The Mathematical Theory of Relativity.

Franklin, Philip; Eddinǵton, A. S.

doi:10.2307/2298148

Cited by 11 publications

(15 citation statements)

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“…The idea of generalizing the Einstein-Hilbert action by including higher-order terms can be traced back to the early years of general relativity (see, e.g., [29]). Nevertheless, only in the last decades these models have attracted more attention, and the main motivation for this comes from the quantum theory.…”

Section: Higher-derivative Gravity Modelsmentioning

confidence: 99%

Regular Black Holes from Higher-Derivative Effective Delta Sources

Giacchini

Netto

2023

Springer Series in Astrophysics and Cosmology

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Certain approaches to quantum gravity and classical modified gravity theories result in effective field equations in which the original source is substituted by an effective one. In these cases, the occurrence of regular spacetime configurations may be related to the regularity of the effective source, regardless of the specific mechanism behind the regularization. In this chapter, we make an introduction to the effective source formalism applied to higher-derivative gravity. The results presented here, however, can be easily transposed to other frameworks that use similar sources. The generality obtained is also because we consider a general higher-derivative gravity model instead of restricting the analysis to some specific theories. In the first part, we discuss the model in the Newtonian limit, which offers a natural context for introducing effective sources. We show how the regularity properties of the effective sources depend on the behavior of the action's form factor in the ultraviolet regime, which leads to results valid for large families of models (or for families of modified delta sources). Subsequently, we use the general results on the effective sources to construct regular black hole metrics. One of our concerns is the higher-order regularity of the solutions, i.e., the possibility that not only the invariants built with curvature tensors but also the ones with covariant derivatives are regular. In this regard, we present some theorems relating the regularity of sets of curvature-derivative invariants with the regularity properties of the effective sources.

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Section: Higher-derivative Gravity Modelsmentioning

confidence: 99%

Regular Black Holes from Higher-Derivative Effective Delta Sources

Giacchini

Netto

2023

Springer Series in Astrophysics and Cosmology

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“…Therefore, Lemaitre knew remarkable observations of redshifts done by V. Slipher [10] 4 and he clearly understood that it was very important to find observational features of a proposed model and really the velocity -distance could be such a test for a proposed cosmological model. Moreover, A. Eddington discussed radial velocities of spiral galaxies observed by V. Slipher as an important criterium to test a cosmological model [19] (he considered the de Sitter model in in his book).…”

Section: Early Cosmological Studiesmentioning

confidence: 99%

Constraints on a Tidal Charge of the Supermassive Black Hole in M87* with the EHT Observations in April 2017

Zakharov

2022

Universe

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More than two years ago the Event Horizon Telescope collaboration presented the first image reconstruction around the shadow for the supermassive black hole in M87*. It gives an opportunity to evaluate the shadow size. Recently, the Event Horizon Telescope collaboration constrained parameters (“charges”) of spherical symmetrical metrics of black holes from an estimated allowed interval for shadow radius from observations of M87* in 2017. Earlier, analytical expressions for the shadow radius as a function of charge (including a tidal one) in the case of Reissner–Nordström metric have been obtained. Some time ago, Bin-Nun proposed to apply a Reissner–Nordström metric with a tidal charge as an alternative to the Schwarzschild metric in Sgr A*. If we assume that a Reissner–Nordström black hole with a tidal charge exists in M87*, therefore, based on results of the shadow size evaluation for M87* done by the Event Horizon Telescope collaboration we constrain a tidal charge. Similarly, we evaluate a tidal charge from shadow size estimates for Sgr A*.

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“…Therefore, it is crucial to comprehend the inherent geometry of spacetime and the procedure for embedding a 4D space-time. In line with this, Karmarkar [58] has embedded 4-dimensional spacetime into 5-dimensional Euclidean space. This embedding simplifies the process of solving the Einstein field equations.…”

Section: Introductionmentioning

confidence: 88%

“…Further, to be a Class I static and non-static spherically symmetric spacetime, it must satisfy the following Karmarkar condition [58]…”

Section: B the Class I Condition For The Decoupled Systemmentioning

confidence: 99%

“…It should also be mentioned that Salako et al [66] have studied the existence of strange starts in gravity, where is the torsion tensor. Waheed et al [67] used the Karmarkar condition [58] to find the physically acceptable solution for compact stars in gravity. In gravity, Ahmed and Abbas [68] have studied the gravitational collapse using the Karmarkar condition [58] to the spherically symmetric non-static radiating star.…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic stars in modified gravity: An extended gravitational decoupling approach*

et al. 2022

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In the work we present investigation on decoupling gravitational sources under the framework of $f(R,T)$ gravity. Basically the complete geometric deformation technique has been employed here which facilitates finding exact solutions to the anisotropic astrophysical system smoothly without imposing any particular ansatz for deformation function. Along with this we have also used 5-dimensional Euclidean spacetime in order to describe the embedding Class I spacetime for getting a solvable spherical physical system. The solutions thus obtained show physically interesting as well as viable with new possibilities to sought for. Especially, from the present investigation it is worthy to note that the mixture $f(R,T)$ + CGD translate the scenario beyond the pure GR realm and hence clearly helps to enhance the features of the interior astrophysical aspects of compact stellar objects. Therefore to check the physical acceptability and stability of the stellar system based on the obtained solutions, we have performed a few physical tests which satisfy all the stability criteria, including nonsingular nature of the density as well as pressure.

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The Mathematical Theory of Relativity.

Cited by 11 publications

References 0 publications

Regular Black Holes from Higher-Derivative Effective Delta Sources

Regular Black Holes from Higher-Derivative Effective Delta Sources

Constraints on a Tidal Charge of the Supermassive Black Hole in M87* with the EHT Observations in April 2017

Anisotropic stars in modified gravity: An extended gravitational decoupling approach*

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