{"title":"The Prediction and Interpretation of Singularities and Black Holes: From Einstein and Schwarzschild to Penrose and Wheeler","authors":"Dennis Lehmkuhl","doi":"10.1007/s00016-025-00331-2","DOIUrl":null,"url":null,"abstract":"<div><p>The Schwarzschild solution was the first exact solution to Einstein’s 1915 field equations, found by Karl Schwarzschild as early as 1916. And yet, physicists, mathematicians and philosophers have struggled for decades with the interpretation of the Schwarzschild solution and the two singularities appearing in it when it is written in polar coordinates. This article distinguishes between eight different ways in which the two singularities have been interpreted between 1916 and the late 1960s, when Penrose’s first singularity theorem shed new and lasting light on the interpretation of the Schwarzschild solution.</p></div>","PeriodicalId":727,"journal":{"name":"Physics in Perspective","volume":"27 2","pages":"176 - 209"},"PeriodicalIF":0.6000,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00016-025-00331-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics in Perspective","FirstCategoryId":"98","ListUrlMain":"https://link.springer.com/article/10.1007/s00016-025-00331-2","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
The Schwarzschild solution was the first exact solution to Einstein’s 1915 field equations, found by Karl Schwarzschild as early as 1916. And yet, physicists, mathematicians and philosophers have struggled for decades with the interpretation of the Schwarzschild solution and the two singularities appearing in it when it is written in polar coordinates. This article distinguishes between eight different ways in which the two singularities have been interpreted between 1916 and the late 1960s, when Penrose’s first singularity theorem shed new and lasting light on the interpretation of the Schwarzschild solution.
期刊介绍:
Physics in Perspective seeks to bridge the gulf between physicists and non-physicists through historical and philosophical studies that typically display the unpredictable as well as the cross-disciplinary interplay of observation, experiment, and theory that has occurred over extended periods of time in academic, governmental, and industrial settings and in allied disciplines such as astrophysics, chemical physics, and geophysics. The journal also publishes first-person accounts by physicists of significant contributions they have made, biographical articles, book reviews, and guided tours of historical sites in cities throughout the world. It strives to make all articles understandable to a broad spectrum of readers – scientists, teachers, students, and the public at large. Bibliographic Data Phys. Perspect. 1 volume per year, 4 issues per volume approx. 500 pages per volume Format: 15.5 x 23.5cm ISSN 1422-6944 (print) ISSN 1422-6960 (electronic)