Quasi-normal modes in non-perturbative quantum gravity

Author(s)

Koshelev, Alexey S., Li, Chenxuan, Tokareva, Anna

Abstract

Non-pertrubative quantum gravity formulated as a unitary four-dimensional theory suggests that certain amount of non-locality, such as infinite-derivative operators, can be present in the action, in both cases of Analytic Infinite Derivative gravity and Asymptotically Safe gravity. Such operators lead to the emergence of Background Induced States on top of any background deviating from the flat spacetime. Quasi-normal modes (QNMs) corresponding to these excitations are analyzed in the present paper with the use of an example of a static nearly Schwarzschild black hole. We mainly target micro-Black Holes, given that they are strongly affected by the details of UV completion for gravity, while real astrophysical black holes can be well described in EFT framework. We find that frequencies of QNMs are deviating from those in a General Relativity setup and, moreover, that the unstable QNMs are also possible. This leads to the necessity of constraints on gravity modifications or lower bounds on masses of the stable micro-Black Holes or both.

Figures

Integration contour of the inverse Fourier transform (\ref{fouriertransform}) in the case of a complex mass $\mu^2=a^2$ where black dots denotes QNMs and the red line denotes the branch cut

Integration contour of the inverse Fourier transform (\ref{fouriertransform}) in the case of a complex mass $\mu^2=a^2$ where black dots denotes QNMs and the red line denotes the branch cut


Integration contour of the inverse Fourier transform (\ref{fouriertransform}) in the asymptotic regime $r\to\infty$ when $\mu^2\to a^2$ and $a$ is real, and where black dots denotes QNMs and the red line denotes the branch cut

Integration contour of the inverse Fourier transform (\ref{fouriertransform}) in the asymptotic regime $r\to\infty$ when $\mu^2\to a^2$ and $a$ is real, and where black dots denotes QNMs and the red line denotes the branch cut


QNM for $a=0$ and $l=0$ with varying pure imaginary parameters $b$ (top left), $c$ (top right), and $d$ (bottom) where the color of points represents the value of the corresponding varying parameter as shown in the bar to the right of each plot

QNM for $a=0$ and $l=0$ with varying pure imaginary parameters $b$ (top left), $c$ (top right), and $d$ (bottom) where the color of points represents the value of the corresponding varying parameter as shown in the bar to the right of each plot


QNM for $a=0$ and $l=0$ with varying pure imaginary parameters $b$ (top left), $c$ (top right), and $d$ (bottom) where the color of points represents the value of the corresponding varying parameter as shown in the bar to the right of each plot

QNM for $a=0$ and $l=0$ with varying pure imaginary parameters $b$ (top left), $c$ (top right), and $d$ (bottom) where the color of points represents the value of the corresponding varying parameter as shown in the bar to the right of each plot


QNM for $a=0$ and $l=0$ with varying pure imaginary parameters $b$ (top left), $c$ (top right), and $d$ (bottom) where the color of points represents the value of the corresponding varying parameter as shown in the bar to the right of each plot

QNM for $a=0$ and $l=0$ with varying pure imaginary parameters $b$ (top left), $c$ (top right), and $d$ (bottom) where the color of points represents the value of the corresponding varying parameter as shown in the bar to the right of each plot


Fundamental mode for varying $c$ (left) and $d$ (right), with $a=0,~0.15,~0.3$

Fundamental mode for varying $c$ (left) and $d$ (right), with $a=0,~0.15,~0.3$


Fundamental mode for varying $c$ (left) and $d$ (right), with $a=0,~0.15,~0.3$

Fundamental mode for varying $c$ (left) and $d$ (right), with $a=0,~0.15,~0.3$


The first overtone with $c=2$ and increasing $a$

The first overtone with $c=2$ and increasing $a$


Stability region of $a$ and $c$ (left), $d$ (right)

Stability region of $a$ and $c$ (left), $d$ (right)


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