Titlebook: Black Hole Information and Thermodynamics; Dieter Lüst,Ward Vleeshouwers Book 2019 The Author(s), under exclusive license to Springer Natu

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https://doi.org/10.1007/978-3-642-91095-1onsider the laws of black hole mechanics as thermodynamical statements. This means that we will define a temperature and an entropy for our black holes. In thermodynamics, we may consider e.g. the grand canonical ensemble, where the system is characterized by quantities ., nammely chemical potential

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Carl Claus,Karl Grobben,Alfred Kühn [8]). These were considered by many to be mere surface similarities, until Hawking showed that semiclassical black holes emit thermal radiation at inverse temperature . (Hawking, Commun Math Phys, 43:199–220, 1975, [9]). That is, black holes seem to be truly thermodynamic objects which radiate at a

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Lehrbuch der angewandten Fluidmechanik99–104, 1996, [15]). We will look at the construction of D- and p-branes, the compactification of superstring theories, and the construction of black holes from charges associated to the branes. Using a stringy version of the electromagnetic duality, we can express the black hole entropy in terms of

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Special Relativity,tial distances (as well as temporal intervals) invariant. For example, in two spatial dimensions with coordinates (.,?.), the squared distance . is invariant under rotations, which are of the form . The invariance of spatial (Euclidean) distance is then given by ..

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Tortuous

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Black Holes,is compressed into a small region of space-time. It is characterized by a curvature singularity at the origin which is ‘screened’ to outside observers by a coordinate singularity at finite radial distance. This coordinate singularity is known as the ., which will be seen to exhibit deep connections

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,Kruskal–Szekeres Coordinates and Geodesics of the Schwarzschild Black Hole,d speed of light .. The space-time has an exterior and an interior region characterized by . and . and denoted by . and ., respectively. Today we will consider a new coordinate system which will allow us to double the space-time and find copies of regions . and ..

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Black Hole Mechanics and Thermodynamics,act that if we throw an object with some entropy into a black hole, the entropy of the total system may not decrease, hence the entropy of a black hole must grow when we throw an object into it. Such thought experiments can be used to derive the laws of black hole mechanics, which turn out to be pro

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Black Holes and Entropy,onsider the laws of black hole mechanics as thermodynamical statements. This means that we will define a temperature and an entropy for our black holes. In thermodynamics, we may consider e.g. the grand canonical ensemble, where the system is characterized by quantities ., nammely chemical potential