The Gross–Pitaevskii equations of a static and spherically symmetric condensate of gravitons

Cunillera, Francesc; Germani, Cristiano

doi:10.1088/1361-6382/aab97b

Cited by 14 publications

(15 citation statements)

References 19 publications

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“…The nature of the corresponding fine-grained description is yet unknown owing, of course, to the unavailability of a consistent quantum theory of gravity. Despite this, however, it may be possible to realize a mean field description of the gravitoncondensate picture of the black hole, say, in terms of an appropriate generalization of the Gross-Pitaevskii equation 62,63 . An interesting implication of this, which seems to have not been adequately appreciated previously, is that dynamics of the modes of perturbations of a black hole near the horizon must be described by an appropriate BdG-like equations, as opposed to, say, Eq.…”

Section: Possibility Of a New Kind Of Gravitational Echomentioning

confidence: 99%

New Kind of Echo from Quantum Black Holes

Manikandan,

Rajeev

2021

Preprint

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We propose that a quantum black hole can produce a new kind of late-time gravitational echoes, facilitated by a near-horizon process analogous to Andreev reflection in condensed matter systems. In comparison to the traditional echo scenarios where the near-horizon region is treated as an ordinary reflector, we argue that, consequent to near-horizon gravitational scattering, this region is better described by an Andreev reflector. Such interactions lead to a novel contribution to gravitational echoes with a characteristic phase difference, an effect which is analogous to how Andreev reflections lead to propagating particle-like and hole-like components with a relative phase in certain condensed matter scenarios. Moreover, this novel contribution to the echo signal encodes information about the 'near-horizon quantum state', hence offering a possible new window to probe the quantum nature of black holes.

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Section: Possibility Of a New Kind Of Gravitational Echomentioning

confidence: 99%

New Kind of Echo from Quantum Black Holes

Manikandan,

Rajeev

2021

Preprint

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“…By means of a binding potential, these constituents can superimpose in one particular quantum state, effectively making the compact object a self-gravitating Bose-Einstein condensate (BEC) [26][27][28][29][30][31][32][33], at least to leading order of approximation. Moreover, the virtual gravitons are expected to be marginally bound in this potential well, giving rise to the so-called maximal packing relation…”

Section: Application To Non-singular Bhsmentioning

confidence: 99%

Horizon quantum fuzziness for non-singular black holes

2018

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We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

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“…3, following Ref. [16], we will discuss a method to determine the size of the interior condensate and demonstrate that the generalization to the f (R) gravity again gives us richer results compared to the case of ordinary gravity. Then in Sec.…”

Section: Introductionmentioning

confidence: 98%

“…Working in the static spherically symmetric setup, Cunillera and Germani in Ref. [16] adapted the derivation of the Gross-Pitaevskii (GP) equation for ordinary BEC to this graviton condensate, namely by varying the condensate energy obtained from the Arnowitt-Deser-Misner (ADM) formalism while the number of gravitons is kept fixed. They found that the interior of the condensate is described by the dS spacetime while the exterior is described by the Schwarzschild spacetime, which is analogous to the picture of gravastar explained earlier.…”

Section: Introductionmentioning

confidence: 99%

Effective spacetime geometry of graviton condensates in $f({\mathcal R})$ gravity

Latief,

Akbar,

Gunara

2019

Preprint

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Working in static spherically symmetric setup, recent study has demonstrated that the effective spacetime geometry of a Bose-Einstein condensate of weakly interacting gravitons is analogous to a gravastar, hence providing a bridge between these two attempts in describing the black hole interior. In this paper we make three generalizations: introducing a composite of two graviton condensates so that the exterior spacetime is not necessarily asymptotically flat, working in f (R) gravity, and extending the calculations to higher dimensions. We find that the effective spacetime geometry is again analogous to a gravastar, but the interior can be de Sitter or Anti-de Sitter and the exterior can be Schwarzschild, Schwarzschild-de Sitter, or Schwarzschild-Anti de Sitter, where the cosmological constant for the exterior must be smaller than the one for the interior. These geometries are determined by the modified gravity function f (R), in contrast to previous works where they were selected by hand. We also presented a new possible value for the size of the interior condensate provided a certain restriction is satisfied, which would not be met if we are still working in ordinary gravity with four spacetime dimensions. This restriction can be seen manifested in the behavior of the interior graviton wavelength as a function of spacetime dimension.

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The Gross–Pitaevskii equations of a static and spherically symmetric condensate of gravitons

Cited by 14 publications

References 19 publications

New Kind of Echo from Quantum Black Holes

New Kind of Echo from Quantum Black Holes

Horizon quantum fuzziness for non-singular black holes

Effective spacetime geometry of graviton condensates in $f({\mathcal R})$ gravity

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