Analysis of some classical and quantum aspects of black holes

Abstract

For ninety years we have known that our universe is in expansion. Cosmological data favor an unknown form of intrinsic and fundamental uniform energy contributing approximately 68% of the total energy budget in the current epoch. The simplest proposal in accordance with observations is the standard cosmological model consisting of a small but positive cosmological constant producing a gravitational repulsive effect driving the accelerated expansion. In standard cosmology general relativity is assumed as the theory for gravity, which in turn predicts that a sufficiently compact mass can deform spacetime and form a black hole. At a mathematical level, these objects are considered vacuum solutions described by very few parameters. For instance, a stationary black hole solution is completely described by its mass, angular momentum, and electric charge; and two black holes that share the same values for these parameters, are indistinguishable from one another.

On the basis of the usual metrics describing black holes, it is generally believed that all contained matter is localized in the center or, if rotating, on an infinitely thin ring. Recent approaches challenge this unintuitive assumption and consider matter just spread throughout the interior. Clearly, this begs for a quantum description in curved space. In past years, a novel approach established a new bridge between quantum information and the physics of black holes when an intriguing proposal was made: black holes could possibly be understood as Bose—Einstein condensates of soft interacting but densely packed gravitons. The aim of this thesis is to discuss how to construct a graviton condensate structure on top of a classical gravitational field describing black holes. A necessary parameter to be introduced for this analogy is a chemical potential which we discuss how to incorporate within general relativity. Next we search for solutions and, employing some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. These results can be extended easily to a Reissner—Nordström black hole. In fact, we find that the phenomenon seems to be rather generic and is associated with the presence of a horizon, acting as a confining potential. In order to see whether a Bose— Einstein condensate is preferred, we use the Brown—York quasilocal energy, finding that a condensate is energetically favourable in all cases in the classically forbidden region. The Brown—York quasilocal energy also allows us to derive a quasilocal potential, whose consequences allow us to suggest a possible mechanism to generate a graviton condensate in black holes. On the contrary, this is not the case for any kind of horizons; for instance, this mechanism appears not to be feasible in order to generate a quantum condensate behind the cosmological de Sitter horizon.

Furthermore, when a pair of black holes merge, an immense amount of energy should be given off as gravitational waves. Their wave forms have been recently confirmed to be perfectly described by general relativity. We discuss why for low frequency gravitational waves aimed to be detected by astrophysical PTA observations the fact that propagation should take place over an expanding (approximately globally de Sitter) spacetime should be taken into account. In this manner, harmonic waves produced in such mergers would

become anharmonic when measured by cosmological observers. This effect is tiny but appears to be observable for gravitational waves to which PTA are sensitive. Therefore we have characterized modifications to the expected signal, and how it is related to the source and pulsar characteristics that are employed by the IPTA collaboration. If the cosmological constant were an intrinsic property, this experiment would be capable of confirming the relevance of lambda at redshift z < 1.

El objetivo de la presente tesis es profundizar en diversos aspectos de la física de los agujeros negros. Tanto en lo que respecta a sus características constitutivas fundamentales, su "estructura" interna, como a la posibilidad de observar o detectar mediante observaciones astrofísicas ciertos efectos producto de su dinámica.

Por un lado, hemos seguido las ideas de Dvali, Gómez et al. quienes han sugerido la posibilidad de que un agujero negro sea un condensado de Bose—Einstein de gravitones débilmente interactuantes. En nuestro caso hemos estudiado la existencia de este tipo de soluciones sobre diferentes métricas de agujero negro (Schwarzschild y Reissner— Nordström) que actuarían como potencial confinante para dichos condensados. Un parámetro necesario para ello, es el equivalente a un potencial químico que debe ser incorporado a la relatividad general. Cabe destacar que la solución encontrada puede ser interpretada como la función de campo medio del condensado. Además resulta fuertemente ligada a la estructura clásica de la métrica que la sustenta.

Por otro lado, es bien sabido que la aceleración de cuerpos muy masivos producen perturbaciones de tipo onda en el espaciotiempo. Son de nuestro interés las ondas gravitatorias de baja frecuencia, provenientes de la colisión de agujeros negros supermasivos y que deberían poder ser detectadas mediante sistemas de púlsares (Pulsar Timing Arrays). De acuerdo a una línea de investigación desarrollada por Espriu et al. la presencian de una constante cosmológica podría tener un efecto en la propagación y por lo tanto en la detección por parte de la colaboración IPTA de estas ondas. En la presente tesis hemos generalizado el método para incluir diferentes tipos de materia (relativista y no relativista) además de la constante cosmológica. Del análisis se deriva que el efecto depende sensiblemente del valor de la constante de Hubble (que engloba todos los tipos de materia presentes). Continuando dicha línea, hemos caracterizado detalladamente el efecto en su dependencia con los parámetros cosmológicas y las distancias involucradas, y cómo podría ser hallado. Esperamos que nuestros resultados puedan contribuir a una definitiva detección por IPTA.