Estudo teórico mostra que os buracos negros de Kerr poderiam amplificar a nova física
Os buracos negros são regiões do espaço caracterizadas por uma gravidade extremamente forte, que impede que toda a matéria e ondas eletromagnéticas escapem dele. Estes fascinantes corpos cósmicos têm sido o foco de inúmeros estudos...
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)
Um buraco negro em rápida rotação. Crédito: Agência Espacial Europeia, 2013.
Os buracos negros são regiões do espaço caracterizadas por uma gravidade extremamente forte, que impede que toda a matéria e ondas eletromagnéticas escapem dele. Estes fascinantes corpos cósmicos têm sido o foco de inúmeros estudos de investigação, mas as suas intrincadas nuances físicas ainda não foram totalmente descobertas.
Pesquisadores da Universidade da Califórnia – Santa Bárbara, da Universidade de Varsóvia e da Universidade de Cambridge realizaram recentemente um estudo teórico focado em uma classe de buracos negros conhecidos como buracos negros extremos de Kerr, que são buracos negros estacionários sem carga com um horizonte interno e externo coincidentes. O seu artigo, publicado na Physical Review Letters , mostra que as características únicas destes buracos negros podem torná-los “amplificadores” ideais de física nova e desconhecida .
“Esta pesquisa tem origem em um projeto anterior iniciado durante minha visita à UC Santa Bárbara”, disse Maciej Kolanowski, um dos pesquisadores que realizou o estudo. "Comecei a discutir buracos negros muito frios (os chamados extremos) com Gary Horowitz (UCSB) e Jorge Santos (em Cambridge). Logo percebemos que, na verdade, os buracos negros extremos genéricos parecem muito diferentes do que se acreditava anteriormente."
Em seu artigo anterior, Kolanowski, Horowitz e Santos mostraram que na presença de uma constante cosmológica os buracos negros extremos são afetados por forças de maré infinitas. Isto significa que se os seres vivos caíssem no buraco negro, seriam esmagados pela gravidade antes de se aproximarem, mesmo que remotamente, do centro do buraco negro. No entanto, a equipa mostrou que se a constante cosmológica for zero, como se supõe que seja em muitos cenários astrofísicos, este efeito desaparece.
“A faísca para o artigo atual surgiu no Gravity Lunch semanal da UC Santa Barbara”, explicou Grant Remmen. "Conversando com Horowitz depois de uma palestra sobre seu trabalho sobre singularidades no horizonte de buracos negros, perguntei se outros efeitos poderiam dar origem a tais fenômenos. Meu trabalho anterior sobre teorias de campos efetivos (EFTs), particularmente o desenvolvimento de modelos físicos com correções quânticas, me deu uma ideia. Conversando com Horowitz, me perguntei se os termos de derivadas superiores em uma EFT gravitacional (ou seja, correções quânticas para as equações de Einstein) poderiam eles próprios levar a singularidades nos horizontes de buracos negros extremos."
Depois que Remmen compartilhou sua ideia com Horowitz, eles iniciaram uma colaboração com Kolanowski e Santos, com o objetivo de testar essa ideia por meio de uma série de cálculos. Em seus cálculos, os pesquisadores consideraram a gravidade de Einstein acoplada às suas principais correções quânticas.
“As equações de Einstein são lineares no tensor de Riemann, um objeto matemático que descreve a curvatura do espaço-tempo”, explicou Remmen. "Em três dimensões espaciais, as principais correções para Einstein são termos cúbicos (terceira potência) e quárticos (quarta potência) na curvatura. Como a curvatura é uma medida de derivadas da geometria do espaço-tempo, tais termos são chamados de 'derivada superior termos.' Calculámos o efeito destes termos de derivadas superiores em buracos negros de rotação rápida."
Os buracos negros extremos giram a uma taxa máxima possível correspondente ao horizonte movendo-se à velocidade da luz. Os cálculos dos investigadores mostraram que as correções EFT de derivadas superiores de buracos negros extremos tornam os seus horizontes singulares, com forças de maré infinitas. Isto contrasta fortemente com os buracos negros típicos, que têm forças de maré finitas que só se tornam infinitas no centro do buraco negro.
"Surpreendentemente, as correções EFT fazem a singularidade saltar do centro do buraco negro até o horizonte, onde você não esperaria que estivesse", disse Remmen. "O valor do coeficiente na frente de um determinado termo EFT - as 'ajustes do dial' nas leis da física - são ditados pelos acoplamentos e tipos de partículas que estão presentes em altas energias e distâncias curtas. Nesse sentido, os coeficientes EFT são sensíveis à nova física."
Kolanowski, Horowitz, Remmen e Santos também descobriram que a força da divergência nas marés no horizonte dos buracos negros extremos, e a possível ocorrência de singularidade das marés, depende fortemente dos coeficientes EFT. Os resultados dos seus cálculos sugerem, portanto, que a geometria do espaço-tempo perto do horizonte destes buracos negros é sensível à nova física a energias mais elevadas.
“Curiosamente, esta singularidade inesperada está presente nos valores destes coeficientes EFT gerados pelo Modelo Padrão da física de partículas”, disse Remmen.
"Nossos resultados são surpreendentes, pois implicam que a descrição da física de baixa energia pode falhar em uma situação em que você não esperaria que isso acontecesse. Na física, geralmente há uma sensação de 'dissociação' entre diferentes escalas de distância. Para por exemplo, você não precisa conhecer os detalhes das moléculas de água para descrever as ondas usando a hidrodinâmica. No entanto, para buracos negros em rotação rápida, é exatamente isso que acontece: a EFT de baixa energia se desfaz no horizonte."
No geral, os cálculos realizados por esta equipa de investigadores sugerem a promessa de buracos negros extremos de Kerr para sondar novos fenómenos físicos. Embora o horizonte destes buracos negros possa ser muito grande, não se esperava que tivesse uma curvatura infinitamente grande (ou seja, forças de maré infinitas) na EFT. Seus resultados mostram que sim.
“Em trabalhos futuros, estamos interessados em explorar se as singularidades podem ser resolvidas pela física ultravioleta”, acrescentou Remmen. "Uma questão premente é se a sensibilidade do horizonte à nova física persiste até à escala de Planck, ou se o horizonte 'suaviza' na escala de curta distância associada ao EFT. Estamos também à procura de outras situações em quais efeitos de curta distância podem aparecer inesperados em grandes distâncias."
Mais informações: Gary T. Horowitz et al, Extremal Kerr Black Holes as Amplifiers of New Physics, Physical Review Letters (2023). DOI: 10.1103/PhysRevLett.131.091402
Informações do periódico: Cartas de Revisão Física