Institute of Theoretical PhysicsÚstav teoretické fyzikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Krššák, Martin

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On higher dimensional Kerr-Schild spacetimes

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Thesis ReviewFaculty of Mathematics and PhysicsCharles University in Prague0 Supervisor's ReviewQ BSc. ThesisQ Referee's Review **0 MSc. ThesisAuthor:Thesis title:Study program:Submitted:Martin KrssakOn higher dimensional Kerr-Schild spacetimesPhysics / Theoretical Physics2009Supervisor/Referee:Affiliation:E-mail:Marcello Ortaggio, PhD.Institute of Mathematics, AV CRortaggio@math.cas.czThesis quality (technical field and expertise):0 excellent Q very good Q standard U substandard Q nonconformingObjective accuracy (error appearance):0 nearly perfect Q standard Q frequent, but minor Q serious errorsThesis results:Q original 0 both original and compiled Q productive compilation Q copiedThesis size:Q large 0 standard U just acceptable Q insufficientThesis quality' (style and grammar, and graphic arrangement):Q excellent 0 very good U standard Q substandard Q nonconformingMisprints:0 negligible Q acceptable number Q very frequentOverall thesis quality:0 excellent Q very good Q standard Q substandard Q nonconforming** Copy and paste this check box, 0, if it is applicable.Supervisor's/Referee's Comments:Since the pioneering work of Kaluza and Klein in the 1920s, the idea of extra dimensions hasreemerged over the years in modern unified theories and, in particular, supergravity and stringtheory are naturally expressed in more than four dimensions. Furthermore, the recently proposedbrane world scenarios opened a possible, direct link to rich and qualitatively new observablephenomenology. Over the last few years, gravity in higher dimensions has thus developed rapidlyinto an active and interdisciplinary area of ongoing studies.This motivated the submitted thesis, which studies classical aspects of gravity in more than fourspacetime dimensions. More specifically, the present work analyzes an extension to any higherdimensions of the Kerr-Schild ansatz. In four dimensions, this is an important family of exactsolutions which, most remarkably, contains the Kerr metric etc. In more than four dimensions itincludes the generalization of the Kerr black hole found by Myers and Perry in the 1980s.However, after this early paper no systematic study of such geometries had been presented.Mr. Krssak employed the recently developed generalization of the Newman-Penrose formalism,and this is thus one of the first works where this method has been employed in its full strength.The first part of the thesis is therefore a useful, self-contained review of such a technique in higherdimensions. In the second part, this is applied to obtain new general results about Kerr-Schildspacetimes.Using an appropriate coordinate system, all connection and curvature components are computed,and employed to present the corresponding Einstein's equations in vacuum. The general solutionseems very hard to find (even in four dimensions this is given only in implicit form, and thanks tothe "miraculous" Kerr theorem). However, progress has been made with additional assumptions.In particular, using a suitable ansatz for the Kerr-Schild null congruence, Mr. Krssak rediscoveredthe metric for vacuum black strings. Although already known, this had not been systematicallyderived within the Newman-Penrose formalism before, and the details of the derivation are alsouseful as an illustrative example.From a complementary viewpoint, the last section of the work analyzes asymptotic properties ofKerr-Schild spacetimes in full generality. The r-dependence of the curvature tensor is fullydetermined, which enables one, e.g., to discuss peeling behavior of the solutions. This is anothernew result of Mr. Krssak's work. We also believe that the general results of this thesis will providea basis for further investigations, such as finding possible explicit new solutions and a discussionof the uniqueness properties of Myers-Perry black holes.To summarize, the submitted thesis contains useful review parts as well as original new results,and it will also be helpful in future studies. Mr. Krssak diligently followed my recommendationsin his research. He was able to quickly become acquainted with Relativity in higher dimensions, tolearn the relevant new techniques, and to apply these in the specific context. However, he alsoalready demonstrated independent thinking, for example in the derivation of the black stringsolutions. I am very happy with his work.Questions raised (and to be answered by the author during the Thesis Defence):Supervisor's/Reviewer's recommendation on Thesis rating:0 excellent Q very good G standard G rejectDone in PragueDate 15.9.2009Name Marcello OrtaesioSignature

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On higher dimensional Kerr-Schild spacetimes

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