Marcello Ortaggio

Grants
- Exact solutions of gravity theories: black holes, radiative spacetimes and electromagnetic fields (19-09659S)
  from 01/01/2019 to 31/12/2021 investigator
- Objectives: Exact solutions to Einstein gravity play a crucial role in the understanding of many mathematical and physical aspects of the theory. In recent years, for several theoretical reasons, various modifications of Einstein gravity and their solutions have been studied. Due to the complexity of resulting field equations, very few exact solutions of such theories are known. We plan to construct and study exact solutions to Einstein gravity and various higher-order gravities, such as quadratic gravity and Lovelock gravity, with a strong focus on black hole solutions, radiative spacetimes, and p-form fields. We also intend to study generic properties of certain classes of spacetimes, such as asymptotically flat spacetimes. When appropriate, we will benefit from employing mathematical methods, such as algebraic classification and a generalized GHP formalism developed in part by our team.
- Albert Einstein Center for Gravitation and Astrophysics (GB14-37086G)
  from 01/01/2014 to 31/12/2018 investigator
- Objectives: We propose to establish the Albert Einstein Center for Gravitation and Astrophysics, a Project of Excellence that will bring together four leading research teams from the Czech Republic to address outstanding problems in gravitation theory and its astrophysical applications. We will strive to answer questions such as: What are the properties of exact models of gravitational radiation? How will the most important physical processes near rotating black holes change in the presence of large-scale magnetic fields or external sources? What are the mathematical and physical aspects of higher-dimensional relativity, including its implications for other fields of physics? The applying teams have long-term expertise in the relevant areas of theoretical physics, astrophysics, and cosmology. They include internationally recognized leaders as well as young researchers working at the main universities and research institutes in the Czech Republic.
- Higher dimensional gravity (GA13-10042S)
  from 01/02/2013 to 31/12/2017 investigator
- Objectives: Recently our group (with collaborators in Halifax, Canada and Cambridge, UK) has developed a generalization of various fundamental tools of four-dimensional (D=4) general relativity to higher dimensions (Petrov classification, Newman-Penrose and GHP formalisms). In this project we plan to apply these methods to various research problems . i) We will study D>4 Einstein spacetimes , their asymptotic properties and generalization of the Goldberg-Sachs theorem for D>5 and construct exact algebraically special D>4 spacetimes. ii) Following our recent work in quadratic gravity, we plan to find various classes of exact algebraically special vacuum solutions of Lovelock gravity. iii) Recently a duality between solutions of incompressible Navier-Stokes equations in p+1 dimensions with vacuum solutions of Einstein equations in p+2 dimensions (which seem to be algebraically special for p=2 ) has been discussed by Strominger et al. We intend to use our D>4 algebraic classification to study duality between solutions of 3+1 Navier-Stokes equations and 4+1 spacetimes.
- Algebraic classification of tensors on Lorentzian manifolds and its applications (M100191201)
  from 01/07/2012 to 30/06/2015 investigator
- Objectives: We will search for exact vacuum solutions of generalized theories of gravity using the algebraic classification of tensors and the generalization of the Geroch-Held-Penrose formalism to higher dimensions co-developed by our department. Particular focus is on so called universal solutions – vacuum solutions to all theories of gravity derived from the Lagrangian constructed from the metric, the Riemann tensor and its arbitrary covariant derivatives. Another objective is to develop a refinement of the algebraic classifications of tensors in five dimensions.
- General Relativity in higher dimensions (P203/10/0749)
  from 01/01/2010 to 31/12/2012 investigator
- Study of various aspects of higher-dimensional relativity with main emphasis on the algebraic classification of curvature tensors and applications.
- Solutions of the Einstein equations in higher dimensions (KJB100190702)
  from 01/01/2007 to 31/12/2009 investigator
- One of the most important methods used for finding exact solutions of the Einstein equations in four dimensions (4D) is the Petrov classification. Recent rapid development of higher dimensional gravity was motivated by string theory and large extra dimensions scenarios. In our previous joint work with A. Coley and R. Milson, we developed a generalization of the Petrov classification for higher dimensions. This classification has been already used in differential geometry, high energy physics and higher dimensional gravity but in comparison with the situation in four dimensions, possible applications remain largely unexplored. We plan to focus on these applications. We want to study certain classes of spacetimes (the Kundt class, Kerr-Schild metrics) and generalize various 4D theorems to higher dimensions. We also plan to study algebraically special classes (types N, D). Besides vacuum solutions we also plan to study solutions of the Einstein-Maxwell-Chern-Simons equations.