physics Physics is the scientific study of matter, its Elementary particle, 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 whi ...

, a Cauchy horizon is a

light-like In mathematical physics, the causal structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian manifolds can be classified according to the types of causal structures they admit (''ca ...

boundary of the domain of validity of a Cauchy problem (a particular

boundary value problem In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satis ...

of the theory of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s). One side of the horizon contains closed space-like

geodesic In geometry, a geodesic () is a curve representing in some sense the locally 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 conn ...

s and the other side contains closed

time-like In mathematical physics, the causal structure of a Lorentzian manifold describes the possible Causality (physics), causal relationships between points in the manifold. Lorentzian manifolds can be classified according to the types of causal structu ...

geodesics. The concept is named after

Augustin-Louis Cauchy Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real a ...

. 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 (or Casimir force) is a physical force (physics), force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field (physics), field. The term Casim ...

caused by periodic boundary conditions, do exist, and since the region of spacetime inside the Cauchy horizon has closed timelike curves 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, 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 language, 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 Rivers ...

'', 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 Character (arts), 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. Time loops are co ...

. In the pilot episode of 2021

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

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 outside 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 c ...

References

External links

On Crossing the Cauchy Horizon
General relativity {{relativity-stub

In popular media

Related

References

External links