On
Space-Time Quasiconcave Solutions of the Heat Equation
It might, if the researchers are lucky enough, offer clues to the nature of
space-time. Could the cosmic fabric be made up of discrete chunks, atoms of space if you like, rather than being continuous, as is assumed by relativity?
An international team of scientists have detected the largest ever black hole collision through the ripples it made in
space-time, Sky News reports.
We introduce a DTN
space-time graph as a networking paradigm for energy based routing and forwarding across swarms of low orbiting CubeSats or equivalent picosatellites.
Space-time finite element methods for parabolic and hyperbolic partial differential equations (PDEs) go back to the 80s and 90s of the last century [3, 4, 21, 26, 27, 60] and have enjoyed a revival during the last couple of years due to the availability of massively parallel computers with thousands or hundred thousands of cores; see, e.g., [1, 2, 5, 6, 37, 38, 40, 41, 46, 47, 48, 56, 57, 58, 59] for some resent mathematical papers related to parabolic problems.
By employing the
space-time presentation and the concept of
space-time window, the problem is further formulated as the pickup and delivery problem with
space-time windows (PDPSW).
Hawking rightly points out that the very act of splitting
space-time into space and time destroys the spirit of GR (general covariance) and therefore not much can be gained from this approach to quantization of gravity.
General relativity (GR) [1] formulates a physical problem in terms of differential equations as a geometric requirement that a
space-time may correspond to a Riemannian manifold as the interaction of matter and gravitation.
Albert Einstein, in his theory of relativity, imagines gravity as an object making a depression or dent on the "surface" of
space-time. To help understand this better, imagine
space-time as a rubber sheet stretched at its four corners.
He described gravity waves like ripples in a pond, the pond being
space-time. Planets, stars and other heavenly bodies have mass that distort
space-time.
Qualitative Insight 1: Energy, mass and
space-time are related.