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Dieter Brill

Publications and source records attributed to Dieter Brill.

12 recordsLinked to original sources

Tokyo Wheeler or the Epistemic Preconditions of the Renaissance of Relativity

During the period identified as the Rebirth of General Relativity, John Wheeler was instrumental in retrieving the physics of gravity that had become hidden behind the mathematical formalism. For Wheeler himself the change in point of view was not from mathematics to physics; his thinking about gravity arose from, and was largely guided by, physical problems about elementary particles. We recount his development from the view of fields as derivable from particles, to fields as the more fundamental entities in nature. During the more than 10 years of his search for "particles first" Wheeler did not write an orderly sequence of accounts as his views developed, but the story could be pieced together from letters. and particularly from his extensive but seldom sequential notebook entries.

physics.hist-ph

Horizons in 2+1-dimensional collapse of particles

A simple, geometrical construction is given for three-dimensional spacetimes with negative cosmological constant that contain two particles colliding head-on. Depending on parameters like particle masses and distance, the combined geometry will the that of a particle, or of a black hole. In the black hole case the horizon is calculated. It is found that that the horizon typically starts at a point and spreads into a closed curve with corners, which propagate along spacelike caustics and disappear as the horizon passes the particles.

gr-qc

Spacetime and Euclidean Geometry

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".

gr-qc

Closed Timelike Curves in Flat Lorentz Spacetimes

We consider the region of closed timelike curves (CTC's) in three-dimensional flat Lorentz spacetimes. The interest in this global geometrical feature goes beyond the purely mathematical. Such spacetimes may be considered lower-dimensional toy models of sourceless Einstein gravity or cosmology. In particular, our interest in this note will be to find the set free of CTC's for $E/<γ>$, where $E$ is modeled on Minkowski space and $γ$ is a Poincaré transformation. We describe the set free of CTC's where $γ$ is hyperbolic, parabolic and elliptic.

math.DG

2+1-dimensional black holes with momentum and angular momentum

Exact solutions of Einstein's equations in 2+1-dimensional anti-de Sitter space containing any number of black holes are described. In addition to the black holes these spacetimes can possess ``internal'' structure. Accordingly the generic spacetime of this type depends on a large number of parameters. Half of these can be taken as mass parameters, and the rest as the conjugate (angular) momenta. The time development and horizon structure of some of these spacetimes are sketched.

gr-qc

Black Holes and Wormholes in 2+1 Dimensions

Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter" spaces is treated in an elementary way, using visualizable models. Among the objects discussed are black holes, spaces with multiple black holes, their horizon structure, closed universes, and the topologies that are possible.

gr-qc

Black Holes and Wormholes in 2+1 Dimensions

A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained under a restriction to time symmetric initial data and one asymptotic region only. The resulting spacetimes are non-eternal black holes with collapsing wormhole topologies. Our approach is geometrical, and we discuss in detail: The allowed topologies, the shape of the event horizons, topological censorship and trapped curves.

gr-qc

Geometry of Black Holes and Multi-Black-Holes in 2+1 dimensions

Lecture given at ``Raychaudhuri session," ICGC-95 conference, Pune (India), December 1995. Contents: I. Introduction II. (2+1)-Dimensional Initial Values in Stereographic Projection A. The single, non-rotating black hole B. Non-rotating multi-black-holes C. ``Black Hole" Universe Initial Values III. Time Development: Enter the Raychaudhuri Equation IV. Time Development in Stereographic Projection A. The BTZ black hole spacetime B. Multi-Black-Hole Spacetimes V. Black Holes with Angular Momentum VI. Analogous 3+1-Dimensional Black Holes VII. Conclusions

gr-qc

Is the gravitational action additive?

The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss possible implications for the superposition law of quantum gravity. We present a definition of `generalized additivity' which does hold for arbitrary spacetime composition.

gr-qc

Testing Cosmic Censorship with Black Hole Collisions

There exists an upper limit on the mass of black holes when the cosmological constant $Λ$ is positive. We study the collision of two black holes whose total mass exceeds this limit. Our investigation is based on a recently discovered exact solution describing the collision of $Q=M$ black holes with $Λ> 0$. The global structure of this solution is analyzed. We find that if the total mass is less than the extremal limit, then the black holes coalesce. If it is greater, then a naked singularity forms to the future of a Cauchy horizon. However, the horizon is not smooth. Generically, there is a mild curvature singularity, which still allows geodesics to be extended. The implications of these results for cosmic censorship are discussed.

gr-qc

A Pictorial History of Some Gravitational Instantons

Four-dimensional Euclidean spaces that solve Einstein's equations are interpreted as WKB approximations to wavefunctionals of quantum geometry. These spaces are represented graphically by suppressing inessential dimensions and drawing the resulting figures in perspective representation of three-dimensional space, some of them stereoscopically. The figures are also related to the physical interpretation of the corresponding quantum processes.

gr-qc

Euclidean Maxwell-Einstein Theory

After reviewing the context in which Euclidean propagation is useful we compare and contrast Euclidean and Lorentzian Maxwell-Einstein theory and give some examples of Euclidean solutions.

gr-qc