In
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 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 prob ...
(a particular
boundary value problem of the theory of
partial differential equations). One side of the horizon contains closed
space-like geodesics and the other side contains closed
time-like geodesics. The concept is named after
Augustin-Louis Cauchy.
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 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 technolog ...
original series ''
Solos'', the character Leah solves time travel with "the Cauchy horizon", which is central to the episode.
Related
*
Augustin-Louis Cauchy
*
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 ob ...
References
External links
On Crossing the Cauchy Horizon
Theory of relativity
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