In general relativity, a spacetime is said to be static if it does not change over time and is also irrotational. It is a special case of a stationary spacetime, which is the geometry of a stationary spacetime that does not change in time but can rotate. Thus, the Kerr solution provides an example of a stationary spacetime that is not static; the non-rotating Schwarzschild solution is an example that is static. Formally, a spacetime is static if it admits a global, non-vanishing, timelike Killing vector field which is irrotational, i.e., whose orthogonal distribution is involutive. (Note that the leaves of the associated foliation are necessarily space-like hypersurfaces.) Thus, a static spacetime is a stationary spacetime satisfying this additional integrability condition. These spacetimes form one of the simplest classes of Lorentzian manifolds. Locally, every static spacetime looks like a standard static spacetime which is a Lorentzian warped product R S with a metric of the form , where R is the real line, is a (positive definite) metric and is a positive function on the Riemannian manifold S. In such a local coordinate representation the Killing field may be identified with and S, the manifold of -trajectories, may be regarded as the instantaneous 3-space of stationary observers. If is the square of the norm of the Killing vector field, , both and are independent of time (in fact ). It is from the latter fact that a static spacetime obtains its name, as the geometry of the space-like slice S does not change over time. (Wikipedia).
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From playlist Science Unplugged: Special Relativity
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
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From playlist Science Unplugged: General Relativity
What is Einstein's cosmological constant?
Einstein's cosmological constant resulted from a prejudice regarding how the universe should behave. Brian Greene explains why the great physicist edited his equations to include it. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.w
From playlist Science Unplugged: General Relativity
If the universe is spatially infinite, what can we say about reality...
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From playlist Science Unplugged: Cosmology
What is the difference between Special and General Relativity?
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From playlist Science Unplugged: General Relativity
What the HECK is Time?! (in Einstein’s Relativity)
In special and general relativity, we imagine time as just another dimension of space in something called "spacetime." Unfortunately, this picture leads to questions about determinism and free will. Is that really how it works? What does the concept of spacetime actually say about the univ
From playlist Gravity as Spacetime Curvature
Learn more at https://www.brilliant.org/spacetime PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE Black holes are crazy enough on their own – but crash two together and you end up with a roiling blob of inescapable space
From playlist Space Time!
What is General Relativity? Lesson 36: Introduction to the Einstein Equation
What is General Relativity? Lesson 36: Introduction to the Einstein Equation This lesson sets the stage for our attack on the Einstein equation. NOTE and ERATA: At 11:26 I called the Ricci Tensor the "Riemann Curvature Tensor" by mistake! R_ab is the "Ricci tensor"! The paper by Kostic
From playlist What is General Relativity?
Stability of the spacetime positive mass theorem in spherical symmetry - Marcus Khuri
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From playlist Mathematics
Are Space and Time An Illusion?
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From playlist Space Time!
Why Time and Space swap in a Black Hole
What is the difference between time and space? Why do time and space swap roles in a black hole? What is a Penrose diagram? All these answers in 12 minutes! 0:00 - Light cones 2:45 - Space and time 4:56 - General relativity 6:20 - Black holes 10:13 - Collapse diagrams This video is narra
From playlist Astrophysics and Cosmos
Can You Believe It? #36 What is Space (2 of TBD) The Speed of Light
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn how was the speed of light calculated by James Maxwell. Previous video in this series can be seen at: https://youtu.be
From playlist CAN YOU BELIEVE IT?
Christian Gérard - Introduction to field theory on curved spacetimes (Part 4)
The aim of these lectures is to give an introduction to quantum field theory on curved spacetimes, from the point of view of partial differential equations and microlocal analysis. I will concentrate on free fields and quasi-free states, and say very little on interacting fields or perturb
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Teach Astronomy - Fine Tuning in Cosmology
http://www.teachastronomy.com/ One of the very difficult things to explain in standard cosmology is the flatness of space. Remember that the early universe was small and dense, and space-time was actually curved and knotted in the quantum era so the current flatness of space is an unusual
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
Secrets of the Cosmic Microwave Background
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From playlist The Cosmic Microwave Background Explained!
Can You Trust Your Eyes in Spacetime?
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From playlist Space Time!
20. Spherical compact sources I
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 Spherically symmetric and compact bodies. We develop the spacetime of a sph
From playlist MIT 8.962 General Relativity, Spring 2020
Einstein's Biggest Blunder, Explained
Thanks to Brilliant for supporting MinutePhysics. Get 20% off a premium subscription at https://brilliant.org/MinutePhysics/ This video is about how Albert Einstein made a mistake when applying the Field Equations of General Relativity to cosmology (in particular, to a static, constant de
From playlist MinutePhysics
Special Relativity: 2 - Spacetime Diagrams
An introduction to spacetime diagrams which are a valuable tool used to understand special relativity. The second in a series on special and general relativity. Let us know what you think of these videos by filling out our short survey at http://tinyurl.com/astronomy-pulsar. Thank you!
From playlist Special Relativity