Efecto Faraday-Cartan y propagación anómala de la polarización de ondas gravitacionales con torsión.
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad de Concepción
Abstract
En el año 2016, comenzó la medición sistemática de ondas gravitacionales con una precisión tal que su existencia se convirtió en un hecho irrefutable. En 2017, se registró por primera vez la radiación gravitacional proveniente de un sistema binario de estrellas de neutrones (GW170817), simultáneamente con su contraparte electromagnética (GRB170817A). Esta medición impone restricciones significativas en familias de teorías torsionales, refutando aquellas que predijeron una velocidad y relación de dispersión diferentes a las de la luz. En este sentido, la teoría Einstein-Cartan-Sciama-Kibble (ECSK) ha demostrado ser consistente con las observaciones actuales. Al estudiar la generalización de los operadores de onda de De Rahm y Beltrami sobre una geometría de Riemann-Cartan, encontramos que en el orden dominante de la expansión eikonal, la relación de dispersión coincide con los datos observacionales. Sin embargo, en el límite subdominante, predice una propagación anómala en la amplitud y polarización con respecto a la relatividad general. La influencia de la torsión en la amplitud ha sido calculada, descartando su medición en el futuro próximo. En esta tesis, calculamos la propagación anómala de la polarización sobre una geometría de fondo cosmológico. Observamos que solamente se propagaran los modos de Relatividad General (RG), pero su propagación presentará un comportamiento que llamamos efecto Faraday-Cartan, donde los modos de polarización oscilarán en un ángulo de rotación proporcional al parámetro de la geodésica, con un orden de magnitud de 1 grado cada 5 millones de años luz.
In 2016, the systematic measurement of gravitational waves began with such precision that their existence became an irrefutable fact. In 2017, gravitational radiation from a binary neutron star system (GW170817) was observed for the first time, simultaneously with its electromagnetic counterpart (GRB170817A). This measurement imposes significant constraints on families of torsional theories, refuting those that predicted a speed and dispersion relation different from that of light. In this regard, the ECSK theory has shown to be consistent with current observations. By studying the generalization of the De Rahm and Beltrami wave operators on a Riemann-Cartan geometry, we find that at leading order in the eikonal expansion, the dispersion relation coincides with observational data. However, at the next order, it predicts an anomalous propagation in amplitude and polarization with respect to General Relativity. Recently, the influence of torsion on the amplitude was estimated to be extremely small, an effect inaccessible by current and near-future measurements. In this thesis, we calculate the anomalous propagation of polarization over a cosmological background geometry. We observe that the same polarization modes as in General Relativity propagate. However, its propagation will exhibit a behavior which we call the Faraday-Cartan effect, where the polarization modes will oscillate at a rotation angle proportional to the geodesic parameter, with an order of magnitude of 1 degree every 5 million light-years.
In 2016, the systematic measurement of gravitational waves began with such precision that their existence became an irrefutable fact. In 2017, gravitational radiation from a binary neutron star system (GW170817) was observed for the first time, simultaneously with its electromagnetic counterpart (GRB170817A). This measurement imposes significant constraints on families of torsional theories, refuting those that predicted a speed and dispersion relation different from that of light. In this regard, the ECSK theory has shown to be consistent with current observations. By studying the generalization of the De Rahm and Beltrami wave operators on a Riemann-Cartan geometry, we find that at leading order in the eikonal expansion, the dispersion relation coincides with observational data. However, at the next order, it predicts an anomalous propagation in amplitude and polarization with respect to General Relativity. Recently, the influence of torsion on the amplitude was estimated to be extremely small, an effect inaccessible by current and near-future measurements. In this thesis, we calculate the anomalous propagation of polarization over a cosmological background geometry. We observe that the same polarization modes as in General Relativity propagate. However, its propagation will exhibit a behavior which we call the Faraday-Cartan effect, where the polarization modes will oscillate at a rotation angle proportional to the geodesic parameter, with an order of magnitude of 1 degree every 5 million light-years.
Description
Tesis presentada para optar al grado de Magíster en Ciencias con Mención en Física
Keywords
Ondas gravitacionales, Geometría de Riemann, Curvatura, Torsión