Spacetime singularity, singular bounds and compactness for solutions of the Poisson's equation

• Carlos Cesar Aranda ^[1]
  1. [1] Blue Angel Navire research laboratory
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 17, Nº. 2, 2015, págs. 97-122
• Idioma: inglés
• DOI: 10.4067/S0719-06462015000200007
• Enlaces
  • Texto completo
• Resumen
  • español

    Un hoyo negro es una región espacio-temporal en cuyo interior hay una estructura llamada singularidad espacio-temporal cuya descripción científica es difícil de encontrar, y que depende de la áun inexistente teoría de la gravedad cuántica. Usando el clásico principio de comparación débil, aquí probamos nuevas cotas, resultados de compacidad y fenómenos de concentración en la teoría de potenciales Newtonianos de distribuciones de soporte compacto, que dan una teoría matemática adecuada de la singularidad espacio-temporal. Derivamos una rigurosa renormalización de la ley de gravitación Newtoniana usando análisis funcional no lineal y tenemos un contundente conjunto de datos de observaciones astronómicas que apoyan nuestra nueva ecuación. Este marco general introduce una nueva forma de problema mal-puesto con una interpretación física muy simple.

  • English

    A black hole is a spacetime region in whose interior lies a structure known as a spacetime singularity whose scientific description is profoundly elusive, and which depends upon the still missing theory of quantum gravity. Using the classical weak comparison principle we are able to obtain new bounds, compactness results and concentration phenomena in the theory of Newtonian potentials of distributions with compact support which gives a suitable mathematical theory of spacetime singularity. We derive a rigorous renormalization of the Newtonian gravity law using nonlinear functional analysis and we have a solid set of astronomical observations supporting our new equation. This general setting introduces a new kind of ill posed problem with a very simple physical interpretation.

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