Spherical Gravitational Collapse of Anisotropic Radiating Fluid Sphere

We here present a relativistic model for a spherically symmetric anisotropic fluid to study the various factors of physical and thermal phenomenon during the evolution of a collapsing star dissipating energy in the form of radial heat flow. We also proposed a table of some new parametric class of solutions which will be useful for constructing the new compact star models. The constructed algorithm obeys all the relevant requirements of a realistic model and matched with Vaidya exterior metric over the boundary. At the initial stage the interior solutions represent a static configuration of perfect fluid which then gradually starts evolving into radiating collapse. The apparent luminosity as observed by the distant observer at rest at infinity and the effective surface temperature are zero in remote past at the instant when collapse begins and at the stage when collapsing configuration reaches the horizon of the black hole.

Gravitational Collapse of a Spherical Star with Heat Flow as a Possible Energy Mechanism of Gamma-Ray Bursts

We investigate the gravitational collapse of a spherically symmetric, inhomogeneous star, which is described by a perfect fluid with heat flow and satisfies the equation of state p = p/3 at its center. In the process of the gravitational collapse, the energy of the whole star is emitted into space. And the remaining spacetime is a Minkowski one without a remnant at the end of the process. For a star with a solar mass and solar radius, the total energy emitted is at the order of 10^54 erg, and the time-scale of the process is about 8 s. These are in the typical values for a gamma-ray burst. Thus, we suggest the gravitational collapse of a spherical star with heat flow as a possible energy mechanism of gamma-ray bursts.

New Solutions of Gravitational Collapse in General Relativity and in the Newtonian Limit

We discuss the Oppenheimer-Snyder-Datt (OSD) solution from a new perspective, introduce a completely new formulation of the problem exclusively in external Schwarzschild space-time (ESM) and present a new treatment of the singularities in this new formulation. We also give a new Newtonian approximation of the problem. Furthermore, we present new numerical solutions of the modified OSD-model and of the ball-to-ball-collapse with 4 different numerical methods.

Spherical Gravitational Collapse in f(R) Gravity with Linear Equation of State

In a paper [Gen. Relativ. Gravit. 48(2016) 57] Chakrabarti and Banerjee investigated perfect fluid collapse in f(R) gravity model and claimed that such a collapse is possible. In this paper we show that without the assumption of dark energy it is not possible that perfect fluid spherical gravitational collapse will occur. We have solved the field equations by assuming linear equation of state(p = ωμ) in metric f(R) gravity with ω =-1. It is shown that Chakrabarti and Banerjee reached to false conclusion as they derived wrong field equations. We have also discussed formation of apparent horizon and singularity.

Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.

Relationship between gravitational flap structures in the backlimb of anticlinal breakthrough Fault-Propagation Folds:case study of the Southern-Central Tunisian Atlas

The development of orogenic belts structures in the Southern-Central Tunisian Atlas is influenced by the evolution of tectonic activities during different phases,which are also closely linked to the formation of gravitational collapse structure.The typical example is that of the northern flank of the Jebel Orbata particularly the Ben Zannouch fold.It is an asymmetrical anticline interpreted by the model of“Fault Propagation Folds”.The development of the Ben Zannouch structures is resulted from landslides,scree falls and inverted layers plunging to the south.The direction of resulted gravitational structure is parallel to the main thrust direction of the Bou Omrane anticline.The thrust activity of Bou Omrane fault is associated to the important paleo-slope facing south and plastic lithology(incompetent marl layers)of outcropped series,facilitates the development of the Ben Zannouch Flap structure.The definition of gravitational collapse structures for the first time in Tunisia particularly in the northern flank of the Jebel Orbata is controlled by many principal structural conditions:fragmentation of the landslide surfaces,rheology and topography.Other regional factors can be distinguished in the Southern-Central Tunisian Atlas as the seismic activity of the pre-existing Gafsa fault reactivated during compressive phases and the weather conditions during the postglacial period.

On the Critical Behavior of Gapped Gravitational Collapse in Confined Spacetime

The gravitational collapse of a massless scalar with a cosmological constant A is investigated. The mass field enclosed with a perfectly reflecting wall in a spacetime scaling for the gapped collapse MAH -- Mg oc （ec -- e） is confirmed and a new time scaling for the gapped collapse Tall -- Tg c（ （ec - e）〈 is found. For both the critical exponents, we find strong evidence to show that they are non-universal. Especially when A ~ O, we find that both of these two critical exponents depend on the combination AR2, where R is the radial position of the reflecting wall. We find an evolution of the critical exponent from 0.37 in the confined asymptotic dS case with AR2 = 1.75 to 0.68 in the confined asymptotic AdS case with AR2 -- -1.75, while the critical exponent （ varies from 0.10 to 0.26, which shows that the new critical behavior for the gapped collapse is essentially different from the Choptuik＇s case.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime

We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime.Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field.Through our numerical results,we obtain a formula that determines critical amplitude in terms of cosmological constantΛ:A^(*)∝(0.01360σ/v_(0)+0.001751)Λ,whereσdenotes the initial width of the scalar field and is the initial position of the scalar field.Notably,we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.

Normal Faulting Type Earthquake Activities in the Tibetan Plateau and Its Tectonic Implication

This paper analyzes various earthquake fault types, mechanism solutions, stress field as well as other geophysical data to study the crust movement in the Tibetan plateau and its tectonic implications. The results show that a lot of normal faulting type earthquakes concentrate in the central Tibetan plateau. Many of them are nearly perfect normal fault events. The strikes of the fault planes of the normal faulting earthquakes are almost in the N-S direction based on the analyses of the equal area projection diagrams of fault plane solutions. It implies that the dislocation slip vectors of the normal faulting type events have quite great components in the E-W direction. The extension is probably an eastward extensional motion, mainly a tectonic active regime in the altitudes of the plateau. The tensional stress in the E-W or WNW-ESE direction predominates the earthquake occurrence in the normal event region of the central plateau. A number of thrust fault and strike-slip fault type earthquakes with strong compressive stress nearly in the NNE-SSW direction occurred on the edges of the plateau. The eastward extensional motion in the Tibetan plateau is attributable to the eastward movement of materials in the upper mantle based on_seismo-tomographic results. The eastward extensional motion in the Tibetan plateau may be related to the eastward extrusion of hotter mantle materials beneath the east boundary of the plateau. The northward motion of the Tibetan plateau shortened in the N-S direction probably encounters strong obstructions at the western and northern margins. Extensional motions from the relaxation of the topography and/or gravitational collapse in the altitudes of the plateau occur hardly in the N-S direction. The obstruction for the plateau to move eastward is rather weak.

Evolution, Migration, Controlling Factors and Forming Setting of Mesozoic Basins in Western Shandong

The distinctive topography in western Shandong province consists of several NW-WNW-trending mountain ranges and intervening basins. Basins, in which late-stage sediments to the south have progressively overlapped the earlier sediments and ＂basement＂ rocks of the hanging-wall block, are bounded by S-SW-dipping normal faults to the north. Basin analysis reveals the Jurassic-Cretaceous sedimentary rocks accumulated both within the area of crustal extension and during extensional deformation; they contain a record of a sequence of tectonic events during stretching and can be divided into four tectonic-sequence episodes. These basins were initially developed as early as ca. 200 Ma in the northern part of the study area, extending dominantly N-S from the Early Jurassic until the Late Cretaceous. Although with a brief hiatus due to changes in stress field, to keep uniform N-S extensional polarity in such a long time as 130 Ma requires a relatively stable tectonic controlling factor responsible for the NW- and E-W-extensional basins. The formation of the extensional basins is partly concurrent with regional magmatism, but preceded magmatism by 40 Ma. This precludes a genetic link between local magmatism and extension during the Mesozoic. Based on integrated studies of basins and deformation, we consider that the gravitational collapse of the early overthickened continental crust may be the main tectonic driver for the Mesozoic extensional basins. From the Early Jurassic, dramatic reduction in north-south horizontal compressive stress made the western Shandong deformation belt switch from a state of failure under shortening to one dominated by extension and the belt gravitationally collapsed and horizontally spread to the south until equilibrium was established; synchronously, the normal faults and basins were developed based on the model of simple-shear extensional deformation. This may be relative to the gravitational collapse of the Mesozoic plateau in eastern China.

Survival Conditions of Folding in Different Depth During Orogenesis-Deformation in Texas Creek and Chester Dome, USA

A succession of 5 FIA trends（foliation intersection or inflection axes in porphyroblasts） preserved in high temperature-low pressure regime PreCambrian rocks in the Texas Creek, Arkansas River region reflected by the fold axial plane traces and schistosity data in this region. Similar fold axial plane trace data measured in Palaeozoic rocks in Chester Dome, Vermont, which is high temperature to medium pressure regime, only preserve the effects of the youngest FIAs of the all 5 FIA sets that obtained in this region. The other three FIA sets have no equivalent fold axial planes. This difference from shallow to deeper orogenic regimes reflects decreasing competency at greater pressure with collapse and unfolding of earlier formed folds. The greater overlying load of rocks has tended to flatten all but the very largest early-formed structures, preserving only those folds that were more recently developed.

The stability of a shearing viscous star with an electromagnetic field

We analyze the role of the electromagnetic field for the stability of a shearing viscous star with spherical symmetry. Matching conditions are given for the interior and the exterior metrics. We use a perturbation scheme to construct the collapse equation. The range of instability is explored in Newtonian and post Newtonian （pN） limits. We conclude that the electromagnetic field diminishes the effects of the shearing viscosity in the instability range and makes the system more unstable in both Newtonian and post Newtonian approximations.

Law of Physics 20^th-Century Scientists Overlooked (Part 4): Mass Extinction by Aether Deprivation

Extreme gravitational collapse is explored by utilizing two fundamental properties and one reasonable assumption, which together lead logically to an end-state gravitating structure. This structure, called a Terminal state neutron star, manifests nature’s ultimate density of mass and possesses the ultimate electromagnetic barrier. It is then shown how this structure is central to the remarkable mechanism whereby the density is prevented from going higher. A simple process assures that such density is not exceeded—regardless of the quantity of additional mass. As an example, the discourse focuses on the expected progression and outcome when a compact star of —far more mass than can be accommodated by the basic Terminal state structure—undergoes total gravitational collapse. An examination of what happens to the considerable excess mass leads the discussion to the principle of mass extinction by the process of aether deprivation and its profound implications for black-hole physics and the current revolution in cosmology.

Mesozoic contraction deformation in the Yanshan and northern Taihang mountains and its implications to the destruction of the North China Craton

Mesozoic contraction deformation in the Yanshan and Taihang mountains is characterized by basement-involved thrust tectonics,basement-cored buckling anticlines and ductile thrust and nappe tectonics.Most of these deformations are orientated west-east,west-northwest and northeast to north-northeast.The contraction deformations began in the Permian,continued through the Triassic and Jurassic and terminated in the Early Cretaceous,and constitute an important part of the destruction of the North China Craton.It is estimated,from balanced cross-section reconstructions,that the north-south shortening of the central part of the Yanshan belt before 135 Ma was around 38%.The initial crust thickness,pre-dating the major contraction deformation in late Paleozoic and early Mesozoic,was estimated to be around 35 km based on paleogeographic characteristics.Assuming that the inferred depth of ductile thrusting deformation,20-25 km,was the crust thickness involved in the contraction deformation,and also assuming that the N-S contraction deformation was accommodated by vertical crust thickening,the thickness of the crust after the contraction deformation was expected to be around 47-50 km.This was the approximate crust thickness required for the eclogitization of the lower crust for delamination.The gravity potential accumulated by the isostatic uplift of the thickened crust,together with the decrease in crustal strength caused by the coeval magmatisms associated with the contraction deformation,led to the subsequent extensional collapse of the middle and upper crust although the regional stress regime associated with the plate interactions remained constant.It is inferred that the Mesozoic contraction deformations in the Yanshan and Taihang mountains were not only a significant tectonic process contributing to the destruction of the craton in middle and upper crust but also stimulated delamination at a deep level and the extension of the shallow crust.In other words,both the suspected delamination of the lower crust and upper mantle and the well constrained extension deformations of the shallow crust in the eastern North China Craton during the late Mesozoic are a consequence of crust thickening due to previous contractions.Extensional deformations could be expected to occur independently in the shallow crust,and are not necessarily associated with or responding to delamination at a deep level.

Deformation geometry and timing of the Wupoer thrust belt in the NE Pamir and its tectonic implications

The Pamir region, located to the northwest of the Tibetan Plateau, provides important information that can aid the understanding of the plateau＇s tectonic evolution. Here we present new findings on the deforma- tion geometry and timing of the Wupoer thrust belt at the northeastem margin of Pamir. Field investigations and interpretations of seismic profiles indicate that the eastern portion of the Wupoer thrust belt is dominated by an underlying foreland basin and an overlying piggy-back basin. A regional unconformity occurs between the Pliocene （N2） and the underlying Miocene （NI） or Paleogene （Pg） strata associated with two other local unconformities between Lower Pleistocene （Q1） and N2 and between Middle Pleistocene （Q2-4） and Q1 strata. Results of structural restorations suggest that compres- sional deformation was initiated during the latest Miocene to earliest Pliocene, contributing a total shortening magnitude of 48.6 km with a total shortening rate of 48.12%, most of which occurred in the period from the latest Miocene to earliest Pliocene. These results, com- bined with previous studies on the Kongur and Tarshkor- gan extensional system, suggest an interesting picture of strong piedmont compressional thrusting activity concur- rent with interorogen extensional rifting. Combining these results with previously published work on the lithospheric architecture of the Pamir, we propose that gravitational collapse drove the formation of simultaneous extensional and compressional structures with a weak, ductile middle crustal layer acting as a decollement along which both the extensional and compressional faults merged.

Continental Dynamics in High Tibetan Plateau: Normal Faulting Type Earthquake Activities and Mechanisms

Various earthquake fault types were analyzed for this study on the crust movement in the high region of the Tibetan plateau by analyzing mechanism solutions and stress fields. The results show that a lot of normal faulting type earthquakes are concentrated in the central High Tibetan plateau. Many of them are nearly perfect normal fault events. The strikes of the fault planes of normal faulting earthquakes are almost in an N-S direction based on the analyses of the Wulff stereonet diagrams of fault plane solutions. It implies that the dislocation slip vectors of the normal faulting type events have quite great components in the E-W direction. The extensions probably are an eastward extensional mo- tion, being mainly a tectonic active regime in the plateau altitudes. The tensional stress in the E-W or NWW-SEE direction predominates earthquake occurrences in the normal event region of the central plateau. The eastward extensional motion in the high Tibetan plateau is attributable to the gravitational collapse of the high plateau and the eastward extrusion of hotter mantle materials beneath the east boundary of the plateau. Extensional motions from the relaxation of the topography and/or gravitational collapse in the high plateau hardly occurred along the N-S direction. The obstruction for the plateau to move eastward is rather weak.