Stationary black holes in a generalized three-dimensional theory of gravity

Sá, Paulo M.; Lemos, José P. S.

doi:10.1016/s0370-2693(98)00084-7

Cited by 20 publications

(11 citation statements)

References 23 publications

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“…In the string frame, a set of static and stationary solutions of Brans-Dicke theory, β = 4 and F = 0, was found in [10,11]. Here we consider similar solutions in the Einstein frame.…”

Section: Brans-dicke Theorymentioning

confidence: 95%

“…For the Brans-Dicke case we had found a set of static and stationary solutions which are similar to [10,11] but are obtained in the Einstein frame. For the EMD case we found two new classes of spinning solutions: electric and magnetic.…”

Section: Introductionmentioning

confidence: 90%

“…In this paper we consider the action including the dilaton and the Maxwell field with arbitrary coupling constants. In the general case, the T -duality locally is just a general coordinate transformation and part of it was used to get stationary solutions previously [8,11]. Here we want to emphasize that globally the coordinate transformations used to generate spinning solutions from static ones have more appropriate interpretation as T -duality of the reduced 2 + 1 theory.…”

Section: Introductionmentioning

confidence: 99%

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T-duality and spinning solutions in 2 + 1 gravity

Chen¹

1999

Nuclear Physics B

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Starting with the 2 + 1 Einstein-Maxwell-Dilaton system with a cosmological constant and assuming two commuting Killing symmetries we derive the corresponding 1 + 0 σ-model. It is shown that, for general values of the coupling parameters, the T -duality group is SL(2, R), which coincides with the group of linear coordinate transformations along the Killing orbits. This duality, along with a suitable parameter choice, is applied to obtain some new spinning solutions in the alternative gravity theories: Einstein-Maxwell, Brans-Dicke and Einstein-Maxwell-Dilaton.

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“…In the string frame, a set of static and stationary solutions of Brans-Dicke theory, β = 4 and F = 0, was found in [10,11]. Here we consider similar solutions in the Einstein frame.…”

Section: Brans-dicke Theorymentioning

confidence: 95%

Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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T-duality and spinning solutions in 2 + 1 gravity

Chen¹

1999

Nuclear Physics B

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“…Each different ω has a very rich and non-trivial structure of solutions with many black holes, which can be considered on its own. Here we do not attempt to comment on the whole set of solutions of the different theories 51,52 . For electric and magnetic rotating solutions see 56,57 .…”

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confidence: 99%

Black Holes With Toroidal, Cylindrical and Planar Horizons in Anti-De Sitter Spacetimes in General Relativity and Their Properties

Lemos¹

2001

Astronomy and Astrophysics

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We review the toroidal, cylindrical and planar black hole solutions in anti-de Sitter spacetimes and present their properties. IntroductionBlack holes have been objects of astrophysical interest after it was shown that they are the inevitable outcome of complete gravitational collapse of a massive star or a cluster of stars. They are likely to power the spectacular phenomena seen in x-ray emitting star accretion disks, in active galactic nuclei and quasars, and should also inhabit, in a quiescent state, the center of normal galaxies, such as our own.Black holes appear naturally as exact solutions in general relativity. Their theoretical properties, such as their stability, the no hair theorems (stating they are characterized by three parameters only, the mass, the angular momentum and the electric charge), and the physics of matter around them, have been established. These black holes live in an asymptotically flat spacetime.Black holes became important, not only to astrophysics, but also to physics, after the discovery that, due to quantum processes, they can emit radiation with a specific temperature, the Hawking temperature. It was also shown that they have a well defined entropy. Thus, black holes turned to be objects subject to the laws of thermodynamics.Once they have entered the domain of physics it also became clear that one should study them not only in asymptotically flat spacetimes, but also in spacetimes with a positive cosmological constant Λ > 0, i.e., asymptotically de Sitter spacetimes, and spacetimes with a negative cosmological constant Λ < 0, i.e., asymptotically anti-de Sitter spacetimes. From recent astronomical observations, it seems now that we live in a world with Λ > 0. However, a spacetime with Λ < 0 is also worth of investigation, since it allows a consistent a in Astronomy and Astrophysics: Recent Developments,

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“…The interest in lower-dimensional theories of gravity has dramatically increased with the discovery [1,2] that three-dimensional general relativity with a negative cosmological constant admits a black hole solution (called BTZ), which, apart from being asymptotically anti-de Sitter, exhibits features closely related to the Schwarzschild and Kerr solutions. Further generalizations have shown that three-dimensional theories of gravity have a very rich structure of black hole solutions [3][4][5][6][7][8][9][10][11].…”

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confidence: 99%

Polytropic stars in three-dimensional spacetime

Sá¹

1999

Physics Letters B

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We investigate three-dimensional perfect fluid stars with polytropic equation of state, matched to the exterior three-dimensional black hole geometry of Bañados, Teitelboim and Zanelli. A new class of exact solutions for a generic polytropic index is found and analysed.In the past decade, lower-dimensional theories of gravity have been intensively investigated, primarily because of the insights they can provide into conceptual issues arising in four-dimensional general relativity. The interest in lower-dimensional theories of gravity has dramatically increased with the discovery [1,2] that three-dimensional general relativity with a negative cosmological constant admits a black hole solution (called BTZ), which, apart from being asymptotically anti-de Sitter, exhibits features closely related to the Schwarzschild and Kerr solutions. Further generalizations have shown that three-dimensional theories of gravity have a very rich structure of black hole solutions [3][4][5][6][7][8][9][10][11].The BTZ black hole metric can be matched to a three-dimensional perfect fluid star. Cruz e Zanelli [12], studying the stability of these stars for the case of a generic equation of state p = p(ρ), concluded that they can undergo gravitational collapse into a black hole. For the particular case of pressureless dust, Mann and Ross [13] have investigated the circunstances under which a BTZ black hole can be formed from gravitational collapse, concluding that it occurs naturally, in a way that parallels the Oppenheimer-Snyder collapse in four dimensions.In this letter, we consider three-dimensional perfect fluid stars in hydrostatic equilibrium, matched to the BTZ black hole exterior geometry. The equation of state relating the pressure and the energy density is assumed to be of the polytropic type,where n is the polytropic index and K is the polytropic constant. This equation of state encompasses a wide range of physically interesting cases, namely constant energy density for n = 0, nonrelativistic degenerate fermions for n = 1, pure radiation for n = ∞ and K = 1/2, and stiff matter for n = ∞ and K = 1. For constant energy density an exact solution is known [12]. Here, exact solutions for a generic polytropic index are found and analysed. Note that in four spacetime dimensions analytical solutions for polytropic stars are known just for a few particular values of the polytropic index and only in the Newtonian approximation. For the three-dimensional spherically symmetric, static metric,the Einstein equations with a negative cosmological constant Λ < 0 in the presence of a perfect fluid with energy density ρ and pressure p related by a polytropic equation of state,

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Stationary black holes in a generalized three-dimensional theory of gravity

Cited by 20 publications

References 23 publications

T-duality and spinning solutions in 2 + 1 gravity

T-duality and spinning solutions in 2 + 1 gravity

Black Holes With Toroidal, Cylindrical and Planar Horizons in Anti-De Sitter Spacetimes in General Relativity and Their Properties

Polytropic stars in three-dimensional spacetime

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