scholarly journals Compensated compactness and corrector stress tensor for the Einstein equations in $\mathbb T^2$ symmetry

2020 ◽  
Vol 77 (3) ◽  
pp. 409-421
Author(s):  
Bruno Le Floch ◽  
Philippe LeFloch
Keyword(s):  
Stress Tensor ◽  
Einstein Equations ◽  
Compensated Compactness

scholarly journals Large D black holes in an environment

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Taniya Mandal ◽  
Arunabha Saha
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Stress Tensor ◽  
Einstein Equations ◽  
Leading Order ◽  
Conservation Equations ◽  
Stress Tensors ◽  
Black Hole Solutions

Abstract We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of $$ \mathcal{O} $$ O (D0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D.

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor

2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak
Keyword(s):  
Stress Tensor ◽  
Elastic Energy ◽  
Yield Condition ◽  
The Third ◽  
Third Invariant ◽  
Lode Angle

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.

Einstein equations for a Finsler-Larange space with canonical N-linear connections

2020 ◽  
Vol 4 (1) ◽  
pp. 240-247
Author(s):  
Roopa M. K ◽  
◽  
Narasimhamurthy S. K ◽  
Keyword(s):  
Einstein Equations ◽  
Linear Connections

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

scholarly journals Driving stress and seismotectonic implications of the 2013 Mw5.8 Awaji Island earthquake, southwestern Japan, based on earthquake focal mechanisms before and after the mainshock

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Kazutoshi Imanishi ◽  
Makiko Ohtani ◽  
Takahiko Uchide
Keyword(s):  
Stress Field ◽  
Stress Tensor ◽  
Nankai Trough ◽  
Source Region ◽  
Local Scale ◽  
Southwest Japan ◽  
Stress Tensor Inversion ◽  
Earthquake Fault ◽  
Reverse Faulting ◽  
Before And After

Abstract A driving stress of the Mw5.8 reverse-faulting Awaji Island earthquake (2013), southwest Japan, was investigated using focal mechanism solutions of earthquakes before and after the mainshock. The seismic records from regional high-sensitivity seismic stations were used. Further, the stress tensor inversion method was applied to infer the stress fields in the source region. The results of the stress tensor inversion and the slip tendency analysis revealed that the stress field within the source region deviates from the surrounding area, in which the stress field locally contains a reverse-faulting component with ENE–WSW compression. This local fluctuation in the stress field is key to producing reverse-faulting earthquakes. The existing knowledge on regional-scale stress (tens to hundreds of km) cannot predict the occurrence of the Awaji Island earthquake, emphasizing the importance of estimating local-scale (< tens of km) stress information. It is possible that the local-scale stress heterogeneity has been formed by local tectonic movement, i.e., the formation of flexures in combination with recurring deep aseismic slips. The coseismic Coulomb stress change, induced by the disastrous 1995 Mw6.9 Kobe earthquake, increased along the fault plane of the Awaji Island earthquake; however, the postseismic stress change was negative. We concluded that the gradual stress build-up, due to the interseismic plate locking along the Nankai trough, overcame the postseismic stress reduction in a few years, pushing the Awaji Island earthquake fault over its failure threshold in 2013. The observation that the earthquake occurred in response to the interseismic plate locking has an important implication in terms of seismotectonics in southwest Japan, facilitating further research on the causal relationship between the inland earthquake activity and the Nankai trough earthquake. Furthermore, this study highlighted that the dataset before the mainshock may not have sufficient information to reflect the stress field in the source region due to the lack of earthquakes in that region. This is because the earthquake fault is generally locked prior to the mainshock. Further research is needed for estimating the stress field in the vicinity of an earthquake fault via seismicity before the mainshock alone.

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