Analogue black holes for light rays in static dielectrics

Bittencourt, Eduardo; Lorenci, V. A. De; Klippert, R.; Novello, M.; Salim, J. M.

doi:10.1088/0264-9381/31/14/145007

Cited by 5 publications

(8 citation statements)

References 30 publications

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“…While the quantum black holes are interesting but rather speculative [17], the semi-classical quantization of fields in a black hole background is believed to yield Hawking radiation [18]. If such a Hawking radiation is to be found also in effective black holes as the one discussed in the present work, then the Hawking temperature corresponding to the numerical values provided in the preceeding paragraph is expected to be T H =hcκ/(2πk B ) ≈ 3.64 · 10 −3 K according with previous estimations [1].…”

Section: Kinematics Of the Light Rayssupporting

confidence: 81%

“…All the discussion presented in this work can easily be generalized to the case of any spherically symmetric static black hole as described by an arbitrary radial function A(r) with minor modifications [1], thus including the electrically charged Reissner-Norström and the cosmological constant Schwarszchild-de Sitter solutions among others.…”

Section: Resultsmentioning

confidence: 99%

“…Partial derivatives of a quantity Q with respect to spacetime coordinates x μ = (t, x) = (t, x, y, z) are denoted as ∂ μ Q = Q ,μ = (∂ Q/∂t, ∇Q) while covariant derivatives of Q are denoted as ∇ μ Q = Q ;μ . Geometrical units are chosen 1 Work based on a recently published paper [1] by the authors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The light rays analogue of a static black hole1)

Bittencourt

Lorenci

Klippert

et al. 2015

AIP Conference Proceedings

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Articles you may be interested inExistence of static dyonic black holes in 4d N = 1 supergravity with finite energy Abstract. The propagation of light pulses inside nonlinear static media is described in the limit of geometrical optics. A spherically symmetric dielectric model for a nonlinear medium at rest is obtained, with the help of which an exact analogue model of static black holes can be built. Such an optical model may improve the feasibility in laboratory of the null geodesics near a compact object with an observable gravitational Schwarzschild radius.

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Section: Kinematics Of the Light Rayssupporting

confidence: 81%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The light rays analogue of a static black hole1)

Bittencourt

Lorenci

Klippert

et al. 2015

AIP Conference Proceedings

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“…In this work, we are interested to analyze dielectric mediums. The most general case (2.11) can not be described by an effective metric (see for instance [22]), but there are other cases that by imposing some restrictions on the constitutive relations (2.6-2.7) permit us to find an effective metric, see [24,25,27,36]. Some works extended this analysis to anisotropic material mediums [24,27,29,31], and showed that in some cases it is also possible to find an effective metric associated to the solution.…”

Section: Propagating Waves On a Dielectric Mediummentioning

confidence: 99%

“…Dielectric mediums have been extensively studied in literature, both theoretically [1][2][3][4][5] and experimentally [6][7][8][9]. In the past years, analogue models of gravity [10][11][12][13][14][15][16][17][18][19][20] considering a nonlinear dielectric medium received attention in the scientific community [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. These models predicted that nonlinear materials can produce, in laboratory, an effective (optical) horizon with similar properties to the event horizon of black holes [40].…”

Section: Introductionmentioning

confidence: 99%

Photon propagation in a material medium on a curved spacetime

Guerrieri¹,

Novello²

2022

Preprint

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We consider a nonlinear dielectric medium surrounding a static, charged and spherically symmetric compact body which gravitational field is driven by General Relativity (GR). Considering the propagating waves on the dielectric medium, we describe the trajectory of light as geodesics on an effective geometry given by Hadamard's discontinuities. We analyze some consequences of the effective geometry in the propagation of light, with relation to the predictions of the background gravitational field, that includes corrections on the geometrical redshift and on the gravitational deflection of light. We show that the background electromagnetic field polarize the material medium, such that different polarizations of light are distinguished by different corrections on these quantities. As a consequence, we have two possible paths for the trajectory of light in such configuration, that coincide if we turn off the electromagnetic field or if the permittivity is constant. We show that the effective metric associated to the negative polarization, for a given dependence of the dielectric permittivity, is conformally flat.

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Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

Novello¹,

Bittencourt

2015

Braz J Phys

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We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric g µν which is responsible to map the path of any accelerated body in Minkowski space-time onto a geodesic motion in such associated g geometry.Only recently the method introduced by Einstein in general relativity was used beyond the domain of gravitational forces to map arbitrary accelerated bodies submitted to non-Newtonian attractions onto geodesics of a modified geometry. This process has its roots in the very ancient idea to treat any dynamical problem in Classical Mechanics as nothing but a problem of static where all forces acting on a body annihilates themselves including the inertial ones. This general procedure, that concerns arbitrary forces -beyond the uses of General Relativity that is limited only to gravitational processes -is nothing but the relativistic version of the d'Alembert method in classical mechanics and consists in the principle of Metric Relativity. The main difference between gravitational interaction and all other forces concerns the universality of gravity which added to the interpretation of the Equivalence Principle allows all associated geometries -one for each different body in the case of non-gravitational forces -to be unified into a unique Riemannian space-time structure. The same geometrical description appears for electromagnetic waves in the optical limit within the context of nonlinear theories or material medium. Once it is largely discussed in the literature, the so-called analogue models of gravity, we will dedicate few sections on this emphasizing their relation with the new concepts introduced here.Then we pass to the description of the Dynamical Bridge formalism which states the dynamic equivalence of non-linear theories (driven by arbitrary scalar, spinor or vector fields) that occur in Minkowski background to theories described in associated curved geometries generated by each one of these fields. We shall see that it is possible to map the dynamical properties of a theory, say Maxwell electrodynamics in Minkowski space-time, into Born-Infeld electrodynamics described in a curved space-time the metric of which is defined in terms of the electromagnetic field itself in such way that it yields the same dynamics. It is clear that when considered in whatever unique geometrical structure these two theories are not the same, they do not describe the same phenomenon. However we shall see that by a convenient modification of the metric of space-time an 2 equivalence appears that establishes a bridge between these two theories making they represent the same phenomenon. This method was recently used to achieve a successful geometric scalar theory of gravity. At the end we briefly review the proposal of geometrization of quantum mechan...

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Analogue black holes for light rays in static dielectrics

Cited by 5 publications

References 30 publications

The light rays analogue of a static black hole1)

The light rays analogue of a static black hole1)

Photon propagation in a material medium on a curved spacetime

Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

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