Search results for "RELATIVITY"
showing 3 items of 1213 documents
Remembering an Era: Roger Penrose’s Paper on “Gravitational Collapse: The Role of General Relativity”
2018
Back in the 1960s, Einstein’s theory of general relativity re-emerged as a field of important research activity. Much of the impetus behind this resurgence came from powerful new mathematical ideas that Roger Penrose and Stephen Hawking applied to prove general singularity theorems for global space-time structures. Their results stirred the imaginations of astrophysicists and gave relativistic cosmology an entirely new research agenda. A decade later, black holes and the big hang model were on the tongues of nearly everyone who followed recent trends in science. As popular expositions dealing with quasars, pulsars, and the geometry of black holes began to appear in magazines and textbooks, …
Anomaly-free scale symmetry and gravity
2023
In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmetry. Besides that, the fundamental theory must include gravity, whereas all known extensions of the conformal invariance to the curved space-time suffer from the Weyl anomaly. We show that conformal symmetry can be made free from the quantum anomaly only in the flat space. The presence of gravity would reduce the global symmetry group of the fundamental theory to the scale invariance only. We discuss how the effective Lagrangian respecting …
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.