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Lecture# Holography in Classical Gravity

Description

This lecture explores hints of holography in classical black hole thermodynamics, focusing on trapped surfaces, Eddington-Finkelstein coordinates, geodesic congruences, and the four laws of black hole mechanics.

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Related concepts (306)

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X-ray

X-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.

Finite morphism

In algebraic geometry, a finite morphism between two affine varieties is a dense regular map which induces isomorphic inclusion between their coordinate rings, such that is integral over . This definition can be extended to the quasi-projective varieties, such that a regular map between quasiprojective varieties is finite if any point like has an affine neighbourhood V such that is affine and is a finite map (in view of the previous definition, because it is between affine varieties).

Proper morphism

In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces. Some authors call a proper variety over a field k a complete variety. For example, every projective variety over a field k is proper over k. A scheme X of finite type over the complex numbers (for example, a variety) is proper over C if and only if the space X(C) of complex points with the classical (Euclidean) topology is compact and Hausdorff. A closed immersion is proper.

X-ray tube

An X-ray tube is a vacuum tube that converts electrical input power into X-rays. The availability of this controllable source of X-rays created the field of radiography, the imaging of partly opaque objects with penetrating radiation. In contrast to other sources of ionizing radiation, X-rays are only produced as long as the X-ray tube is energized. X-ray tubes are also used in CT scanners, airport luggage scanners, X-ray crystallography, material and structure analysis, and for industrial inspection.

Killing horizon

In physics, a Killing horizon is a geometrical construct used in general relativity and its generalizations to delineate spacetime boundaries without reference to the dynamic Einstein field equations. Mathematically a Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killing vector field (both are named after Wilhelm Killing). It can also be defined as a null hypersurface generated by a Killing vector, which in turn is null at that surface.

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