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Cauchy horizon
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem
Cauchy problem

The Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain side conditions which are given on a hypersurface in the domain....
 (a particular boundary value problem
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 restraints, called the boundary conditions....
 of the theory of partial differential equation
Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a Relation involving an unknown Function of several independent variables and its partial derivatives with respect to those variables....
s). One side of the horizon contains closed space-like geodesic
Geodesic

In mathematics, a geodesic [jee-uh-des-ik, -dee-sik] is a generalization of the notion of a "Line " to "manifolds".In presence of a Metric , geodesics are defined to be the shortest path between points on the space....
s and the other side contains closed time-like geodesics.

Waves traveling in Misner space
Misner space

Misner space is an abstract mathematical spacetime, discovered by Charles Misner of the University of Maryland, College Park. It is also known as the Lorentzian manifold orbifold....
 approaching a Cauchy horizon would receive a frequency boost proportional to

each time they pass through the identification world line
World line

In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" by the time dimension, and typically encompasses a large area of spacetime wherein perception straight paths are recalculated to...
.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem
Cauchy problem

The Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain side conditions which are given on a hypersurface in the domain....
 (a particular boundary value problem
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 restraints, called the boundary conditions....
 of the theory of partial differential equation
Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a Relation involving an unknown Function of several independent variables and its partial derivatives with respect to those variables....
s). One side of the horizon contains closed space-like geodesic
Geodesic

In mathematics, a geodesic [jee-uh-des-ik, -dee-sik] is a generalization of the notion of a "Line " to "manifolds".In presence of a Metric , geodesics are defined to be the shortest path between points on the space....
s and the other side contains closed time-like geodesics.

Waves traveling in Misner space
Misner space

Misner space is an abstract mathematical spacetime, discovered by Charles Misner of the University of Maryland, College Park. It is also known as the Lorentzian manifold orbifold....
 approaching a Cauchy horizon would receive a frequency boost proportional to

each time they pass through the identification world line
World line

In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" by the time dimension, and typically encompasses a large area of spacetime wherein perception straight paths are recalculated to...
. As this happens infinitely many times while approaching the horizon, the stress-energy tensor
Stress-energy tensor

The stress-energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress of Newtonian physics....
 diverges at the horizon. Presumably, this prevents spacetime
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
 from developing closed time-like curves that would otherwise be feasible.

Under the averaged weak energy condition
Energy condition

In theory of relativity classical field theory of gravitation, particularly general relativity, an energy condition is one of various alternative conditions which can be applied to the matter content of the theory, when it is either not possible or desirable to specify this content explicitly....
 (AWEC), Cauchy horizons are inherently unstable. However, cases of AWEC violation, such as the Casimir effect
Casimir effect

In physics, the Casimir effect and the Casimir-Polder force are physical force arising from a quantum field theory. The typical example is of two electric charge metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field....
, do exist. If we can assume that 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
Cosmic censorship hypothesis

The weak and the strong Cosmic Censorship Hypotheses are two mathematical conjectures about the structure of gravitational singularity arising in general relativity....
 conjecture.

The simplest example is the internal horizon of a Reissner-Nordström black hole.

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