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Reinstating Schwarzschild's original manifold and its singularity

S Antoci;
2006
2006
Istituto per i Processi Chimico-Fisici - IPCF
Nova Science Publishers
Hauppauge
STATI UNITI D'AMERICA
General relativity
Exact solutions
Schwarzschild solution
singularity
The second main defect of Hilbert's metric is constituted by the presence of an invariant, local, intrinsic quantity that diverges when it is calculated at a position closer and closer to Schwarzschild's surface, i.e. at an internal position in Hilbert's metric. The diverging quantity is the norm of the four-acceleration of a test particle whose worldline is the unique orbit of absolute rest defined, through a given event, by the unique timelike, hypersurface orthogonal Killing vector. It is an intrinsic quantity, whose definition only requires the knowledge of the metric and of its derivatives at a given event, just like it happens with the polynomial invariants built with the Riemann tensor and with its covariant derivatives. The regularity of the latter invariants at a given event has been considered by many a relativist like a "rule of thumb" proof of regularity for the manifold at that event, in the persistent lack of a satisfactory definition of local singularity in general relativity. The divergence of the above mentioned norm of the four-acceleration, i.e. of the first curvature of the world line, is a geometric fact. It can be proved however with an exact argument, relying on a two-body solution found by Bach, that a physical quantity, the norm of the force per unit mass exerted on a test particle on the unique orbit of absolute rest, is equal to the norm of the four-acceleration, hence it diverges too on approaching Schwarzschild's surface.
2
02 Contributo in Volume::02.01 Contributo in volume (Capitolo o Saggio)
268
reserved
Antoci, S; Liebscher, De
info:eu-repo/semantics/bookPart
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/129433
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