Dec 2, 2023 08:45 AM
https://www.quantamagazine.org/a-century...-20231130/
INTRO: Albert Einstein’s general theory of relativity has been wildly successful at describing how gravity works and how it shapes the large-scale structure of the universe. It’s summed up in a saying by the physicist John Wheeler: “Space-time tells matter how to move; matter tells space-time how to curve.” Yet the mathematics of general relativity is also profoundly counterintuitive.
Because its basic equations are so complicated, even the simplest-sounding statements are difficult to prove. For example, it was not until around 1980 that mathematicians proved, as part of a major theorem in general relativity, that an isolated physical system, or space, without any mass in it must be flat.
This left unresolved the question of what a space looks like if it is almost a vacuum, having just a tiny amount of mass. Is it necessarily almost flat?
While it might seem obvious that smaller mass would lead to smaller curvature, things are not so cut and dry when it comes to general relativity. According to the theory, dense concentrations of matter can “warp” a portion of space, making it highly curved. In some cases, this curvature can be extreme, possibly leading to the formation of black holes. This could occur even in a space with small amounts of matter, if it’s concentrated strongly enough.
In a recent paper, Conghan Dong, a graduate student at Stony Brook University, and Antoine Song, an assistant professor at the California Institute of Technology, proved that a sequence of curved spaces with smaller and smaller amounts of mass will eventually converge to a flat space with zero curvature.
This result is a noteworthy advance in the mathematical exploration of general relativity — a pursuit that continues to pay dividends more than a century after Einstein devised his theory. Dan Lee, a mathematician at Queens College who studies the mathematics of general relativity but was not involved in this research, said that Dong and Song’s proof reflects a deep understanding of how curvature and mass interact... (MORE - details)
INTRO: Albert Einstein’s general theory of relativity has been wildly successful at describing how gravity works and how it shapes the large-scale structure of the universe. It’s summed up in a saying by the physicist John Wheeler: “Space-time tells matter how to move; matter tells space-time how to curve.” Yet the mathematics of general relativity is also profoundly counterintuitive.
Because its basic equations are so complicated, even the simplest-sounding statements are difficult to prove. For example, it was not until around 1980 that mathematicians proved, as part of a major theorem in general relativity, that an isolated physical system, or space, without any mass in it must be flat.
This left unresolved the question of what a space looks like if it is almost a vacuum, having just a tiny amount of mass. Is it necessarily almost flat?
While it might seem obvious that smaller mass would lead to smaller curvature, things are not so cut and dry when it comes to general relativity. According to the theory, dense concentrations of matter can “warp” a portion of space, making it highly curved. In some cases, this curvature can be extreme, possibly leading to the formation of black holes. This could occur even in a space with small amounts of matter, if it’s concentrated strongly enough.
In a recent paper, Conghan Dong, a graduate student at Stony Brook University, and Antoine Song, an assistant professor at the California Institute of Technology, proved that a sequence of curved spaces with smaller and smaller amounts of mass will eventually converge to a flat space with zero curvature.
This result is a noteworthy advance in the mathematical exploration of general relativity — a pursuit that continues to pay dividends more than a century after Einstein devised his theory. Dan Lee, a mathematician at Queens College who studies the mathematics of general relativity but was not involved in this research, said that Dong and Song’s proof reflects a deep understanding of how curvature and mass interact... (MORE - details)