Stability of geodesic incompleteness for Robertson-Walker space-times

1981 ◽  
Vol 13 (3) ◽  
pp. 239-255 ◽  
Author(s):  
John K. Beem ◽  
Paul E. Ehrlich
Keyword(s):  
Geodesic Incompleteness

scholarly journals Non-Geodesic Incompleteness in Poincaré Gauge Gravity

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 280 ◽  
Author(s):  
José Cembranos ◽  
Jorge Valcarcel ◽  
Francisco Torralba
Keyword(s):  
Black Hole ◽  
Gauge Theories ◽  
Arbitrary Dimension ◽  
Singular Behavior ◽  
Theories Of Gravity ◽  
Gauge Gravity ◽  
Geodesic Incompleteness

In this work, we review the study of singularities in Poincaré gauge theories of gravity. Since one of the most recent studies used the appearance of black hole regions of arbitrary dimension as an indicator of singular behavior, we also give some explicit examples of these structures and study how particles behave around them.

scholarly journals Geodesic Incompleteness and Partially Covariant Gravity

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 126
Author(s):  
Ignatios Antoniadis ◽  
Spiros Cotsakis
Keyword(s):  
Symmetry Groups ◽  
Gravity Theories ◽  
The Difference ◽  
Geodesic Incompleteness

We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided that certain asymptotic conditions hold, this relation allows us to transfer analytic criteria for the standard spacetime length to be finite and the Perelman length to be likewise finite, and therefore formulate conditions for geodesic incompleteness in partially covariant theories. We also discuss implications of this result for the issue of singularities in the context of such theories.

Sprays, universality and stability

1988 ◽  
Vol 103 (3) ◽  
pp. 515-534 ◽  
Author(s):  
L. Del Riego ◽  
C. T. J. Dodson
Keyword(s):  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Second Order Differential Equations ◽  
Linear Connections ◽  
Natural Context ◽  
Vertical Distributions ◽  
Nijenhuis Bracket ◽  
Horizontal And Vertical Distributions ◽  
Geodesic Incompleteness

AbstractAn important class of systems of second order differential equations can be represented as sprays on a manifold M with tangent bundle TM↠ M; that is, as certain sections of the second tangent bundle TTM ↠ TM. We consider here quadratic sprays; they correspond to symmetric linear connections on TM ↠ M and hence to principal connections on the frame bundle LM ↠ M. Such connections over M constitute a system of connections, on which there is a universal connection and through which individual connections can be studied geometrically. Correspondingly, we obtain a universal spray-like field for the system of connections and each spray on M arises as a pullback of this ‘universal spray’. The Frölicher-Nijenhuis bracket determines for each spray (or connection) a Lie subalgebra of the Lie algebra of vector fields on M and this subalgebra consists precisely of those morphisms of TTM over TM which preserve the horizontal and vertical distributions; there is a universal version of this result. Each spray induces also a Riemannian structure on LM; it isometrically embeds this manifold as a section of the space of principal connections and gives a corresponding representation of TM as a section of the space of sprays. Such embeddings allow the formulation of global criteria for properties of sprays, in a natural context. For example, if LM is incomplete in a spray-metric then it is incomplete also in the spray-metric induced by a nearby spray, because that spray induces a nearby embedding. For Riemannian manifolds, completeness of LM is equivalent to completeness of M so in the above sense we can say that geodesic incompleteness is stable; it is known to be Whitney stable.

scholarly journals Null geodesic incompleteness of spacetimes with no CMC Cauchy surfaces

2019 ◽  
Vol 15 (3) ◽  
pp. 839-849
Author(s):  
Madeleine Burkhart ◽  
Martin Lesourd ◽  
Daniel Pollack
Keyword(s):  
Null Geodesic ◽  
Geodesic Incompleteness

Kinks and geodesic incompleteness

1996 ◽  
Vol 37 (11) ◽  
pp. 5637-5651 ◽  
Author(s):  
K. A. Dunn ◽  
Tina A. Harriott ◽  
J. G. Williams
Keyword(s):  
Geodesic Incompleteness
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