physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, a Cauchy horizon is a

light-like In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...

boundary of the domain of validity of a

Cauchy problem A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value proble ...

(a particular

boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

of the theory of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s). One side of the horizon contains closed

space-like In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why diffe ...

geodesic In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...

s and the other side contains closed

time-like In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...

geodesics. The concept is named after

Augustin-Louis Cauchy Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He ...

. Under the averaged weak energy condition (AWEC), Cauchy horizons are inherently unstable. However, cases of AWEC violation, such as the

Casimir effect In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pr ...

caused by periodic boundary conditions, do exist, and since the region of spacetime inside the Cauchy horizon has

closed timelike curves In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Sto ...

it is subject to periodic boundary conditions. If the spacetime inside the Cauchy horizon violates AWEC, then the horizon becomes stable and frequency boosting effects would be canceled out by the tendency of the spacetime to act as a divergent lens. Were this conjecture to be shown empirically true, it would provide a counter-example to the strong cosmic censorship conjecture. In 2018, it was shown that the spacetime behind the Cauchy horizon of a charged, rotating black hole exists, but is not

smooth Smooth may refer to: Mathematics * Smooth function, a function that is infinitely differentiable; used in calculus and topology * Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions * Smooth algebrai ...

, so the strong cosmic censorship conjecture is false. The simplest example is the internal horizon of a Reissner–Nordström black hole.

In popular media

In the 2020 film ''

Palm Springs Palm Springs (Cahuilla: ''Séc-he'') is a desert resort city in Riverside County, California, United States, within the Colorado Desert's Coachella Valley. The city covers approximately , making it the largest city in Riverside County by land ...

'', the character Sarah mentions the Cauchy horizon as she formulates a plan to escape a

time loop The time loop or temporal loop is a plot device in fiction whereby characters re-experience a span of time which is repeated, sometimes more than once, with some hope of breaking out of the cycle of repetition. The term "time loop" is sometimes us ...

. In the pilot episode of 2021

Amazon Amazon most often refers to: * Amazons, a tribe of female warriors in Greek mythology * Amazon rainforest, a rainforest covering most of the Amazon basin * Amazon River, in South America * Amazon (company), an American multinational technology c ...

original series '' Solos'', the character Leah solves time travel with "the Cauchy horizon", which is central to the episode.

Event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...

References

External links

On Crossing the Cauchy Horizon
Theory of relativity {{relativity-stub

In popular media

Related

References

External links