamic properties do not depend on whether one uses the closed or open string metric. Analogous statements hold in the more general context of non-linear electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld action to second order might be obtained from higher-curvature gravity in Kaluza-Klein theory. Finally we point out some intriguing analogies with Einstein-Schrödinger theory.

hep-th↗

arXiv2000

Special Properties of Five Dimensional BPS Rotating Black Holes

Supersymmetric, rotating, asymptotically flat black holes with a regular horizon are rare configurations in String Theory. One example is known in five spacetime dimensions, within the toroidal compactification of type IIB string theory. Such special solution is allowed by the existence of a Chern-Simons coupling in the Supergravity theory and by the possibility of imposing a self duality condition on the `rotation 2-form'. We explore three peculiar features of such black holes: 1) Oxidising to D=10 the five dimensional configuration may be interpreted as a system of $D1-D5$ branes with a Brinkmann wave propagating along their worldvolume. Unlike its five dimensional Kaluza-Klein compactification, the universal covering space of this manifold has no causality violations. In other words, causal anomalies can be solved in higher dimensions. From the dual SCFT viewpoint, the causality bound for the compactified spacetime arises as the unitarity bound; 2) The vanishing of the scattering cross section for uncharged scalars and sufficiently high angular momentum of the background is shown still to hold at the level of charged interactions. The same is verified when a non-minimal coupling to the geometry is used. Therefore, the `repulson' behaviour previously found is universal for non accelerated observers; 3) The solutions are shown to have a non-standard gyromagnetic ratio of $g=3$. In contrast, the superpartners of a static, BPS, five dimensional black hole have $g=1$. At the semi-classical level, we find that a Dirac fermion propagating in the rotating hole background has $g=2\pm1$, depending on the spinor direction of the fermion being parallel to Killing or `anti-Killing' spinors.

hep-th↗

arXiv1999

Supersymmetric Rotating Black Holes and Causality Violation

The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the Hamilton-Jacobi equation. This allows us to obtain the Stäckel-Killing tensor. We use these facts to give the maximal analytic extension of the spacetime and discuss some aspects of its causal structure. In particular, we exhibit a `repulson'-like behaviour occuring when there are naked closed timelike curves. In this case we find that the spacetime is geodesically complete (with respect to causal geodesics) and free of singularities. When a partial Cauchy surface exists, we show, by solving the Klein-Gordon equation, that the absorption cross-section for massless waves at small frequencies is given by the area of the hole. At high frequencies a dependence on the angular quantum numbers of the wave develops. We comment on some aspects of `inertial time travel' and argue that such time machines cannot be constructed by spinning up a black hole with no naked closed timelike curves.

hep-th↗