Compactness Criterion for the Formation of Averaged Trapped Surfaces in Gravitational Collapse

1973 ◽  
Vol 31 (1) ◽  
pp. 60-63 ◽  
Author(s):  
J. B. Hartle ◽  
D. C. Wilkins
Keyword(s):  
Gravitational Collapse ◽  
Compactness Criterion ◽  
Trapped Surfaces

DOES PRESSURE ACCENTUATE GENERAL RELATIVISTIC GRAVITATIONAL COLLAPSE AND FORMATION OF TRAPPED SURFACES?

2013 ◽  
Vol 22 (05) ◽  
pp. 1350021 ◽  
Author(s):  
ABHAS MITRA
Keyword(s):  
General Relativity ◽  
Gravitational Collapse ◽  
Fluid Pressure ◽  
Free Fall ◽  
Newtonian Gravity ◽  
Tangential Pressure ◽  
Trapped Surfaces ◽  
Imperfect Fluid ◽  
Newtonian Case ◽  
General Relativistic

It is widely believed that though pressure resists gravitational collapse in Newtonian gravity, it aids the same in general relativity (GR) so that GR collapse should eventually be similar to the monotonous free fall case. But we show that, even in the context of radiationless adiabatic collapse of a perfect fluid, pressure tends to resist GR collapse in a manner which is more pronounced than the corresponding Newtonian case and formation of trapped surfaces is inhibited. In fact there are many works which show such collapse to rebound or become oscillatory implying a tug of war between attractive gravity and repulsive pressure gradient. Furthermore, for an imperfect fluid, the resistive effect of pressure could be significant due to likely dramatic increase of tangential pressure beyond the "photon sphere." Indeed, with inclusion of tangential pressure, in principle, there can be static objects with surface gravitational redshift z → ∞. Therefore, pressure can certainly oppose gravitational contraction in GR in a significant manner in contradiction to the idea of Roger Penrose that GR continued collapse must be unstoppable.

scholarly journals Cylindrically symmetric models of gravitational collapse to black holes: A short review

2015 ◽  
Vol 24 (09) ◽  
pp. 1542021 ◽  
Author(s):  
Filipe C. Mena
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Collapse ◽  
A Priori ◽  
Short Review ◽  
Gravitational Energy ◽  
Open Problems ◽  
Trapped Surfaces ◽  
Cylindrically Symmetric ◽  
Survey Results

We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vacuum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching boundary of a particular collapsing region. Along the way, we point out several interesting open problems.

Marginally trapped surfaces in null normal foliation spacetimes: A one step generalization of LRS II spacetimes

2020 ◽  
Vol 17 (07) ◽  
pp. 2050097
Author(s):  
Abbas Sherif ◽  
Rituparno Goswami ◽  
Sunil D. Maharaj
Keyword(s):  
Stability Analysis ◽  
Gravitational Collapse ◽  
Covariant Formalism ◽  
Geometrical Properties ◽  
Trapped Surfaces ◽  
Dimensional Spacetime ◽  
One Step ◽  
Marginally Trapped Surfaces

In this paper, we study geometrical properties of marginally trapped surfaces in gravitational collapse, using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables. We first define a generalization (in a sense to be specified in the introduction) of LRS II spacetime — which we call NNF spacetimes — and show that the marginally trapped surfaces in NNF spacetimes (and the 3-surfaces they foliate) are topologically equivalently those of LRS II spacetimes. We then study the evolution of MTTs (3-surfaces foliated by marginally trapped surfaces), extending earlier work on LRS II spacetimes to NNF spacetimes, and in general any 4-dimensional spacetime. In addition, we perform a stability analysis for the marginally trapped surfaces in this formalism, using simple spacetimes as examples to demonstrate the applicability of our approach.

scholarly journals CAN GRAVITATIONAL COLLAPSE SUSTAIN SINGULARITY-FREE TRAPPED SURFACES?

2008 ◽  
Vol 17 (01) ◽  
pp. 165-177 ◽  
Author(s):  
MANASSE R. MBONYE ◽  
DEMOS KAZANAS
Keyword(s):  
Black Hole ◽  
Gravitational Collapse ◽  
Null Geodesic ◽  
Space Time ◽  
Test Case ◽  
Hole Center ◽  
Singularity Formation ◽  
Trapped Surfaces ◽  
Type D ◽  
Fluid Formation

In singularity-generating space–times both the outgoing and the ingoing expansions of null geodesic congruences θ+ and θ- should become increasingly negative without bound, inside the horizon. This behavior leads to geodetic incompleteness, which in turn predicts the existence of a singularity. In this work we inquire whether, in gravitational collapse, space–time can sustain singularity-free trapped surfaces, in the sense that such a space–time remains geodetically complete. As a test case, we consider a type D space–time of Dymnikova which is Schwarzschild-like at large distances and consists of a fluid with a p = -ρ equation of state near r = 0. By following both the expansion parameters θ+ and θ- across the horizon and into the black hole, we find that both θ+ and θ+θ- have turning points inside the trapped region. Further, we find that deep inside the black hole there is a region, 0 ≤ r < r0 (which includes the black hole center), which is not trapped. Thus the trapped region is bounded from both outside and inside. The space–time is geodetically complete, a result which violates a condition for singularity formation. It is inferred that, in general, if gravitational collapse were to proceed with a p =-ρ fluid formation, the resulting black hole might be singularity-free.

scholarly journals Marginally trapped surfaces in spherical gravitational collapse

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Ayan Chatterjee ◽  
Amit Ghosh ◽  
Suresh C. Jaryal
Keyword(s):  
Gravitational Collapse ◽  
Trapped Surfaces ◽  
Marginally Trapped Surfaces

Introduction

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gravitational Collapse ◽  
Present State ◽  
Strong Gravity ◽  
Shape Dynamics

Shape Dynamics (SD) is a field theory that describes gravity in a different way than General Relativity (GR): it assumes a preferred notion of simultaneity, and the dynamical content of the theory consists of conformal 3- geometries. SD coincides with (GR) in most situations, in particular in the experimentally well-tested regimes, but it departs from it in some strong-gravity situations, for example at cosmological singularities or upon gravitational collapse. This chapter provides a quick introduction to the theory and a brief description of its present state.

scholarly journals Magnetic field amplification in newly-born neutron stars

1996 ◽  
Vol 160 ◽  
pp. 435-436
Author(s):  
H.-J. Wiebicke ◽  
U. Geppert
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Gravitational Collapse ◽  
Dipole Field ◽  
Numerical Calculations ◽  
Selection Effects ◽  
Thermoelectric Effects ◽  
Field Amplification ◽  
Seed Field ◽  
Flux Conservation

AbstractWe present a scenario of magnetic field (MF) evolution of newly-born neutron stars (NSs). Numerical calculations show that in the hot phase of young NSs the MF can be amplified by thermoelectric effects, starting from a moderately strong seed-field. Therefore, there is no need to assume a 1012G dipole field immediately after the gravitational collapse of the supernova (SN) event. The widely accepted scenario for such a field to be produced by flux conservation during the collapse is critically discussed. Instead, it can be generated by amplification and selection effects in the first 104yrs, and by the subsequent fast ohmic decay of higher multipole components, when the NS cools down.

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