Numerical relativity, compact objects, and fundamental fields

Las recientes detecciones de ondas gravitacionales están abriendo una nueva ventana al Universo. La naturaleza de los agujeros negros y las estrellas de neutrones ahora puede ser desvelada, pero la radiación gravitacional también puede conducir a descubrimientos emocionantes de nuevos y exóticos objetos compactos, ajenos a las ondas electromagnéticas. En esta tesis, he investigado tres temas principales que involucran campos bosónicos escalares y vectoriales fundamentales acoplados a la gravedad dentro de la Relatividad General y en simetría esférica: (i) configuraciones cuasiestacionarias de campos escalares reales alrededor de agujeros negros de Schwarzschild como modelos de materia oscura como campo escalar, (ii) la inestabilidad superradiante y la formación de agujeros negros cargados con pelo, y (iii) estrellas bosónicas. Estos sistemas podrían tener una relevancia astrofísica importante, si existen campos bosónicos ultraligeros en la Naturaleza. En 2012, se descubrió la primera partícula de bosón no gauge, el bosón de Higgs, en el Gran Colisionador de Hadrones (LHC). El trabajo principal en esta tesis consiste en evoluciones de relatividad numéricas de campos bosónicos en el régimen de campo intenso de la gravedad. Recientemente, se han estudiado configuraciones de campo escalar alrededor de agujeros negros en el régimen linealizado, tomando el espacio-tiempo fijo. Se descubrió que se pueden formar estados cuasiligados de campo escalar de muy larga vida alrededor del agujero negro. Para investigar las evoluciones temporales en escenarios altamente dinámicos, se requiere realizar simulaciones numéricas de los sistemas acoplados no lineales Einstein-Klein-Gordon o Einstein-Proca. Con este objetivo he extendido códigos de relatividad numérica en 1D y 3D que usan coordenadas esféricas y que resuelven las ecuaciones de hidrodinámica relativista acopladas a las ecuaciones de Einstein, implementando las ecuaciones fundamentales que describen los campos bosónicos. En primer lugar, he llevado a cabo evoluciones numéricas de los campos escalares alrededor de los agujeros negros, teniendo en cuenta la reacción del campo escalar en la dinámica del campo gravitacional. Por lo tanto, el espacio-tiempo podía cambiar dinámicamente: aumento de la masa del agujero negro debido a la absorción de parte del campo escalar autogravitante o debido a la acreción adiabática de alguna otra forma de materia, o formación de agujeros negros del colapso gravitacional de una estrella politrópica descrita con un ecuación de estado (EOS) similar a la de una estrella supermasiva. En todos los casos, mis simulaciones no lineales han revelado una frecuencia de oscilación bien determinada que apunta a la presencia de los estados cuasiligados descritos en la literatura en el régimen linealizado. Otro fenómeno interesante que involucra campos bosónicos y agujeros negros es la inestabilidad súperradiante, que puede ser desencadenada por la dispersión del campo por el agujero negro. Un campo bosónico puede extraer energía del agujero negro y, si se introduce un mecanismo de captura, puede crecer exponencialmente. Sobre la base de trabajos numéricos previos en el régimen linealizado, he estudiado la inestabilidad de un campo escalar cargado alrededor de un agujero negro de Reissner-Nordström (cargado) en una cavidad, mostrando que el punto final es una solución en la que el agujero negro y el campo bosónico están en equilibrio, es decir, un agujero negro con pelo. Además, descubrí que el colapso de los solitones de campo escalar cargados en una cavidad también puede formar estas soluciones. Finalmente, he considerado los modelos de equilibrio de las estrellas bosónicas autogravitantes, condensados Bose-Einstein no singulares y sin horizontes, de campos masivos, en concreto, estrellas de bosones con y sin autointeracción y estrellas de Proca. Estos objetos compactos son considerados imitadores de agujeros negros ya que solo interactúan con la gravedad. Observamos que las estrellas Proca se parecen en muchos aspectos a sus primos escalares, incluso con un término de interacción propia. Una separación entre configuraciones estables e inestables que ocurre en la solución con la máxima masa ADM ha sido obtenido por estudios previos de la teoría de perturbaciones lineal. Mis simulaciones no solo confirman este resultado sino que además muestran que los diferentes resultados de los modelos inestables, es decir, la migración a la rama estable, la dispersión total del campo escalar o el colapso a un agujero negro de Schwarzschild, están presentes en ambos campos. En este último caso, un remanente del campo permanece fuera del horizonte, formando un estado cuasiligado. Se puede establecer un paralelismo adicional con las estrellas de neutrones, para las cuales también se ha encontrado numéricamente el colapso y la migración, pero no la dispersión. Con respecto al marco de la relatividad numérica, en esta tesis he modificado la formulación CCZ4, que es una descomposición conforme y sin traza de las ecuaciones de Einstein, para hacer que sus ecuaciones de evolución sean adecuadas para coordenadas curvilíneas. Descubrí que las violaciones de restricción Hamiltoniana podían reducirse de uno a tres órdenes de magnitud para los espacios espaciales al vacío con respecto a la formulación BSSN estándar. Para los agujeros negros de Schwarzschild, sin embargo, los resultados no fueron significativamente mejores. Esta tesis también contiene algunos trabajos de investigación sobre dos temas adicionales, a saber, estrellas (fermiónicas) de rotación lenta y mi contribución a la Colaboración de Virgo. Esta última ha consistido en producir patrones de onda gravitacionales a partir de simulaciones numéricas de estrellas que colapsan descritas por una ecuación de estado no convexa (EOS). Para el primero, he estudiado numéricamente el modelo de Hartle modificado recientemente de estrellas que giran lentamente dentro de la teoría de perturbaciones, que correctamente toma en cuenta las discontinuidades de densidad en la superficie de la estrella para la corrección de la masa, dM, para diferentes EOS . He ayudado a desarrollar un código numérico que proporciona modelos iniciales de estrellas en rotación para una cantidad de EOS, más allá de estrellas polítrópicas y la idealización con densidad constante. Pudimos determinar e incluir la universalidad de dM en las llamadas relaciones I-Love-Q.The recent detections of gravitational waves are opening a new window to the Universe. The nature of black holes and neutron stars may now be unveiled, but gravitational radiation may also lead to exciting discoveries of new exotic compact objects, oblivious to electromagnetic waves. In this thesis, I have investigated three main topics involving fundamental scalar and vector bosonic fields coupled to gravity within General Relativity and under the assumption of spherical symmetry: (i) quasistationary configurations of real scalar fields around Schwarzschild black holes as scalar field dark matter models, (ii) the superradiant instability and the formation of charged hairy black holes, and (iii) bosonic stars. These systems could have important astrophysical relevance, if ultralight bosonic fields exist in Nature. In 2012, the first non-gauge boson particle, the Higgs boson, was discovered in the Large Hadron Collider (LHC). The main work in this thesis deals with numerical-relativity evolutions of bosonic fields in the strong-field regime of gravity. Recently, scalar field configurations around black holes have been studied in the linearized regime, taking the spacetime as a background. It was found that very long-lived scalar field quasibound states may form around the black hole. To investigate time evolutions in highly dynamical scenarios, it is required to perform numerical simulations of the fully non-linear Einstein-Klein-Gordon or Einstein-Proca coupled systems. To this aim I have extended numerical-relativity codes in 1D and 3D using spherical coordinates that solve the relativistic hydrodynamics equations coupled to the Einstein equations, implementing the fundamental equations describing the bosonic fields. Firstly, I have carried out numerical evolutions of scalar fields around black holes, taking into account the back-reaction of the field onto the gravitational field dynamics. Therefore, the spacetime could dynamically change: mass growth due to the absorption of part of a self-gravitating scalar field or from the adiabatic accretion of some other form of matter, or black hole formation from the gravitational collapse of a polytropic star described with an equation of state (EOS) similar to that of a supermassive star. In all cases, my non-linear simulations have revealed a well-determined oscillating frequency that pointed out to the presence of the quasibound states described in the linearized literature. Another interesting phenomena involving bosonic fields and black holes is the superradiant instability, that can be triggered by the scattering of the field off the black hole. A bosonic field may then extract energy from the black hole and, if a trapping mechanism is introduced, it can grow exponentially. Building on previous numerical works in the linearized regime, I have studied the instability for a charged scalar field around a Reissner-Nordström (charged) black hole in a cavity, showing that the endpoint is a solution in which the black hole and the bosonic field are in equilibrium, i.e. a hairy black hole. Moreover, I found that the collapse of charged scalar field solitons in a cavity may also form these solutions. Finally, I have considered equilibrium models of bosonic stars as self-gravitating, everywhere non-singular, horizonless Bose-Einstein condensates of massive fields, namely boson stars with and without self interaction and Proca stars. These compact objects are regarded as black hole mimickers as they only interact through gravity. By performing accurate numerical simulations, I have observed that Proca stars resemble in many ways its scalar cousins, even with a self-interaction term. A separation between stable and unstable configurations occuring at the solution with maximal ADM mass has been indicated by previous results from linear perturbation theory. My simulations not only confirm this result but furthermore they show that the different outcomes of unstable models, namely migration to the stable branch, total dispersion of the scalar field, or collapse to a Schwarzschild black hole, are present for both fields. In the latter case, a field remnant lingers outside the horizon, forming a quasibound state. A further parallelism can be established with neutron stars, for which the collapse and the migration, but not the dispersion, has also been found numerically. Regarding the numerical-relativity framework, in this thesis I have modified the CCZ4 formulation, which is a conformal and traceless decomposition of the Einstein equations, to make its evolution equations suitable for curvilinear coordinates. I have found that the Hamiltonian constraint violations could be reduced by one to three orders of magnitude for non-vacuum spacetimes with respect to the standard BSSN formulation. For Schwarzschild black holes, however, the results were not significantly better. This thesis also contains some miscellaneous research work on two topics, namely slowly-rotating (fermionic) stars and my contribution to the Virgo Collaboration. The latter has consisted in producing gravitational waveforms from numerical simulations of collapsing stars described by a non-convex equation of state (EOS). For the former I have studied numerically the recently amended Hartle's model of slowly-rotating stars within perturbation theory, which correctly takes into account density discontinuities in the surface of the star for the correction of the mass, dM, for different EOS. I have helped to develop a numerical code providing initial models of rotating stars for a number of EOS, beyond polytropes and the constant-density idealization. We were able to determine and include the universality of dM in the so-called I-Love-Q relations

Precessing binary black holes as engines of electromagnetic helicity

We show that binary black hole mergers with precessing evolution can potentially excite photons from the quantum vacuum in such a way that total helicity is not preserved in the process. Helicity violation is allowed by quantum fluctuations that spoil the electric-magnetic duality symmetry of the classical Maxwell theory without charges. We show here that precessing binary black hole systems in astrophysics generate a flux of circularly polarized gravitational waves which, in turn, provides the required helical background that triggers this quantum effect. Solving the fully non-linear Einstein's equations with numerical relativity we explore the parameter space of binary systems and extract the detailed dependence of the quantum effect with the spins of the two black holes. We also introduce a set of diagrammatic techniques that allows us to predict when a binary black hole merger can or cannot emit circularly polarized gravitational radiation, based on mirror-symmetry considerations. This framework allows to understand and to interpret correctly the numerical results, and to predict the outcomes in potentially interesting astrophysical systems.Comment: 10 page

Self-interactions can stabilize excited boson stars

We study the time evolution of spherical, excited (i.e. nodeful) boson star (BS) models. We consider a model including quartic self-interactions, controlled by a coupling Λ. Performing non-linear simulations of the Einstein- (complex)–Klein–Gordon system, using as initial data equilibrium BSs solutions of that system, we assess the impact of Λ in the stability properties of the BSs. In the absence of self-interactions (Λ = 0), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a nonexcited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about t ∼ 104). The stabilization of the excited states for large enough selfinteractions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning BSs.publishe

Electromagnetic emission from axionic boson star collisions

We explore the dynamics of boson stars in the presence of axionic couplings through nonlinear evolutions of Einstein's field equations. We show that, for large axionic couplings, isolated boson stars become unstable, and decay via a large burst of electromagnetic radiation, becoming less massive and more dilute. Our full nonlinear results are in good agreement with flat-space estimates for the critical couplings. We then consider head-on collisions of sub-critical boson stars and study the electromagnetic and gravitational signal. Boson stars cluster around the critical point via interactions, and we argue that mergers will generically be also sources of electromagnetic radiation, in addition to gravitational waves, which can be used to place constraints on the axionic coupling if such multimessenger signals are detected.Comment: 12 pages, 10 figure

Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry

We adopt a reference-metric approach to generalize a covariant and conformal version of the Z4 system of the Einstein equations. We refer to the resulting system as ``fully covariant and conformal", or fCCZ4 for short, since it is well suited for curvilinear as well as Cartesian coordinates. We implement this fCCZ4 formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. Our method does not require regularization of the equations to handle coordinate singularities, nor does it depend on constraint-preserving outer boundary conditions, nor does it need any modifications of the equations for evolutions of black holes. We perform several tests and compare the performance of the fCCZ4 system, for different choices of certain free parameters, with that of BSSN. Confirming earlier results we find that, for an optimal choice of these parameters, and for neutron-star spacetimes, the violations of the Hamiltonian constraint can be between 1 and 3 orders of magnitude smaller in the fCCZ4 system than in the BSSN formulation. For black-hole spacetimes, on the other hand, any advantages of fCCZ4 over BSSN are less evident.Comment: 13 pages, 10 figure