scholarly journals Deformed General Relativity and Quantum Black Holes Interior

Universe ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. 39 ◽  
Author(s):  
Denis Arruga ◽  
Jibril Ben Achour ◽  
Karim Noui

Effective models of black holes interior have led to several proposals for regular black holes. In the so-called polymer models, based on effective deformations of the phase space of spherically symmetric general relativity in vacuum, one considers a deformed Hamiltonian constraint while keeping a non-deformed vectorial constraint, leading under some conditions to a notion of deformed covariance. In this article, we revisit and study further the question of covariance in these deformed gravity models. In particular, we propose a Lagrangian formulation for these deformed gravity models where polymer-like deformations are introduced at the level of the full theory prior to the symmetry reduction and prior to the Legendre transformation. This enables us to test whether the concept of deformed covariance found in spherically symmetric vacuum gravity can be extended to the full theory, and we show that, in the large class of models we are considering, the deformed covariance cannot be realized beyond spherical symmetry in the sense that the only deformed theory which leads to a closed constraints algebra is general relativity. Hence, we focus on the spherically symmetric sector, where there exist non-trivial deformed but closed constraints algebras. We investigate the possibility to deform the vectorial constraint as well and we prove that non-trivial deformations of the vectorial constraint with the condition that the constraints algebra remains closed do not exist. Then, we compute the most general deformed Hamiltonian constraint which admits a closed constraints algebra and thus leads to a well-defined effective theory associated with a notion of deformed covariance. Finally, we study static solutions of these effective theories and, remarkably, we solve explicitly and in full generality the corresponding modified Einstein equations, even for the effective theories which do not satisfy the closeness condition. In particular, we give the expressions of the components of the effective metric (for spherically symmetric black holes interior) in terms of the functions that govern the deformations of the theory.

2017 ◽  
Vol 9 (5) ◽  
pp. 29
Author(s):  
Valery Vasiliev

The paper is concerned with the spherically symmetric static problem of the General Relativity Theory. The classical solution of this problem found in 1916 by K. Schwarzschild for a particular metric form results in singular space metric coefficient and provides the basis of the objects referred to as Black Holes. A more general metric form applied in the paper allows us to obtain the solution which is not singular. The critical radius of the fluid sphere, following from this solution does not coincide with the traditional gravitational radius. For the spheres with radii that are less than the critical value, the solution of GRT problem does not exist.


Universe ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 25 ◽  
Author(s):  
Stanislav Alexeyev ◽  
Maxim Sendyuk

We discuss black hole type solutions and wormhole type ones in the effective gravity models. Such models appear during the attempts to construct the quantum theory of gravity. The mentioned solutions, being, mostly, the perturbative generalisations of well-known ones in general relativity, carry out additional set of parameters and, therefore could help, for example, in the studying of the last stages of Hawking evaporation, in extracting the possibilities for the experimental or observational search and in helping to constrain by astrophysical data.


2021 ◽  
Author(s):  
◽  
Alexander Simpson

<p>Various spacetime candidates for traversable wormholes, regular black holes, and ‘black-bounces’ are presented and thoroughly explored in the context of the gravitational theory of general relativity. All candidate spacetimes belong to the mathematically simple class of spherically symmetric geometries; the majority are static (time-independent as well as nonrotational), with a single dynamical (time-dependent) geometry explored. To the extent possible, the candidates are presented through the use of a global coordinate patch – some of the prior literature (especially concerning traversable wormholes) has often proposed coordinate systems for desirable solutions to the Einstein equations requiring a multi-patch atlas. The most interesting cases include the so-called ‘exponential metric’ – well-favoured by proponents of alternative theories of gravity but which actually has a standard classical interpretation, and the ‘black-bounce’ to traversable wormhole case – where a metric is explored which represents either a traversable wormhole or a regular black hole, depending on the value of the newly introduced scalar parameter a. This notion of ‘blackbounce’ is defined as the case where the spherical boundary of a regular black hole forces one to travel towards a one-way traversable ‘bounce’ into a future reincarnation of our own universe. The metric of interest is then explored further in the context of a time-dependent spacetime, where the line element is rephrased with a Vaidya-like time-dependence imposed on the mass of the object, and in terms of outgoing/ingoing EddingtonFinkelstein coordinates. Analysing these candidate spacetimes extends the pre-existing discussion concerning the viability of non-singular black hole solutions in the context of general relativity, as well as contributing to the dialogue on whether an arbitrarily advanced civilization would be able to construct a traversable wormhole.</p>


2009 ◽  
Vol 18 (14) ◽  
pp. 2221-2229 ◽  
Author(s):  
R. MAIER ◽  
I. DAMIÃO SOARES

The dynamics of gravitational collapse is examined in the realm of string-based formalism of D-branes which encompasses general relativity as a low energy limit. A complete analytical solution is given to the spherically symmetric collapse of a pure dust star, including its matching with a corrected Schwarzschild exterior space–time. The collapse forms a black hole (an exterior event horizon) enclosing not a singularity but perpetually bouncing matter in the infinite chain of space–time maximal analytical extensions inside the outer event horizon. This chain of analytical extensions has a structure analogous to that of the Reissner–Nordstrom solution. The interior trapped bouncing matter has the possibility of being expelled by disruptive nonlinear resonance mechanisms.


Author(s):  
Sayak Datta ◽  
Sukanta Bose

AbstractWe study the quasi-normal modes (QNMs) of static, spherically symmetric black holes in f(R) theories. We show how these modes in theories with non-trivial f(R) are fundamentally different from those in general relativity. In the special case of $$f(R) = \alpha R^2$$f(R)=αR2 theories, it has been recently argued that iso-spectrality between scalar and vector modes breaks down. Here, we show that such a break down is quite general across all f(R) theories, as long as they satisfy $$f''(0)/(1+f''(0)) \ne 0$$f′′(0)/(1+f′′(0))≠0, where a prime denotes derivative of the function with respect to its argument. We specifically discuss the origin of the breaking of isospectrality. We also show that along with this breaking the QNMs receive a correction that arises when $$f''(0)/(1+f'(0)) \ne 0$$f′′(0)/(1+f′(0))≠0 owing to the inhomogeneous term that it introduces in the mode equation. We discuss how these differences affect the “ringdown” phase of binary black hole mergers and the possibility of constraining f(R) models with gravitational-wave observations. We also find that even though the iso-spectrality is broken in f(R) theories, in general, nevertheless in the corresponding scalar-tensor theories in the Einstein frame it is unbroken.


2014 ◽  
Vol 12 (2) ◽  
pp. 77-83
Author(s):  
Neven Bilic ◽  
Dijana Tolic

Analog gravity models of general relativity seem promising routes to providing laboratory tests of the foundation of quantum field theory in curved space-time. In contrast to general relativity, where geometry of a spacetime is determined by the Einstein equations, in analog models geometry and evolution of analog spacetime are determined by the equations of fluid mechanics. In this paper we study the analogue gravity model based on massless pions propagating in a expanding hadronic fluid. The analog expanding spacetime takes the form of an FRW universe, with the apparent and trapping horizons defined in the standard way.


2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Hamani Daouda ◽  
Manuel E. Rodrigues ◽  
M. J. S. Houndjo

We present some basic concepts of a theory of modified gravity, inspired by the gauge theories, where the commutator algebra of covariant derivative gives us an added term with respect to the General Relativity, which represents the interaction of gravity with a substratum. New spherically symmetric solutions of this theory are obtained and can be viewed as solutions that reproduce the mass, the charge, the cosmological constant, and the Rindler acceleration, without coupling with the matter content, that is, in the vacuum.


2019 ◽  
Vol 64 (3) ◽  
pp. 189 ◽  
Author(s):  
O. S. Stashko ◽  
V. I. Zhdanov

We study static spherically symmetric configurations in the presence of linear massive scalar fields within General Relativity. Static solutions of the Einstein equations are considered under conditions of asymptotic flatness. Each solution is fixed by the configuration mass and the field strength parameter, which are defined at spatial infinity. The metric coefficients and the scalar field for a specific configuration are obtained numerically. Then we study the time-like geodesics describing the test particle motion. The focus is on the distribution of stable circular orbits (SCOs) of the test particles around a configuration. We found that, for the continuum of configuration parameters, there exist two unlinked regions of SCOs that are separated by some annular region, where SCOs do not exist.


2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Ben Heidenreich

Abstract It is well known that an identical pair of extremal Reissner-Nordström black holes placed a large distance apart will exert no force on each other. In this paper, I establish that the same result holds in a very large class of two-derivative effective theories containing an arbitrary number of gauge fields and moduli, where the appropriate analog of an extremal Reissner-Nordström black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanishing horizon area. Analogous results hold for black branes.


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