Consequences of a minimal length in a pseudo-complex extension of general relativity

Maghlaoui, Leila; Hess, Peter O.

doi:10.1142/s0218271822500687

Cited by 1 publication

(4 citation statements)

References 36 publications

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“…The action of the theory for the Schwarzschild limit is given by

\begin{array}{ll}\kern-1em S& =\int {\sigma}^2\left(l,r\right)\Big\{\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right){\dot{t}}^2\\ {}& \kern1em -\frac{1}{\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right)}{\dot{r}}^2-{r}^2\left({\dot{\theta}}^2+{\sin}^2\theta \kern0.1em {\dot{\phi}}^2\right)\Big\} d\omega, \end{array}

which leads to the equation (Maghlaoui & Hess 2022).

\begin{matrix} lefttrue \\ {((), \frac{italicdr}{d ω})}^{2} = (1 - \frac{2 m}{r} + \frac{B_{4}}{6 r^{4}}) \\ \times [\frac{E^{2}}{σ^{4} false(r false) (1 - \frac{2 m}{r} + - \frac{B_{4}}{6 r^{4}})} - \frac{L^{2}}{σ^{4} false(r false) r^{2}} - \frac{1}{σ^{2} false(r false)}] \\ = E^{2} ... \end{matrix}

…”

Section: Pseudo‐complex Kerr Solution and The Minimal Lengthmentioning

confidence: 99%

“…

{\sigma}^2

as a function in the radial distance in the equatorial plane, for different values of

\alpha

, see Equation (30) of Maghlaoui and Hess (2022).

\alpha =8

is below the critical value (dashed line),

\alpha =\frac{81}{8}

is at the critical value and

\alpha =12

is above the critical value.…”

Section: Pseudo‐complex Kerr Solution and The Minimal Lengthmentioning

confidence: 99%

“…In what follows, we list the form of

{\sigma}^2

for the Schwarzschild case and the Kerr metric (Maghlaoui & Hess 2022):

\begin{array}{ll}{\sigma}_{\mathrm{Schw}\ (1)}^2(r)& =1-\frac{l^2}{c^4}\left|-\kern-0.1em {c}^2\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right){\ddot{t}}^2\right.\\ {}& \kern1em \left.+\kern.2em \frac{1}{\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right)}{\ddot{r}}^2+{r}^2{\ddot{\phi}}^2\right|,\end{array}

and

\begin{matrix} lefttrue \\ σ_{Kerr false(1 false)}^{2} false(r false) & = 1 - \frac{l^{2}}{c^{4}} |c^{2} ((), 1 goodbreak- \frac{Ψ}{r^{2}}) {false(\overset{t}{true} false)}^{2} goodbreak- \frac{r^{2}}{Δ} {false(\overset{r}{true} false)}^{2} \\ goodbreak- ((), ((), r^{2} goodbreak+ α^{2}) goodbreak+ \frac{α^{2} normalΨ}{r^{2}}) false(| \end{matrix}

…”

Section: Pseudo‐complex Kerr Solution and The Minimal Lengthmentioning

confidence: 99%

“…In pcGR, the effects of the minimal length were neglected up to now. Recently, in Maghlaoui & Hess (2022) we have investigated the effects of the minimal length for non‐rotating black holes (Schwarzschild solution). In this contribution, we will resume the approximate influence of the existence of a minimal length on the behavior of the dynamics of a particle near the event horizon and propose an extension to rotating black holes (Kerr solution).…”

Section: Introductionmentioning

confidence: 99%

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The pseudo‐complex General Relativity and effects of a minimal length on the structure of black holes

Maghlaoui

Hess

2022

Astron Nachr

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After resuming some main predictions of the pseudo‐complex General Relativity (pcGR), the effects of a minimal length, on the structure near the event horizon of a Schwarzschild and Kerr black hole, are investigated within the pcGR. It is shown that for small mass black holes there are strong effects, for example, avoiding the accumulation of mass, which might be important in the formation of primordial black holes during the Big Bang. The pcGR adds to the metric a contribution characterized by a parameter α$$ \alpha $$, which has a critical value at which barely an event horizon exists. For macroscopic black holes, these effects vanished for below and above this critical value, but at the critical value effects still persist up to m=10−13$$ m={10}^{-13} $$ cm, though quickly disappearing. For very large mass black holes the minimal length can be safely neglected. The limit between a small and a macroscopic black hole, in units of length, is between 10−15$$ {10}^{-15} $$ cm and 10−13$$ {10}^{-13} $$ cm.

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“…The action of the theory for the Schwarzschild limit is given by

\begin{array}{ll}\kern-1em S& =\int {\sigma}^2\left(l,r\right)\Big\{\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right){\dot{t}}^2\\ {}& \kern1em -\frac{1}{\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right)}{\dot{r}}^2-{r}^2\left({\dot{\theta}}^2+{\sin}^2\theta \kern0.1em {\dot{\phi}}^2\right)\Big\} d\omega, \end{array}

which leads to the equation (Maghlaoui & Hess 2022).

\begin{matrix} lefttrue \\ {((), \frac{italicdr}{d ω})}^{2} = (1 - \frac{2 m}{r} + \frac{B_{4}}{6 r^{4}}) \\ \times [\frac{E^{2}}{σ^{4} false(r false) (1 - \frac{2 m}{r} + - \frac{B_{4}}{6 r^{4}})} - \frac{L^{2}}{σ^{4} false(r false) r^{2}} - \frac{1}{σ^{2} false(r false)}] \\ = E^{2} ... \end{matrix}

…”

Section: Pseudo‐complex Kerr Solution and The Minimal Lengthmentioning

confidence: 99%

“…

{\sigma}^2

as a function in the radial distance in the equatorial plane, for different values of

\alpha

, see Equation (30) of Maghlaoui and Hess (2022).

\alpha =8

is below the critical value (dashed line),

\alpha =\frac{81}{8}

is at the critical value and

\alpha =12

is above the critical value.…”

Section: Pseudo‐complex Kerr Solution and The Minimal Lengthmentioning

confidence: 99%

“…In what follows, we list the form of

{\sigma}^2

for the Schwarzschild case and the Kerr metric (Maghlaoui & Hess 2022):

\begin{array}{ll}{\sigma}_{\mathrm{Schw}\ (1)}^2(r)& =1-\frac{l^2}{c^4}\left|-\kern-0.1em {c}^2\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right){\ddot{t}}^2\right.\\ {}& \kern1em \left.+\kern.2em \frac{1}{\left(1-\frac{2m}{r}+\frac{B_4}{6{r}^4}\right)}{\ddot{r}}^2+{r}^2{\ddot{\phi}}^2\right|,\end{array}

and

\begin{matrix} lefttrue \\ σ_{Kerr false(1 false)}^{2} false(r false) & = 1 - \frac{l^{2}}{c^{4}} |c^{2} ((), 1 goodbreak- \frac{Ψ}{r^{2}}) {false(\overset{t}{true} false)}^{2} goodbreak- \frac{r^{2}}{Δ} {false(\overset{r}{true} false)}^{2} \\ goodbreak- ((), ((), r^{2} goodbreak+ α^{2}) goodbreak+ \frac{α^{2} normalΨ}{r^{2}}) false(| \end{matrix}

…”

Section: Pseudo‐complex Kerr Solution and The Minimal Lengthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The pseudo‐complex General Relativity and effects of a minimal length on the structure of black holes

Maghlaoui

Hess

2022

Astron Nachr

Self Cite

View full text Add to dashboard Cite

show abstract

Consequences of a minimal length in a pseudo-complex extension of general relativity

Cited by 1 publication

References 36 publications

The pseudo‐complex General Relativity and effects of a minimal length on the structure of black holes

The pseudo‐complex General Relativity and effects of a minimal length on the structure of black holes

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