Schwarzschild black hole

Schwarzschild black hole
Name	Schwarzschild black hole

Schwarzschild black hole

Introduction

A Schwarzschild black hole is the spherically symmetric, non-rotating, uncharged exact solution of Albert Einstein's field equations in General relativity, discovered by Karl Schwarzschild; it is foundational to studies by Albert Einstein, Subrahmanyan Chandrasekhar, Roger Penrose, Stephen Hawking, and John Wheeler and appears in contexts ranging from the Schwarzschild metric derivation to analyses used in Event Horizon Telescope observations and theoretical work at institutions like Princeton University, Cambridge University, and Institute for Advanced Study.

Schwarzschild metric

The Schwarzschild metric is expressed in Schwarzschild coordinates and was first obtained by Karl Schwarzschild while corresponding with Max von Laue and Albert Einstein; its line element defines spacetime curvature crucial to solutions studied by Roy Kerr and compared with metrics such as the Reissner–Nordström metric and the Kerr–Newman metric. The metric components g_tt and g_rr produce the characteristic Schwarzschild radius derived from Newtonian limits used by Isaac Newton in historical analogies and refined in work by Arthur Eddington and Leopold Infeld.

Event horizon and singularity

The solution features an event horizon at the Schwarzschild radius and a central curvature singularity; analyses by Roger Penrose on singularity theorems and by Stephen Hawking on global structure formalized their causal nature. Studies by Subrahmanyan Chandrasekhar and mathematical formalism from André Lichnerowicz and Yakov Zel'dovich contrast coordinate singularities removable by transformations used by David Finkelstein and genuine singularities addressed in proofs by Penrose and Hawking.

Geodesics and particle motion

Test-particle and photon geodesics in the Schwarzschild spacetime were computed in classical treatments by Arthur Eddington, Karl Schwarzschild, and later by Chandrasekhar in his monograph; bound orbits, precession of perihelion measured in the Mercury problem, and light deflection explored during the 1919 solar eclipse expedition connect observational tests by Arthur Eddington and theoretical work by Albert Einstein and Isaac Newton. Analysis of timelike and null geodesics uses techniques developed at Cambridge University and in lectures by John Wheeler and Wald, Robert M..

Thermodynamics and Hawking radiation

Thermodynamic properties, including a temperature and entropy, were derived by Stephen Hawking and Jacob Bekenstein leading to the Bekenstein–Hawking entropy relation that connects with quantum field theory results investigated at University of Cambridge, Harvard University, and CERN. Hawking radiation calculations tie into semiclassical analyses by Gerard 't Hooft, Leonard Susskind, and debates involving the Information loss paradox discussed at conferences like those at the Perimeter Institute and KITP.

Extensions and coordinate systems

Extensions and alternate coordinate charts for the Schwarzschild solution include Kruskal–Szekeres coordinates introduced by Martin Kruskal and George Szekeres, Eddington–Finkelstein coordinates related to work by Arthur Eddington and David Finkelstein, and isotropic coordinates used in comparisons by Einstein and Hermann Weyl; these facilitate maximal analytic extension studied in seminars at Princeton University and in textbooks by Misner, Thorne, Wheeler.

Physical and astrophysical implications

Schwarzschild black holes serve as idealized models for compact objects in astrophysics, informing models of stellar collapse analyzed by Subrahmanyan Chandrasekhar and observational programs such as LIGO and the Event Horizon Telescope; comparative studies include rotating solutions by Roy Kerr and charged solutions by Hans Reissner and Gunnar Nordström in contexts explored by researchers at Caltech, MIT, and Max Planck Institute for Gravitational Physics.

Historical development and derivation

The derivation by Karl Schwarzschild emerged during World War I in correspondence with Albert Einstein and was contextualized historically by subsequent commentators including Hermann Weyl, Arthur Eddington, and historians at Cambridge University and Princeton University; later rigorous formulations and pedagogical expositions were provided by Subrahmanyan Chandrasekhar, John Wheeler, and textbook authors like Robert Wald and Misner, Thorne, Wheeler.

Category:Black holes