In mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvature invariants of all orders vanishing. Although the only Riemannian manifold with VSI property is flat space, the Lorentzian case admits nontrivial spacetimes with this property. Distinguishing these VSI spacetimes from Minkowski spacetime requires comparing non-polynomial invariants or carrying out the full Cartan–Karlhede algorithm on non-scalar quantities. All VSI spacetimes are Kundt spacetimes. An example with this property in four dimensions is a pp-wave. VSI spacetimes however also contain some other four-dimensional Kundt spacetimes of Petrov type N and III. VSI spacetimes in higher dimensions have similar properties as in the four-dimensional case. (Wikipedia).
Relativity 8 - the yardstick of spacetime
The final piece of the puzzle falls in place. Herman Minkowski showed that Special Relativity defines a spacetime invariant - the "proper time" - between two events. Einstein's insight into the equivalence between falling and floating allowed him to realize that this also applied to Genera
From playlist Relativity
Yuguang Shi - Quasi-local mass and geometry of scalar curvature
Quasi-local mass is a basic notion in General Relativity. Geometrically, it can be regarded as a geometric quantity of a boundary of a 3-dimensional compact Riemannian manifold. Usually, it is in terms of area and mean curvature of the boundary. It is interesting to see that some of quasi
From playlist Not Only Scalar Curvature Seminar
Intrinsic Curvature and Singularities
Positively, negatively, and infinitely curved space explained. Covers Ricci scalar (scalar curvature) and Gaussian curvature. Useful for Einstein's General Theory of Relativity. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
Physics 2 - Motion In One-Dimension (1 of 22) Definition
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the definition vector and the difference between a scalar and vector.
From playlist MOST POPULAR VIDEOS
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4
Calculus 3: Integration - Equations of Lines & Planes (10 of 27) Plane - General Scalar Equation
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the general scalar equation of a plane in 3-D space. Next video in the series can be seen at: https://youtu.be/tHqu-bpUlho
From playlist CALCULUS 3 CH 2 LINES & PLANES
Minkowski Space-Time: Spacetime in Special Relativity
Includes discussion of the space-time invariant interval and how the axes for time and space transform in Special Relativity.
From playlist Physics
16/11/2015 - Robert Wald - Dynamic and Thermodynamic Stability of Black Holes and Black Branes
https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-robertwald.pdf Abstract. I describe work with Stefan Hollands that establishes a general criterion for the dynamical stability of black holes and black branes in arbitrary spacetime dimensions with respect to axisymmetric perturb
From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
Lattice Supersymmetric Field Theories (Lecture 1) by David Schaich
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
Philippe G LeFloch - Weakly regular spacetimes with T2 symmetry
I will discuss the initial value problem for the Einstein equations and present results concerning the existence and asymptotic behavior of spacetimes, when the initial data set is assumed to be T2 symmetric and satisfies weak regularity conditions so that the spacetimes may exhibit impul
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Matrix Theory: Let T: R^4 to R^4 be the linear transformation that sends v to Av where A = [0 0 0 -1 \ 1 0 0 0 \ 0 1 0 -2 \ 0 0 1 0]. Find all subspaces invariant under T.
From playlist Matrix Theory
20/11/2015 - Georges Ellis - The Steps Along The Way Whereby Einstein’s General Theory...
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From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
Spacetime positive mass theorem - Lan-Hsuan Huang
Workshop on Geometric Functionals: Analysis and Applications Topic: Spacetime positive mass theorem Speaker: Lan-Hsuan Huang Affiliation: University of Connecticut; von Neumann Fellow, School of Mathematics Date: March 5, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
A New Poisson Bracket Identity for Gravity by Madhavan Varadarajan
Bangalore Area String Meeting URL: http://www.icts.res.in/discussion_meeting/BASM2016/ DATES: Monday 25 Jul, 2016 - Wednesday 27 Jul, 2016 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore DESCRIPTION: This meeting is designed to bring together string theorists working in the Bangalore
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What Every Physicist Should Know About String Theory: Edward Witten
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From playlist Strings 2015 conference
MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx Cosmology and cosmological spacetimes. This is the first spacetime we compu
From playlist MIT 8.962 General Relativity, Spring 2020
Progress and Prospects of Lattice Supersymmetry by David Schaich
PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)
The Hilbert--Einstein functional and the Sasaki-Futaki invariant - Eveline Legendre [2016]
Abstract: I will show how the Hilbert--Einstein functional detects the Reeb vector fields having a vanishing transversal Futaki invariant and so that it is an obstruction to the existence of constant scalar curvature Sasaki metrics. I will also discuss the relation of this functional with
From playlist Mathematics
Is space-time fragmented, segmented into quantized bits of information, or causal sets? Or is space-time smooth and continuous, with curves, bends, and warps; just as Einstein had predicted? Is what we call space-time even part of objective reality or is it just a mathematical construct
From playlist Science
Consistent quantum histories and the probability for singularity resolution by Parampreet Singh
21 November 2016 to 10 December 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Quantum Theory has passed all experimental tests, with impressive accuracy. It applies to light and matter from the smallest scales so far explored, up to the mesoscopic scale. It is also a necessary ingredie
From playlist Fundamental Problems of Quantum Physics