Paul Klinger

Paul Klinger

Greater London, England, United Kingdom
250 followers 242 connections

About

Physicist turned Data Scientist

Activity

Experience

  • Deliveroo Graphic

    Deliveroo

    London, England, United Kingdom

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    London, England, United Kingdom

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    London, United Kingdom

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    London, United Kingdom

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    Vienna, Austria

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Education

Licenses & Certifications

Publications

Projects

  • Master Thesis - "A New Class of Asymptotically Non-Chaotic Vacuum Singularities"

    The BKL conjecture, stated in the 60s and early 70s by Belinski, Khalatnikov and Lifshitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields.
    Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show…

    The BKL conjecture, stated in the 60s and early 70s by Belinski, Khalatnikov and Lifshitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields.
    Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.

    See project
  • PhD Thesis - "Asymptotic problems in non-spatially symmetric spacetimes"

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    Many crucial problems in general relativity concern the asymptotic
    behavior of solutions to the Einstein equations, both in time and space.
    These are commonly studied under the assumption of symmetry
    conditions on the spatial slices of the spacetime, which greatly simplifies the analysis. In this thesis we investigate several such problems
    without relying on spatial symmetry.

    In the first part of this thesis we start with
    asymptotic data, given on the conformal boundary…

    Many crucial problems in general relativity concern the asymptotic
    behavior of solutions to the Einstein equations, both in time and space.
    These are commonly studied under the assumption of symmetry
    conditions on the spatial slices of the spacetime, which greatly simplifies the analysis. In this thesis we investigate several such problems
    without relying on spatial symmetry.

    In the first part of this thesis we start with
    asymptotic data, given on the conformal boundary and construct
    stationary spacetimes solving the Einstein equations with a negative
    cosmological constant coupled to a wide variety of matter fields. Here
    the boundary is timelike and corresponds to the limit of large radii. As
    there are only mild restrictions on the asymptotic data, our solutions
    possess no spatial Killing vector fields in general. Spacetimes of this
    type are of interest both within general relativity and within the context of the AdS/CFT conjecture.

    Another class of asymptotic problems of interest, at the “opposite
    end” of spacetimes, concerns their behavior near singularities. We
    know from the singularity theorems of Penrose and Hawking that
    singularities are a generic feature of general relativity, but their detailed structure is still unclear. Here we construct nakedly singular
    vacuum spacetimes without symmetries from asymptotic data at the
    singularity. They show so-called non-chaotic BKL behavior, which provides the building blocks for the
    more complicated chaotic behavior expected in the general case.

    A related issue of recent interest is the possible existence of lower
    regularity extensions through the singular boundary, which is connected to the cosmic censorship conjecture. For a class of “expanding
    singularities” (which includes spacetimes without any symmetries) we analyze the properties of C^0-extensions across the singularity by extending methods used in the Schwarzschild case.

  • Personal software/electronics/3d printing projects

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    In my spare time I like to tinker with programming, electronics, and 3D printing. The linked page shows some of my favorite projects. They include web applications, an android app, embedded C programming, custom PCB design, CAD,...

    See project

Honors & Awards

  • Dean's list award

    University of Vienna

  • uniːdocs PhD scholarship

    University of Vienna

    3 year, fully funded PhD scholarship. 16% acceptance rate

Languages

  • German

    Native or bilingual proficiency

  • English

    Full professional proficiency

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