Summary
The effects of temperature in a theory of general relativity containing higher-derivative terms modulated by a coefficient depending on lnR are studied. The theory contains a false vacuum at a value of the Higgs field close to the Planck mass, and it is shown that the false vacuum cannot exist at temperatures lower than the characteristic mass of the theory. The homogeneous field equations are solved for the case of a static, spherically symmetric gravitational system, finding that the solution corresponds exactly to the Schwarzschild line element. Also considered is the process of temperature-dependent phase transition in the framework of this theory. Reasons are given which support the proposal that black holes could be considered as bubbles of false vacuum, ending with some arguments that seem to prevent the existence of black holes.
Riassunto
Si studiano gli effetti della temperatura in una teoria della relatività generale che contiene termini a derivata piú alta modulati da un coefficiente dipendente da lnR. La teoria contiene un falso vuoto ad un valore del campo di Higgs vicino alla massa di Planck e si mostra che il falso vuoto non può esistere a temperature piú basse della massa caratteristica della teoria. Le equazioni di campo omogenee sono risolte per il caso di un sistema gravitazionale statico a simmetria sferica, e si trova che la soluzione corrisponde esattamente all'elemento di linea di Schwarzschild. Si considera anche il processo della transizione di fase che dipende dalla temperatura nel sistema di questa teoria. Si forniscono ragioni a favore della proposta che i buchi neri possano essere considerati come bolle di falso vuoto, concludendo con alcuni argomenti che sembrano prevenire l'esistenza di buchi neri.
Резюме
Исследуются температурные эффекты в общей теории относительности, содержащей члены высших производных с коэффициентами, зависящими от lnR. Указанная теория содержит ложный вакуум при значении поля Хиггса, близком к массе Планка. Показывается, что ложный вакуум не может существовать при температурах, ниже характеристической массы теопии Уравнения для однородного поля решаются в случае статической сферически симметричной гравитационной системы. Получается, что решение точно соответствует линейному элементу Шварцшильда. В рамках предложенной теории также рассматривают процесс фазового перехода, зависящего от температуры. Приводятся причины, которые подтверждают предположение, что черные дыры можно рассмтривать как пузыри ложного вакуума. Указываются некоторые аргументы, которые не допускают существование черных дыр.
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González-Díaz, P.F. Bubbles of false vacuum in general relativity. Nuov Cim B 98, 37–52 (1987). https://doi.org/10.1007/BF02721456
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DOI: https://doi.org/10.1007/BF02721456