Exact Solutions in Three-Dimensional Gravity

García-Diaz, Alberto A.

doi:10.1017/9781316556566

Cited by 43 publications

(77 citation statements)

References 124 publications

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“…The latter are theories which in the perturbative regime recover the Fierz-Pauli threedimensional limit; in this sense, they are analogous to dRGT and bigravity theories in lower dimensions. All of these three-dimensional theories support exact gravitational-wave configurations that exhibit the particular dynamics of each theory beyond the perturbative level, and consist of the pure gauge modes of standard (2 þ 1) gravity plus nontrivial contributions reflecting their respective massive excitations [16][17][18][19][20] (see also the recent review [21]). It is expected to have similar revealing behavior in bigravity, i.e., that exact gravitational waves decompose the complex dynamical structure of the theory into elementary exact massless and massive excitations.…”

Section: Introductionmentioning

confidence: 87%

Exact ghost-free bigravitational waves

et al. 2018

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We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type-N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This entails a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-wave dynamics, using an integral representation originally due to Poisson. Inspired by this progress, we tackle the subtle problem of how matter couples to bigravity and, more concretely, if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported by either a massless free scalar field or a wavefront-homogeneous Maxwell field. Considering the most general allowed Maxwell source instead is a highly nontrivial task, which we accomplish by again exploiting the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this eventually allows us to find the most general configurations for any matter source.

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Section: Introductionmentioning

confidence: 87%

Exact ghost-free bigravitational waves

et al. 2018

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“…where F = 2q 4 log a 2 r + 2Λq 2 a 2 r + Λ 2 a 4 r + 2M q 2 + q 4 2 , (40) reveal that the solution is regular everywhere whenever Λ r = Λ a 2 + r 2 +q 2 = 0, which can be satisfied if Λ > 0.…”

Section: Isotropic Sector Of a Regular Black Hole In 2+1 Dimensionsmentioning

confidence: 95%

Gravitational decoupling in 2 + 1 dimensional space-times with cosmological term

Contreras

2019

Class. Quantum Grav.

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In this work we implement the Minimal Geometric Deformation method to obtain the isotropic sector and the decoupler matter content of any anisotropic solution of the Einstein field equations with cosmological constant in 2 + 1 dimensional space-times. We obtain that the solutions of both sectors can be expressed analytically in terms of the metric functions of the original anisotropic solutions instead of formal integral as in its 3 + 1 counterpart. As a particular example we study a regular black hole solution and we show that, depending on the sign of the cosmological constant, the solutions correspond to regular black holes violating the null energy condition or to a nonregular black hole without exotic hair. The exotic/non-exotic and the regular/non-regular black hole dualities are discussed.

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“…corresponds to a perfect fluid solution of the Einstein field equations whenever [38] G 2 = C − Λr 2 − 16π r rρ(r)dr (34) N = n 0 + n 1 r r G(r) dr (35) where C, n 0 and n 1 are integration constants and ρ stands for the energy density. From the Einstein's equations, the pressure can be written as…”

Section: Static Perfect Fluid Solutions With λmentioning

confidence: 99%

A general interior anisotropic solution for a BTZ vacuum in the context of the minimal geometric deformation decoupling approach

2019

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In this work we implement the Minimal Geometric Deformation decoupling method to obtain general static interior solutions for a BTZ vacuum from the most general isotropic solution in 2 + 1 dimensions including the cosmological constant Λ. We obtain that the general solution can be generated only by the energy density of the original isotropic sector, so that this quantity plays the role of a generating function. Although as a particular example we study the static star with constant density, the method here developed can be easily applied to more complex situations described by other energy density profiles.

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Exact Solutions in Three-Dimensional Gravity

Cited by 43 publications

References 124 publications

Exact ghost-free bigravitational waves

Exact ghost-free bigravitational waves

Gravitational decoupling in 2 + 1 dimensional space-times with cosmological term

A general interior anisotropic solution for a BTZ vacuum in the context of the minimal geometric deformation decoupling approach

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