Quasinormal Modes of Slowly-Spinning Horizonless Compact Objects: An Analysis Using the Membrane Paradigm

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Spinning horizonless compact objects, as opposed to black holes, can be differentiated by their unique quasinormal mode (QNM) spectrum, which is influenced by their compactness and reflectivity, properties best analyzed through the membrane paradigm framework.

Samenvatting

Bibliographic Information:

Saketh, M.V.S., & Maggio, E. (2024). Quasinormal modes of slowly-spinning horizonless compact objects. arXiv preprint arXiv:2406.10070v3.

Research Objective:

This paper investigates the quasinormal mode (QNM) spectrum of slowly-spinning horizonless compact objects (HCOs) as a means to distinguish them from black holes. The authors aim to understand the relationship between QNMs, object reflectivity, and the parameters of the membrane paradigm, a framework used to model HCOs.

Methodology:

The authors extend the membrane paradigm to incorporate spin effects to the linear order. They derive boundary conditions for metric perturbations at the membrane surface using the Israel-Darmois junction conditions. These boundary conditions, along with the Regge-Wheeler and Zerilli equations governing perturbations, are used to numerically compute the reflectivity and QNM frequencies of HCOs.

Key Findings:

• The reflectivity of HCOs is controlled by the shear viscosity of the fictitious fluid in the membrane paradigm, with perfectly reflecting objects achieved in the limits of zero and infinite viscosity.
• The presence of spin breaks the isospectrality between axial and polar modes for partially reflecting or non-black hole compactness.
• Increasing spin can lead to instability in some modes of reflective ultracompact objects.
• Spin amplifies deviations from the black hole QNM spectrum as compactness decreases, making spinning HCOs potentially easier to differentiate from black holes than their non-spinning counterparts.

Main Conclusions:

The study demonstrates that the membrane paradigm, extended to include spin, provides a valuable framework for analyzing the QNM spectrum of HCOs. The findings suggest that the spin of these objects plays a crucial role in their detectability through gravitational wave observations, particularly during the ringdown phase.

Significance:

This research contributes to the ongoing effort to understand the nature of compact objects and test the predictions of general relativity. The ability to distinguish HCOs from black holes through their QNM spectrum has significant implications for gravitational wave astronomy and our understanding of gravity in the strong-field regime.

Limitations and Future Research:

The study focuses on the linear-in-spin approximation, which limits its applicability to slowly rotating objects. Future research could extend the analysis to higher orders in spin to capture a wider range of astrophysical scenarios. Additionally, exploring specific models of HCOs and their corresponding membrane parameters would provide more concrete predictions for gravitational wave observations.

Statistieken

The object's radius is located at r0 = r+(1 + ϵ), where ϵ > 0.
For compact objects with Planckian corrections at the horizon scale, ϵ = O(10−40).
For objects whose compactness is comparable to that of a neutron star, ϵ = O(1).
The reflectivity of a compact object with ϵ = 10−10 and η = ηBH, obtained without asymptotic series solutions at infinity and using a nineteenth-order asymptotic series solution in powers of 1/r, differ by less than 0.1% at the frequency Mω = 0.37.

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Quasinormal modes of slowly-spinning horizonless compact objects

by M. V. S. Sak... om arxiv.org 10-10-2024

https://arxiv.org/pdf/2406.10070.pdf

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How might the inclusion of higher-order spin effects alter the QNM spectrum and detectability of horizonless compact objects?

Incorporating higher-order spin effects would lead to significant modifications in the study of QNM spectra and the detectability of horizonless compact objects. Here's how:

Breaking of Isospectrality: While the linear-in-spin approximation suggests a breaking of isospectrality between axial and polar modes for horizonless objects, higher-order spin effects would introduce further deviations. This is because higher-order spin terms couple the axial and polar perturbations in a more intricate way, leading to a richer and more distinct QNM spectrum for each type of compact object.

Shift in QNM Frequencies: Higher-order spin terms would introduce nonlinear corrections to the real and imaginary parts of the QNM frequencies. These shifts would be more pronounced for objects with larger spin values and could potentially be detectable with future GW observatories like the Einstein Telescope or Cosmic Explorer.

New QNM Families: It's possible that new families of QNMs, not present in the linear-in-spin approximation, could emerge due to the nonlinear coupling of perturbations. These new modes might have distinct frequencies and damping times, providing additional signatures for differentiating between black holes and horizonless objects.

Improved Accuracy for Fast-Spinning Objects: The linear-in-spin approximation is inherently limited for objects with high spin values. Including higher-order terms would significantly improve the accuracy of QNM calculations for such objects, allowing for more robust tests of gravity in the strong-field regime.

Enhanced Detectability: The unique deviations in the QNM spectrum due to higher-order spin effects would serve as a more sensitive probe for horizonless compact objects. This is particularly relevant for objects with compactness close to that of black holes, where the differences in the QNM spectrum are subtle and require high-precision measurements.
In summary, incorporating higher-order spin effects is crucial for a complete and accurate characterization of the QNM spectrum of horizonless compact objects. These effects could enhance the detectability of such objects and provide more stringent tests for the existence of horizons in astrophysical objects.

Could alternative theories of gravity, which predict deviations from the Kerr metric, be tested using the QNM signatures of compact objects?

Yes, alternative theories of gravity, particularly those predicting deviations from the Kerr metric, can be effectively tested using the QNM signatures of compact objects. Here's why:

Unique QNM Fingerprints: Each theory of gravity predicts a specific spacetime geometry around compact objects, leading to unique QNM frequencies and damping times. These QNMs act as a "fingerprint" for the underlying theory, allowing us to differentiate between GR and alternative models.

Sensitivity to Strong-Field Gravity: QNMs are generated in the strong gravitational field near compact objects, where deviations from GR are expected to be most prominent. This makes them ideal probes for testing the strong-field regime of gravity, which is difficult to access through other astrophysical observations.

Parametrized Tests: One can perform parametrized tests of gravity by introducing deviations from the Kerr metric in the QNM calculations. By comparing the predicted QNM spectrum with observations, constraints can be placed on the parameters of the alternative theory.

Examples of Deviations: Several alternative theories predict specific deviations from the Kerr QNM spectrum. For instance, theories with extra dimensions might lead to the excitation of additional QNM modes, while scalar-tensor theories could modify the damping times of the modes.

Multi-Messenger Approach: Combining QNM observations with other astrophysical measurements, such as the inspiral waveform or the shadow of the compact object, can provide even stronger constraints on alternative theories of gravity.
In conclusion, the QNM signatures of compact objects offer a powerful tool for testing alternative theories of gravity. By carefully analyzing the frequencies and damping times of these modes, we can gain valuable insights into the nature of gravity in the strong-field regime and potentially uncover new physics beyond GR.

What are the broader astrophysical implications of potentially discovering a population of horizonless compact objects in the universe?

Discovering a population of horizonless compact objects would have profound and far-reaching implications for our understanding of astrophysics and fundamental physics:

Revolutionizing Black Hole Physics: The existence of horizonless objects would directly challenge the paradigm of black holes as described by general relativity. It would necessitate a reevaluation of our understanding of gravitational collapse, event horizons, and the nature of spacetime singularities.

New Stellar Evolution Pathways: The formation and evolution of stars would need to be reconsidered. If horizonless objects are possible, they could represent alternative endpoints for stellar evolution, distinct from neutron stars and black holes. This could have implications for the chemical enrichment of galaxies and the overall stellar population.

Probing Quantum Gravity: Horizonless objects are often predicted by theories of quantum gravity, which attempt to unify general relativity with quantum mechanics. Their discovery would provide strong observational evidence for these theories and offer valuable insights into the nature of quantum gravity.

Dark Matter Candidates: Certain types of horizonless objects, such as boson stars or gravastars, have been proposed as potential dark matter candidates. Their existence could contribute to the missing mass problem in cosmology and influence the large-scale structure of the universe.

New Astrophysical Phenomena: The presence of horizonless objects could lead to new and unexpected astrophysical phenomena. For instance, the interaction of these objects with surrounding matter or radiation could produce distinct observational signatures, such as unusual electromagnetic emissions or gravitational wave signals.

Testing Fundamental Physics: The properties of horizonless objects, such as their compactness, reflectivity, and spin, could be used to test fundamental physics beyond the Standard Model. For example, the existence of extra dimensions or new fundamental forces could manifest in the observational characteristics of these objects.
In summary, the discovery of a population of horizonless compact objects would revolutionize our understanding of astrophysics and fundamental physics. It would open up new avenues of research, challenge existing paradigms, and potentially lead to breakthroughs in our understanding of the universe and its constituents.