Thesis

Analysis of the asymptotic region of asymptotically flat and de-Sitter like spacetimes

• Call:

  PT-CERN Call 2021/1

• Academic Year:

  2021

• Domain:

  Astroparticle Physics

• Supervisor:

  Edgar Gasperin Garcia

• Co-Supervisor:

  Alex Vano-Vinuales

• Institution:

  Instituto Superior Técnico (Universidade de Lisboa)

• Host Institution:

  CENTRA - Center for astrophysics and gravitation

• Abstract:

  The asymptotic properties of spacetimes play a central role in many physical aspects of General Relativity (GR), in particular for the concept of gravitational radiation. One of the crucial concepts introduced for the realisation of the latter, was the use of conformal compactifications introduced in General Relativity by Roger Penrose to describe in a geometric way the notion of infinity. Arguably, the formulation that takes Penrose’s idea of conformal compactification --in conjunction with the theory of partial differential equations and the initial value problem-- to its ultimate consequences are, the so-called, Conformal Einstein Field (CEFE) equations introduced by H. Friedrich in [1]. These equations have been used for analytical purposes such as establishing (semi)-global non-linear stability results de-Sitter and Minkowski spacetimes and some partial global non-linear stability results for black hole spacetimes such as Schwarzschild-de Sitter [2]. Although these equations have been available since 1980 the numerical exploration of spacetimes using the CEFEs is still in its infancy compared with other formulations since they have not been systematically exploited as other formulations of GR. One of the alternatives to the CEFEs to reach the conformal boundary is the use of hyperboloidal foliations and scri-fixing techniques and more standard formulations of the Einstein Field Equations such as the Generalised Harmonic Gauge (EFE-GHG). These have also give fruitful results in combination with the weak null condition ---see [6]--- which can be exploited for numerical implementations [7] and for mathematical analysis [8]. By construction, hyperboloidal foliations reach the null-infinity but stays away from the region close to spatial infinity. The CEFEs on the other hand have access to this region via the construction of the so-called cylinder at spatial infinity. The latter has applications in terms of the calculation of asymptotic charges [4]. These met