Shell crossing in generalized Tolman-Bondi spacetimes

Physical Review D

Volumn 63, Issue 12, 2001, Pages

  Gonçalves, Sérgio M C V ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COSMOLOGICAL PHENOMENA; ENERGY; RADIUS; VELOCITY;

EID: 0034889703     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.63.124017     Document Type: Article

References (27)

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4. This also happens in the Newtonian collapse of homogeneous spherical shells, and it is due to the homogeneity of the matter distribution and its spherical symmetry: homogeneity implies that i(r)3:r3 and spherical symmetry guarantees that the gravitational force per unit mass at radius r is Fmr-2. Since the equation of motion for a unit test mass is ir=F
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27. The einbein e(X) is a function of the affine parameter that acts as a gauge field in one dimension for local reparametrizations of the world line. By definition, it transforms under reparametrizations as e(Y)->e'(Y) = e(\)d\Jd\' (which is the transformation rule for the square root of a one-dimensional metric-hence the name "einbein"). The introduction of the einbein in the action (109) has the advantage of (i) making it reparametrization invariant, and (ii) obtaining the in->0 limit (massless particle) in a trivial manner. The einbein action formulation contains the Lagrangian and Hamiltonian action principles in one unified framework. See, e.g., L. Brink, P. di Vecchia, and P. Howe, Phys. Lett. 65B, 471 (1976).